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Constraints on formation of columnar joints in basaltic lava Woodell, Daniel Robert 2012

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! CONSTRAINTS)ON)FORMATION)OF)COLUMNAR)JOINTS)IN)BASALTIC)LAVA))) by))DANIEL)ROBERT)WOODELL))B.A.,)Colorado)College,)2009)))))) A)THESIS)SUBMITTED)IN)PARTIAL)FULFILLMENT)OF)THE)REQUIREMENTS)FOR)THE)DEGREE)OF))MASTER)OF)SCIENCE))in))THE)FACULTY)OF)GRADUATE)STUDIES))(Geological)Sciences)))))THE)UNIVERISTY)OF)BRITISH)COLUMBIA))(Vancouver)))December)2012)))©)Daniel)Robert)Woodell,)2012) ! ii! Abstract(!! Columnar!joints!form!as!a!brittle!relaxation!response!to!tensile!stresses!within!cooling!lava!flows!and!magma!bodies,!and!are!found!in!lavas!that!vary!greatly!in!chemistry!and!outcrop!geometry.!!However,!columnar!joints!do!not!form!in!all!cooling!igneous!rocks,!and!the!specific!conditions!under!which!columnar!joints!form!are!unknown.!!In!this!study,!outcrops!containing!columns!in!the!Cheakamus!Valley!basalt!flows!near!Whistler,!BC!are!studied,!and!the!size,!orientation,!and!distribution!of!columns!is!recorded.!!Forward!numerical!models!using!the!finite!element!method!are!created!with!Matlab!using!the!Partial!Differential!Equation!Toolbox!to!model!the!outcrops!in!the!Whistler!field!area,!and!determine!the!cooling!rates!( € ∂T ∂t )"and!thermal!gradients!( € ∂T ∂x )!experienced!by!the!lava!flows!during!their!formation.!!High!temperature!experimentation!involving!basalt!rock!samples!is!then!used!to!determine!the!cooling!rates!and!thermal!gradients!present!during!the!cooling!of!these!samples!under!a!variety!of!naturally!occurring!conditions.!! This!study!finds!that!noticeable!differences!in!the!distribution!of!columns!within!an!outcrop!occur!only!when!there!are!large!differences!in!cooling!rates!between!the!upper!and!lower!outcrop!surfaces.!!Modeling!shows!that!the!cooling!rates!must!differ!by!approximately!an!order!of!magnitude.!!High!temperature!experiments!show!that!extremely!high!cooling!rates!(especially!in!the!small!sample!sizes!used!in!this!study)!between!approximately!700!to!800!˚C!are!necessary!for!the!formation!of!columnar!joints.! ) iii) ) Table!of!Contents!) Abstract............................................................................................................................................. ii) Table!of!Contents.......................................................................................................................... iii) List!of!Tables .................................................................................................................................. vi) List!of!Figures................................................................................................................................ vii) Acknowledgements........................................................................................................................x) 1.) Introduction ............................................................................................................................ 1)1.1.) Approach)to)Studying)Columnar)Joints .................................................................................. 1) 2.) Literature!Review.................................................................................................................. 4)2.1.) Macroscopic)Organization)of)Columns................................................................................... 4)2.2) Geometric)Column)Properties..................................................................................................... 6)2.3.) Formation)Mechanisms.............................................................................................................. 11)2.4.) Previous)Analysis)of)Columns ................................................................................................. 15)2.4.1.) Analog)Modeling)of)Columns........................................................................................... 15)2.4.2.) Numerical)Modeling)of)Columns ................................................................................... 16)2.4.3) Field)Studies)of)Active)Lavas ............................................................................................ 17)2.5.) Unresolved)Issues......................................................................................................................... 18) 3.) Field!Examples......................................................................................................................19)3.1.) Location)and)Extent)of)Flows .................................................................................................. 20)3.2.) Columnar)Structures)in)Outcrop ............................................................................................ 25)3.3.) Field)Observations........................................................................................................................ 28)3.3.1.) Lower)Colonnade ................................................................................................................. 28)3.3.2.) Upper)Colonnade.................................................................................................................. 28)3.3.3.) Colonnade)Interface ............................................................................................................ 29)3.4.) Colonnade)Proportions)and)Measurements...................................................................... 33)3.4.1.) Colonnade)Thickness.......................................................................................................... 33)3.4.2.) Column)Width)Variation.................................................................................................... 36) ) iv) 4.) A!Forward!Model .................................................................................................................40)4.1.) Methodology ................................................................................................................................... 41)4.1.1.) Finite)Element)Method....................................................................................................... 41)4.1.2.) Equations ................................................................................................................................. 41)4.1.3.) Constants)Used ...................................................................................................................... 42)4.1.4.) Double)Checking)Integrity)of)the)Code ....................................................................... 44)4.2.) Model)Testing ................................................................................................................................. 45)4.3.) Identical)Boundary)Conditions ............................................................................................... 46)4.3.1.) SemicInfinite)Slab ................................................................................................................. 46)4.3.2.) Slab)Corner.............................................................................................................................. 47)4.3.3.) Slab)Side ................................................................................................................................... 47)4.3.4.) Identical)Boundary)Code)Integrity ............................................................................... 48)4.4.) EdgecDependent)Boundary)Conditions............................................................................... 53)4.4.1.) SemicInfinite)Slab ................................................................................................................. 53)4.4.2.) Slab)Corner.............................................................................................................................. 54)4.4.3.) Slab)Side ................................................................................................................................... 54)4.4.4.) Finite)Slab ................................................................................................................................ 54)4.4.5.) EdgecDependent)Boundary)Conditions)Integrity................................................... 55)4.5.) Modeling)Results........................................................................................................................... 61)4.5.1.) Temperature)Profiles ......................................................................................................... 61)4.5.2.) Heat)Flow)Gradients)at)Tcolumn ........................................................................................ 62)4.5.3.) Predictions .............................................................................................................................. 64) 5.) High!Temperature!Experiments.....................................................................................68)5.1.) Methodology ................................................................................................................................... 69)5.1.1.) Designing)the)Experiments .............................................................................................. 69)5.1.2.) Textural)Experimental)Grid ............................................................................................. 73)5.1.3.) Gradient)Experimental)Grid............................................................................................. 73)5.2.) Results ............................................................................................................................................... 77)5.2.1.) Internal)Structures)and)Textures .................................................................................. 77)5.2.2) Cooling)Rates)and)Gradients............................................................................................. 83) ) v) 5.3.) Discussion ........................................................................................................................................ 91)5.3.1.) Joint)Formation ..................................................................................................................... 91)5.3.2.) Comparison)of)Experimental)and)Modeled)Temperature)Profiles................. 93)5.3.3.) Limitations)of)Experimental)Setup............................................................................... 95) 6.) Discussion!&!Conclusion ...................................................................................................97)6.1.) Fit)of)Models)to)Outcrops .......................................................................................................... 97)6.1.1) Paleoenvironmental)Conditions)Based)on)Column)Geometries .....................103)6.1.2) Rules)for)Columns ...............................................................................................................104)6.2.) Summary)of)Experiments........................................................................................................112)6.3.) Further)Work................................................................................................................................115) References .................................................................................................................................. 117) Appendix!A!–!Forward!Models ............................................................................................. 122) Appendix!B!–!MATLAB!Code.................................................................................................. 126)B.1.) Finite)Slab ......................................................................................................................................126)B.2.) Thermal)Gradient .......................................................................................................................127) Appendix!C!–!Experiment!Photographs ............................................................................ 130) ! ) vi) List!of!Tables!Table)3.1.))List)of)outcrops)and)their)locations ................................................................................. 21)Table)4.1.))Physical)parameters)and)variables)used)in)the)numerical)modeling................ 42)Table)4.2.))A)summary)of)numerical)models)1)through)9............................................................. 52)Table)4.3.))A)summary)of)numerical)models)10)through)19 ....................................................... 60)Table)5.1.))Experimental)grid)for)textural)experiments ................................................................ 73)Table)5.2.))Thermal)gradient)experiments.......................................................................................... 75)Table)5.3.))Maximum)temperature)difference)between)thermocouples................................ 84)Table)5.4.))Maximum)averaged)heat)flow ............................................................................................ 85)) ) vii) List!of!Figures!Figure)1.1.))An)explanation)of)various)terms)used)throughout)this)study............................... 2)Figure)2.1.))Diagram)of)flow)structures ................................................................................................... 5)Figure)2.2.))Outline)drawing)of)columnar)joints .................................................................................. 5)Figure)2.3.))Outcrop)from)Whistler)field)area,)Railroad)Quarry)outcrop)6.............................. 6)Figure)2.4.))Photo)of)columns)and)chisel)marks ............................................................................... 10)Figure)2.5.))Columns)at)Giant’s)Causeway ........................................................................................... 11)Figure)3.1.))Outcrop)location)map........................................................................................................... 22)Figure)3.2.))Diagram)of)field)areas .......................................................................................................... 23)Figure)3.3.))Thin)sections)of)the)Cheakamus)Valley)basalt........................................................... 24)Figure)3.4.))Structures)of)columns)found)in)outcrops .................................................................... 26)Figure)3.5.))Vertical)columns)pinching)upwards .............................................................................. 27)Figure)3.6.))Eskerclike)outcrop)at)Brandywine)Falls....................................................................... 28)Figure)3.7.))Surficial)chisel)marks)on)columns .................................................................................. 30)Figure)3.8.))Ball)and)socket)joints............................................................................................................ 31)Figure)3.9.))Column)interface)image)series......................................................................................... 32)Figure)3.10.))Colonnade)proportions..................................................................................................... 35)Figure)3.11.))Western)face)of)Outcrop)1)of)the)Railroad)Quarry)area ..................................... 36)Figure)3.12.))ImageJ)analysis)of)the)Pinecrest)outcrop.................................................................. 37)Figure)3.13.))Histograms)of)colonnade)analysis)data ..................................................................... 38)Figure)4.1.))Semicinfinite)slab)model)with)identical)boundary)conditions ........................... 49)Figure)4.2.))Slab)corner)model)with)identical)boundary)conditions........................................ 50)Figure)4.3.))Slab)side)model)with)identical)boundary)conditions ............................................. 51)Figure)4.4.))Independent)measurements)of)the)total)heat)change)for)identical)boundary)conditions........................................................................................... 53)Figure)4.5.))Semicinfinite)slab)model)with)edgecdependent)boundary)conditions ........... 56)Figure)4.6.))Slab)corner)model)with)edgecdependent)boundary)conditions ........................ 57)Figure)4.7.))Slab)side)model)with)edgecdependent)boundary)conditions ............................. 58)Figure)4.8.))Finite)slab)model)with)edgecdependent)boundary)conditions .......................... 59) ) viii) Figure)4.9.))Independent)measurements)of)the)total)heat)change)for)edgecdependent)boundary)conditions........................................................................... 61)Figure)4.10.))Heat)flow)contour)map)with)identical)boundary)conditions ........................... 66)Figure)4.11.))Heat)flow)contour)map)with)edgecdependent)boundary)conditions............ 66)Figure)4.12.))Columnar)joints)superimposed)on)model ................................................................ 67)Figure)5.1.))Phase)diagram)for)high)temperature)experiments ................................................. 72)Figure)5.2.))Experimental)setup............................................................................................................... 76)Figure)5.3.))Photo)of)experiment)2012c21 .......................................................................................... 79)Figure)5.4.))Photo)of)experiment)2012c03 .......................................................................................... 80)Figure)5.5.))Jointing)in)experiment)2012c12 ...................................................................................... 81)Figure)5.6.))Jointing)in)experiment)2012c15 ...................................................................................... 82)Figure)5.7.))Temperaturectime)graphs)of)experiments)2012c21and)2012c22.................... 86)Figure)5.8.))Temperaturectime)graphs)of)experiments)2012c23)and)2012c24................... 87)Figure)5.9.))Temperaturectime)graphs)of)experiments)2012c19)and)2012c20................... 88)Figure)5.10.))Temperaturectime)graphs)of)experiments)2012c25)and)2012c26 ................ 89)Figure)5.11.))Maximum)temperature)differences)in)gradient)experiments.......................... 90)Figure)5.12.))Maximum)averaged)cooling)rates)in)gradient)experiments ............................. 91)Figure)5.13.))Joint)formation)conditions .............................................................................................. 93)Figure)6.1.))Western)face)of)outcrop)1)of)the)Railroad)Quarry)area ........................................ 99)Figure)6.2.))Upper)and)lower)colonnade)with)column)interface)at)Daisy)Lake................... 99)Figure)6.3.))Curving)and)coalescing)columns)at)Railroad)Quarry)outcrop)1 ......................100)Figure)6.4.))Model)with)upper)colonnade)twice)the)thickness)of)lower)colonnade ........107)Figure)6.5.))Comparison)between)Daisy)Lake)outcrop)and)numerical)model ...................108)Figure)6.6.))Comparison)between)Railroad)Quary)outcrop)and)numerical)model ..........109)Figure)6.7.))Differences)in)temperature)for)different) h)factor)values)from)1000)to)6000 .......................................................................................................110)Figure)6.8.))Differences)in)temperature)for)different) h)factor)values)from)25)to)75..................................................................................................................111)Figure)6.9.))Cone)of)depression ..............................................................................................................115)Figure)A.1.))Model)has)h)factor)value)of)6000..................................................................................122)Figure)A.2.))Model)has)h)factor)value)of)1000..................................................................................123) ) ix) Figure)A.3.))Model)has)h)factor)value)of)100.....................................................................................123)Figure)A.4.))Model)has)h)factor)value)of)70 .......................................................................................124)Figure)A.5.))Model)has)h)factor)value)of)25 .......................................................................................124)Figure)A.6.))Model)has)h)factor)value)of)10 .......................................................................................125)Figure)A.7.))Model)has)h)factor)value)of)1..........................................................................................125)Figure)C.1.))Experiment)2012c05 ..........................................................................................................131)Figure)C.2.))Experiment)2012c03 ..........................................................................................................131)Figure)C.3.))Experiment)2012c04 ..........................................................................................................132)Figure)C.4.))Experiment)2012c16 ..........................................................................................................132)Figure)C.5.))Experiment)2012c06 ..........................................................................................................133)Figure)C.6.))Experiment)2012c07 ..........................................................................................................133)Figure)C.7.))Experiment)2012c21 ..........................................................................................................134)Figure)C.8.))Experiment)2012c22 ..........................................................................................................134)Figure)C.9.))Experiment)2012c15 ..........................................................................................................135)Figure)C.10.))Experiment)2012c17........................................................................................................135)Figure)C.11.)Experiment)2012c13.........................................................................................................136)Figure)C.12.))Experiment)2012c18........................................................................................................136)Figure)C.13.))Experiment)2012c11........................................................................................................137)Figure)C.14.))Experiment)2012c12........................................................................................................137)Figure)C.15.))Experiment)2012c14........................................................................................................137))) ) x) Acknowledgements!)) Many)thanks)go)to)Dr.)J.K.)Russell,)without)whose)advice)and)expertise)this)thesis)would)not)have)been)possible.))He)has)provided)invaluable)insight)into)all)aspects)of)this)study,)and)his)inhuman)ability)to)read,)comment)on,)and)return)lengthy)documents)has)been)an)incredible)asset.)) The)other)two)members)of)my)committee,)Lori)Kennedy)and)Erik)Eberhardt,)have)also)contributed)greatly)to)this)thesis)with)their)fresh)viewpoints)on)the)ideas)and)methods)used.)) The)members)of)the)Volcanology)and)Petrology)Lab,)including)Alexandra)Kushnir,)Michelle)Campbell,)Stephan)Kolzenburg,)Chanone)Ryane,)Jenny)Heywood,)Shelly)Oliver,)Betsy)Friedlander,)Luke)Hilchie,)Amy)Ryan,)Nader)Mostaghimi,)Gayle)Febbo,)Terence)Gordon,)and)Lucy)Porritt,)have)been)excellent)resources)to)bounce)ideas)off)of,)for)moral)support,)and)in)the)case)of)Dr.)Porritt,)have)given)excellent)feedback)on)the)contents)of)this)study.))I)would)also)like)to)thank)Dr.)Ben)Edwards)for)his)insightful)comments)on)column)formation.)) Vast)amounts)of)credit)also)go)to)my)parents,)Bob)and)Mary)Anne)Woodell,)for)moral,)emotional,)and)financial)support)throughout)this)thesis.))I)would)also)like)to)thank)my)other)friends,)especially)Sasha)Nollman,)whom)have)supported)me)throughout)this)intellectual)adventure.) ) 1) 1. Introduction! ! ) Columnar)joints)are)contractional)joints)that)form)in)both)extrusive)and)thin)intrusive)melt)bodies,)such)as)sills)or)dykes)(Mallet,)1875;)Budkewitsch)and)Robin,)1994;)Grossenbacher)and)McDuffie,)1995;)Hetényi)et)al.,)2012).))These)joints)intersect)longitudinally)to)produce)columns)(Fig.)1.1),)and)are)formed)by)the)brittle)release)of)tensile)stress)accumulated)from)a)decrease)in)volume)due)to)cooling)(e.g.,)Mallet,)1875;)James,)1920;)Tomkeieff,)1940;)Spry,)1962;)Hetényi)et)al.,)2012).))Columns)often)have)additional)features,)shown)in)Fig.)1.1,)and)described)in)Chapter)2.))) Columnar)joints)are)seen)all)over)the)world)in)various)types)of)rocks,)ranging)from)mafic)to)felsic,)as)well)as)both)coherent)and)fragmental)volcanic)rocks,)including)ignimbrites)(e.g.,)Tomkeieff,)1940;)Spry,)1962;)Michol)et)al.,)2008;)Wright)et)al.,)2011).))However,)columnar)joints)are)not)observed)in)all)cooled)igneous)bodies.))The)specifics)as)to)why)some)cooling)rock)bodies)form)columnar)joints)and)others)do)not)remains)unexplained.))The)purpose)of)this)thesis)is)to)explore)the)relationship)between)the)geometry,)orientation,)and)organization)of)columnar)joints)and)the)cooling)history)and)environment)of)the)lava)body.))Furthermore,)the)thermal)gradients)and)cooling)rates)that)produce)columnar)jointing)are)investigated.))This)increases)the)understanding)of)the)properties)of)cooling)lava,)and)thus)of)intrusive)and)extrusive)emplacement)events)worldwide.)) Proposed)in)this)thesis)is)the)hypothesis)that)there)is)a)range)of)cooling)rates)that)allows)column)formation)at)a)specific)column)forming)temperature,)which)is)near)the)glass)transition)temperature.))Outside)the)limits)of)this)column)forming)cooling)rate,)columnar)joints)do)not)form.) 1.1.! Approach!to!Studying!Columnar!Joints!) There)are)three)main)parts)to)this)thesis:)field)work,)forward)modeling,)and)high)temperature)experiments.))All)contribute)valuable)information)to)the)overall)understanding)of)columnar)joints)in)the)context)of)this)thesis.) ) 2) columnar joint column chisel mark ball and socket joint )Figure)1.1.))An)explanation)of)various)terms)used)throughout)this)study.))While)chisel)marks)are)purely)surficial)features,)and)can)form)slightly)raised)or)depressed)surfaces,)ball)and)socket)joints)completely)penetrate)columns)and)divide)them)into)sections)vertically.))Chisel)marks)and)ball)and)socket)joints)are)discussed)later)in)the)text.)) Starting)with)an)overview)of)the)field)area,)four)outcrops)of)interest)are)identified,)and)the)reader)is)introduced)to)the)overall)structure)of)the)flows,)and)the))geometry)of)the)columns)therein.))Columns)are)first)described)qualitatively,)then)quantitatively)through)measurement)of)the)heights)and)widths)of)the)columns.))In)addition,)the)thicknesses)of)the)colonnades)are)measured)where)present)in)the)outcrop.)) Subsequently,)this)thesis)uses)forward)modeling)to)examine)the)temperature)profiles,)cooling)rates,)and)thermal)gradients)of)modeled)cooling)lava)flows.))Different)boundary)conditions)are)used,)as)well)as)various)geometries)of)lava)flows)(high)and)low)aspect)ratio,)square)and)rectangular).)) Columnar)joints)are)synthesized)using)high)temperature)experiments,)which)enables)textural)analysis)of)the)joints)within)the)experiments.))Thermal)gradients)and)cooling)rates)are)also)measured)within)the)experiments,)to)see)what)kind)of)thermal)gradients)are)necessary)to)produce)columns)at)the)experimental)scale.))The)gradients)from)the)forward)modeling)are)then)compared)with)the)gradients)found)in)the)experiments.) ) 3) ) The)field)area)is)then)revisited,)and)comparisons)are)made)to)the)columnar)joints)in)natural)outcrops)using)previous)knowledge)gleaned)from)the)forward)modeling)and)the)high)temperature)experiments.))Column)propagation)directions)and)geometries)are)examined)with)attention)paid)to)the)actual)and)inferred)boundaries)of)the)lava)flow,)and)how)these)affect)the)columns.))The)column)geometries)in)the)field)are)compared)with)the)modeled)column)propagation)directions,)as)well)as)with)the)synthesized)columns)within)the)high)temperature)experiments.))All)of)these)avenues)are)used)to)extend)knowledge)of)the)formation)conditions)of)columnar)joints.) ) 4) 2. Literature!Review! ) Columns)are)three)dimensional)objects)which)are)bounded)by)two)dimensional)columnar)joint)surfaces,)formed)during)cooling)of)both)extrusive)and)shallow)intrusive)igneous)bodies.))This)section)presents)the)research)past)workers)have)undertaken)that)includes)investigations)into)the)macroscopic)organization)of)columns,)geometric)column)properties,)formation)mechanisms)of)columnar)joints,)previous)studies)of)columns)involving)field)analysis,)as)well)as)analog)and)numerical)modeling,)and)concludes)with)unresolved)issues)that)will)be)elucidated.) 2.1.! Macroscopic!Organization!of!Columns!) Columnar)joints)propagate)parallel)to)heat)flow)and)perpendicular)to)temperature)isotherms)within)the)cooling)body,)and)they)selfcorganize)into)multicsided)polygonal)columns,)whose)long)axis)is)parallel)to)heat)flow)and)perpendicular)to)the)isotherms)(e.g.,)James,)1920;)Degraff)and)Aydin,)1987).)) Columns)within)lava)flows)are)commonly)organized)to)form)two)distinct)zones.))Tomkeieff)(1940))gives)the)terms)colonnade)and)entablature)to)these)two)zones)of)columns.))The)colonnade)is)defined)as)having)linear,)regularly)spaced,)equalcsized,)usually)hexagonal)columns.))The)entablature)is)comprised)of)smaller,)irregular,)curvilinear)columns)that)vary)in)number)of)sides)and)are)not)always)hexagonal)(e.g.,)Tomkeieff,)1940;)Spry,)1962).))The)colonnade)is)split)further)into)two)more)zones,)the)upper)and)lower)colonnade,)with)the)entablature)situated)between)these)two)(Fig.)2.1),)though)the)entablature)is)not)always)present.))When)no)entablature)exists)in)the)outcrop,)the)upper)and)lower)colonnade)meet)at)what)I)call)the)column"interface)(Fig.)2.2).)While)many)flows)have)well)organized)colonnades,)some)flows,)particularly))thick)ones)(though)there)is)no)particular)limitation)on)the)thickness)according)to)Hetényi)et)al.)(2012)),)have)poorly)organized)entablatures.) ) 5) Upper Colonnade Entablature Lower Colonnade )Figure)2.1.))Diagram)of)flow)structures,)including)colonnades)and)entablature.))Fan)structures)in)the)entablature)are)visible.))Drawn)from)picture)of)outcrop)in)Columbia)River)Basalts.))Modified)from)Spry)(1962).) upper colonnade lower colonnade column interface 0 1 m )Figure)2.2.))Outline)drawing)of)columnar)joints)on)east)side)of)Daisy)Lake)outcrop.))Upper)and)lower)colonnades)visible,)with)diffuse)colonnade)interface)between)the)two)(grey)shading).))Bottom)of)outcrop)is)brecciated)flow)base.) ) 6) ) Columnar)joints)do)not)necessarily)always)propagate)linearly)throughout)an)outcrop.))Because)the)joints)propagate)perpendicular)to)isotherms,)if)these)isotherms))curve)within)an)outcrop,)the)joints)will)curve)as)well.))This)can)produce)curving)columns,)like)those)seen)in)Fig.)2.3.) m0 1 )Figure)2.3.))Outcrop)from)Whistler)field)area,)Railroad)Quarry)outcrop)6.))See)Fig.)3.2)for)area)map.))Curving)columns)visible)in)both)foreground)and)background.))Lower)columns)are)vertical,)and)curve)towards)horizontal)as)they)propagate)upwards.))Scale)accurate)for)foreground.))Background)column)diameters)~80)cm.) 2.2! Geometric!Column!Properties!) Columns)generally)consist)of)between)four)and)seven)sides,)with)six)sides)both)the)mean)and)the)mode.))Columns)can)vary)in)diameter)from)millimeters)up)to)several)meters)(e.g.,)Degraff)and)Aydin,)1987).))In)addition,)columns)often)have)interesting)surficial)textures.))These)are)all)detailed)in)this)section.) ) 7) ) The)large)range)in)column)diameters)exists)due)to)the)relationship)between)the)cooling)rate)and)the)size)of)the)columns.))Lower)cooling)rates)(smaller" € ∂T ∂t ,)where)T)is)temperature)and)t)is)time))result)in)columns)with)larger)diameters,)while)higher)cooling)rates)(larger) € ∂T ∂t ))result)in)columns)with)smaller)diameters)(e.g.,)Hetényi)et)al.,)2012).))This)relationship)is)apparent)when)looking)at)a)cross)section)of)a)solidified)lava)flow.))Along)the)top)and)the)bottom,)where)the)cooling)rate)is)highest,)the)columns)can)be)quite)narrow,)on)the)order)of)ones)to)tens)of)centimeters.))On)the)interior)of)the)flow,)where)the)lava)cools)much)more)slowly,)the)columns)are)larger)and)can)have)diameters)of)up)to)several)meters,)depending)on)the)thickness)of)the)flow.))The)thicker)the)flow,)the)longer)the)cooling)time)for)the)interior,)and)thus)the)wider)the)columns.)) Triangles,)squares,)and)hexagons)are)the)only)regular)polygons)that)tessellate)(cover)a)surface)by)repeating)without)any)gaps).))For)columnar)joints)to)form)a)regular)repeating)pattern)in)the)cooling)material,)these)are)the)only)three)regular)shapes)that)are)possible.))According)to)Mallet)(1875),)hexagons)have)the)smallest)ratio)of)“resistance)to)splitting”)over)the)“splitting)effort.”))Mallet)(1875))calculated)this)ratio)as)1.0)for)triangles,)0.68)for)squares,)and)0.519)for)hexagons.))Thus)hexagonal)jointing)patterns)require)the)least)amount)of)energy)to)form.)) This)explains)why)columns)are)hexagonal,)but)not)how)hexagonal)columns)form,)or)how)“triple)junctions”)(a)Ycshaped)junction,)with)120˚)between)each)joint))in)particular)develop.))Spry)(1962))observes)that)sheets)of)cooling)lava)often)first)form)“master)joints”)on)the)surface,)which)are)widely)spaced)(tens)of)meters)apart).))These)then)break)into)what)he)terms)“megaccolumns,”)and)after)this)is)when)hexagonal)columns)start)to)form.))Gray)(1986))mentions)that)on)the)surface)of)lava)flows,)joints)commonly)intersect)at)90˚)angles,)forming)Tcshaped)junctions,)much)like)those)found)in)mudcracks,)and)which)are)also)similar)to)those)found)in)the)drying)experiments)of)Shorlin)et)al.)(2000).))Evolution)of)the)joints)through)propagation)into)a)lava)flow)allows)the)Tcshaped)junctions)to)slowly)develop)into)Ycshaped)junctions)through)a)complex)process)which)involves)modification)and)elimination)of)the)joints)(Gray,)1986).) ) 8) ) This)agrees)with)the)observations)of)Goehring)et)al.)(2006),)who)report)that)columns)evolve)from)fourcsided)towards)sixcsided)as)they)grow.))In)early)forming)column)systems,)which)are)closer)to)the)cooling)surface)and)have)experienced)a)higher) € ∂T ∂t ,)columns)more)often)comprise)square)cross)sections)than)columns)on)the)interior)of)the)flow,)where)the)more)mature)column)systems)have)experienced)a)lower) € ∂T ∂t ,)and)are)more)often)hexagonal)in)cross)section.))Greater)thermal)energy)at)the)cooling)surface)equates)to)less)need)to)conserve)energy)to)form)fractures.))As)the)columnar)joints)propagate)further)away)from)the)cooling)surface,)less)thermal)energy)ensures)hexagons)are)more)likely)to)form)due)to)the)smaller)effort)required)to)produce)them)(Mallet,)1875).)) Igneous)rocks)are)not)the)only)material)to)form)evolving)systems)of)contractional)joints;)joints)in)permafrost)behave)in)a)similar)fashion.))Earlier)formed)cracks)produce)fourcsided)polygons,)while)later)systems)produce)sixcsided)polygons)(Sletten)et)al.,)2003).)) Though)columns)do)not)start)hexagonal)and)equally)sized,)Budkewitsch)and)Robin)(1994))develop)an)algorithm)that)shows)hexagonal)columns)of)unequal)size)will)become)more)equal)over)time,)with)some)reasonable)assumptions)about)the)geometry)of)isotherms)within)the)cooling)flow.))Jagla)and)Rojo)(2002))expand)on)this)to)show)that)any)pattern)of)fractures,)not)just)sixcsided)columns,)will)evolve)into)a)pattern)of)columns)that)are)mostly)sixcsided)and)approximately)equal)in)area.)) Hetényi)et)al.)(2012))perform)shape)analysis)at)several)flows)in)Iceland,)France,)and)Hungary.))With)over)3,000)complete)columns)analyzed,)they)find)that)the)mean)number)of)sides)of)the)columns)studied)is)5.71,)with)about)half)having)6)sides,)and)about)a)third)having)5)sides.))They)also)find)that)the)geometry)and)thickness)of)the)emplaced)magma)body,)as)well)as)the)chemistry)of)the)magma,)play)a)role)in)the)size)of)columns)formed.))Thicker)flows)and)less)effective)boundary)conditions)produce)larger)diameter)columns,)and)given)identical)boundary)conditions)and)thicknesses,)felsic)lavas)will)produce)larger)diameter)columns)than)mafic)lavas.) ) 9) ) Many)columnar)joints)have)surficial)features)known)as)“chisel)marks”)(James,)1920;)Degraff)and)Aydin,)1987))or)“striations”)(Ryan)and)Sammis,)1978).))These)were)first)observed)by)Iddings)(1886),)and)have)been)addressed)by)many)other)workers)since)(e.g.,)James,)1920;)Tomkeieff,)1940;)Spry,)1962;)Ryan)and)Sammis,)1978;)Degraff)and)Aydin,)1987;)Grossenbacher)and)McDuffie,)1995).)) Chisel)marks)(Figs.)1.1)and)2.4))are)planar)features)on)joint)surfaces,)and)are)thought)to)be)a)surface)expression)of)the)incremental)growth)of)columnar)joints)(e.g.,)James,)1920;)Tomkeieff,)1940;)Spry,)1962;)Degraff)and)Aydin,)1987).))As)the)tensile)stresses)increase)within)a)cooling)flow,)a)single)point)eventually)surpasses)the)tensile)strength)of)the)material,)and)a)fracture)forms,)originating)at)this)point.))This)fracture)then)propagates)both)vertically)and)laterally;)laterally)along)the)same)isotherm)as)the)original)point)failure,)and)vertically)towards)the)interior)of)the)flow,)until)the)accumulated)stress)is)no)longer)great)enough)to)induce)brittle)failure.))At)this)point,)the)incremental)joint)growth)halts.))The)result)of)this)process)is)a)single)chisel)mark.)) Ryan)and)Sammis)(1978))investigate)the)formation)of)chisel)marks)in)detail.))They)observe)that)on)fresh)column)surfaces)each)chisel)mark)often)has)smooth)and)rough)sections.))They)interpret)that)the)smooth)section)of)the)chisel)mark)forms)in)the)cooler,)brittle)portion)of)the)flow.))As)the)joint)propagates)into)a)warmer,)less)brittle)area,)the)fracture)surface)starts)to)approach)the)melt)interface)and)increases)in)surface)roughness)as)the)fracture)stops)propagating.))This)enables)the)possibility)to)track)the)propagation)direction)of)columnar)joints)based)on)surficial)features,)if)they)are)present.))Plumose)structures)often)form)on)chisel)marks)as)well)(Aydin)and)DeGraff,)1988).))As)an)example,)Degraff)et)al.)(1989))use)surficial)joint)features,)along)with)petrographic)methods,)to)infer)the)cooling)histories)of)basaltic)flows.)) Grossenbacher)and)McDuffie)(1995))create)a)conductive)cooling)model)that)finds)an)inverse)relationship)between)cooling)rates)and)column)diameters,)as)well)as)between)thermal)gradients)and)chisel)mark)heights.))They)also)predict)that)the)ratio)of)chisel)mark)height)to)column)diameter)should)be)fairly)constant,)based)on)analytical)models,)and)write)that)field)observations)support)this)statement.))Despite)widespread)observation)of)chisel)marks,)not)all)columns)form)chisel)marks,)and)the)reasons)for)this)are)unknown.)) ) 10) ) Ball)and)socket)joints))are)present)in)basalt)flows)around)the)world)(e.g.,)James,)1920;)Tomkeieff,)1940;)Symons,)1967;)Schaefer)and)Kattenhorn,)2004),)including)those)at)the)Giant’s)Causeway)(Fig.)2.5,)Preston)(1930)),)and)in)the)Whistler)field)area)(Fig.)3.6).)Preston)(1930))elucidates)a)model)in)which)a)thermal)gradient)within)each)column)causes)the)formation)of)ball)and)socket)joints,)but)his)model)necessitates)that)the)convex)side)point)towards)the)cooling)surface.))This)is)not)supported)by)field)observations)(Tomkeieff,)1940).))In)Fig.)2.5,)the)ball)and)socket)joints)are)visible,)with)surfaces)both)concave)up)and)concave)down.))The)ball)and)socket)joints)appear)to)be)contractional)in)nature,)but)due)to)the)curviplanar)nature)of)the)joints)and)the)fact)that)their)concavity)direction)does)not)appear)to)be)consistent,)this)means)their)formation)mechanism)remains)elusive.))) 0 1m )Figure)2.4.))Field)photograph)showing)columns)resulting)from)connected)joint)surfaces)(arrows))and)chisel)marks)present)on)the)column)faces.))Chisel)marks)are)planar,)twocdimensional)features,)and)represent)each)increment)of)joint)growth.))Box)indicates)visible)chisel)marks.)) ) 11) )Figure)2.5.)Photo)of)columns)at)Giant’s)Causeway.))Notice)some)columns)have)pools)of)water,)showing)concave)up)surface,)while)other)do)not,)and)show)a)convex)up)surface.))There)is)no)column)interface)of)any)kind)within)this)outcrop,)so)all)columns)experienced)the)same)cooling)history.))Picture)by)Chmee2)(Own)work))[GFDL)(http://www.gnu.org/copyleft/fdl.html))or)CCcBYc3.0)(http://creativecommons.org/licenses/by/3.0)],)via)Wikimedia)Commons.) 2.3.! Formation!Mechanisms!) Columns)have)long)been)observed)and)studied.))Articles)published)as)early)as)the)17th)and)18th)centuries)discuss)the)existence)and)formation)of)basaltic)columns)(e.g.,)Bulkley,)1693;)Keir)and)Fordyce,)1776;)Raspe,)1776),)and)high)temperature)experiments)aimed)at)better)understanding)the)formation)process)of)columns)were)carried)out)over)two)centuries)ago)(Watt,)1804).)) Early)workers)described)columnar)joints)and)the)columns)they)create,)and)speculated)as)to)how)columns)formed,)but)were)often)incorrect.))Bulkley)(1693))described)the)columns)at)the)Giant’s)Causeway)in)Northern)Ireland)as)pillars,)remarking)that)each)one)is)a)single)piece)bounded)by)joints,)which)are)so)narrow)that)nothing)thicker)than)a)knife)will)slide)between)them.))He)does)not)offer)any)method)for)the)formation)of)the)columns,)only)asserting)that)they)are)a)natural)phenomenon.) ) 12) ) Keir)and)Fordyce)(1776))discussed)high)temperature)experiments)conducted)on)glass,)wherein)glass)was)heated)above)its)melting)temperature)and)then)slowly)cooled)and)crystallized.))This)led)them)to)make)the)connection)between)liquid)lava)and)solid)basalt,)hypothesizing)that)basalt)crystallizes)from)lava,)much)like)the)glass)from)their)experiments)crystallized)into)various)materials.))Though)this)seems)like)a)very)basic)connection)to)make,)Keir)and)Fordyce)wrote)this)around)the)same)time)that)Neptunism)became)a)valid)theory)for)the)formation)of)basalt.))Keir)and)Fordyce)discussed)the)shape)of)the)crystals)within)their)crystallized)glass,)and)drew)a)comparison)between)these)crystals)and)columns)found)at)the)Giant’s)Causeway,)based)on)the)similar)prismatic)shape)of)both.))Crystals)and)columns)do)not)form)in)similar)ways,)and)their)inferences)on)the)formation)of)basalt)columns)are)not)correct.)) Around)the)same)time,)Raspe)(1776))published))his)observations)on)a)number)of)lavas)found)in)Germany,)and)specifically)addressed)basaltic)columns.))He)was)the)first)to)propose)the)currently)most)widely)accepted)viewpoint)for)the)formation)of)columnar)joints,)namely)that)the)joints)are)formed)by)contraction)due)to)cooling.)) More)early)high)temperature)experiments)were)performed)by)Watt)(1804),)who)melted)a)mass)of)basalt)and)then)cooled)it)at)two)different)rates.))He)first)cooled)it)rapidly,)producing)a)dark)glass.))In)a)second)experiment,)he)cooled)an)irregular,)wedgecshaped)mass)approximately)1)m)by)75)cm,)with)a)thickness)ranging)from)10)to)45)cm)over)the)course)of)eight)days.))Unlike)the)first)experiment,)crystals)were)present)in)this)sample.))However,)he)was)unable)to)form)columns,)likely)due)to)the)slow)cooling)of)the)sample.)) Watt)(1804))attempts)to)describe)the)formation)of)basaltic)columns)as)arising)from)the)contact)of)spheroids)within)the)molten)basalt.))As)these)spheroids)increase)in)size)and)come)into)contact)with)one)another,)they)do)not)join)but)compress)against)each)other,)taking)up)all)available)space)in)a)single)plane)until)they)have)the)cross)sectional)shape)of)hexagons.))As)the)spheroids)continue)to)increase)in)size,)they)propagate)into)the)interior)of)the)lava)and)form)elongated)columns.))It)is)not)entirely)clear)what)the)spheroids)consist)of,)or)why)they)would)initially)be)spaced)equidistant)from)each)other.))He)also)mentions)that)the)spheroids)could)propagate)due)to)loss)of)either)heat)or)moisture)through)the)top)of)the)lava,)so)despite)his)high)temperature)experiments)with) ) 13) molten)basalt,)he)still)does)not)take)sides)in)the)Neptunism)vs.)Plutonism)debate)of)the)time.)) Early)work)by)Mallet)(1875),)showed)that)there)was)no)agreement)on)whether)columnar)joints)form)from)contraction)during)cooling,)or)from)some)type)of)preexisting)concretion)or)mass)of)crystals.))However,)Mallet)showed)that)hexagons)require)the)least)energy)to)create,)and)are)thus)the)most)common)cross)sectional)shape)of)columns.)) Some)of)the)earliest)explanations)for)the)propagation)of)columnar)joints)perpendicular)to)the)cooling)surface)are)also)addressed)by)Mallet)(1875).))He)gives)examples)of)lava)flows)with)various)geometries,)and)details)when)and)in)what)direction)the)columns)form.))He)also)addresses)the)fact)that)there)must)be)a)certain)“splittingctemperature”)at)which)columnar)joints)form,)when)enough)tensile)stress)is)present)within)the)rock)to)cause)brittle)stress)release,)but)also)when)the)rock)is)cool)enough)that)it)will)not)alleviate)the)stress)through)viscous)flow.))He)estimates)that)this)temperature)is)somewhere)between)600˚)and)900˚F)(315˚)to)482˚C),)based)on)measurements)from)metallurgic)slag.))This)entire)range)of)temperatures)is)much)too)low)(Peck)and)Minakami,)1968).))At)such)low)temperatures,)most)of)the)tensile)stresses)have)either)been)accommodated)for)already,)or)are)no)longer)present,)but)his)study)is)a)starting)point)for)further)investigation.)) Sosman)(1916))investigates)the)difference)between)columns)formed)by)contraction,)and)columns)formed)by)convection)currents)in)melted)wax.))He)concludes)that)while)columns)formed)via)contraction)are)the)most)common,)convection)type)columns)could)exist)in)igneous)rocks,)but)he)does)not)give)any)definitive)field)examples)or)definitely)say)that)these)types)of)columnar)structures)exist.))This)origin)of)columnar)joint)formation)has)been)criticized)in)the)past,)with)a)detailed)account)of)its)drawbacks)by)Spry)(1962).)) James)(1920))mentions)that)as)lava)cools,)it)contracts)in)all)directions.))The)vertical)contraction)is)accounted)for)by)viscous)flow)of)the)still)molten)interior)of)the)lava)flow,)but)the)horizontal)contraction)must)be)accommodated)by)cracking)in)the)already)solid)portion)of)the)flow,)thus)forming)columnar)joints.)) No)other)formation)mechanisms)for)columns)were)proposed)until)Guy)and)Le)Coze)(1990))and)Gilman)(2009))advanced)the)notion)that)columnar)joints)could)form) ) 14) from)“constitutional)supercooling.”))This)is)found)mostly)in)alloys)of)metal)in)which)a)hexagonal)cracking)pattern)develops)due)to)the)compositional)heterogeneity)of)the)metal)at)the)solidus.))Gilman)(2009))proposes)this)because)he)argues)that)basalts)do)not)create)crack)patterns)that)are)consistent)with)homogeneous)solids.))However,)basalts)generally)do)not)change)in)composition)within)the)outcrop)(e.g.,)Spry,)1962).)) The)current)most)widely)accepted)mechanism)for)columnar)joint)formation)is)thermal)contraction)and)brittle)deformation,)and)has)a)large)host)of)supporters)(e.g.,)Raspe,)1776;)Spry,)1962;)Degraff)and)Aydin,)1987),)despite)the)other)theories)that)have)been)hypothesized)over)the)years.)) The)formation)mechanism)for)the)entablature)between)the)upper)and)lower)colonnades)of)lava)flows)is)not)precisely)known.))Long)and)Wood)(1986))suggest)that)the)entablature)is)formed)from)water)penetrating)the)top)of)still)cooling)lava)flows)through)cracks)in)the)lava)crust.))The)convective)heat)loss)from)water)escaping)as)steam)would)produce)a)variety)of)cooling)surfaces)within)the)interior)of)the)flow,)as)well)as)produce)smaller)columns)due)to)the)increased)rate)of)heat)loss.))They)base)this)mostly)on)petrographic)textures)and)phase)abundances,)as)well)as)results)from)a)simple)cooling)model)and)paleoclimate)data.))Degraff)and)Aydin)(1987))and)Degraff)et)al.)(1989))agree)with)this)interpretation,)arguing)that)the)entablature)cannot)be)formed)through)conductive)cooling)alone,)and)therefore)a)convective)cooling)mechanism)must)be)at)play.))In)some)cases)the)entablature)is)over)six)times)as)thick)as)the)lower)colonnade)(Tomkeieff,)1940).)))) While)the)formation)of)the)entablature)within)lava)flows)remains)enigmatic,)the)currently)accepted)formation)mechanism)for)columnar)joints)involves)the)accumulation)of)tensile)stresses)due)to)a)decrease)in)volume,)from)heat)loss,)exceeding)the)viscous)relaxation)rate)of)the)cooling)material.))These)tensile)stresses)are)relieved)through)brittle)deformation)of)the)cooling)material,)specifically)through)Mode)I)tensile)jointing)(Degraff)and)Aydin,)1987).) ) 15) 2.4.! Previous!Analysis!of!Columns!) In)addition)to)geometric)analysis)of)columns)and)columnar)joint)surfaces,)previous)workers)have)used)analog)and)numerical)models)to)study)columns,)and)others)have)carried)out)field)observations)on)the)active)formation)of)columnar)joints.) 2.4.1.! Analog!Modeling!of!Columns!) Shorlin)et)al.)(2000))investigate)cracking)patterns)in)alumina)powder)and)water)mixtures.))A)thin)layer)of)powder)and)water)shrinks)as)it)dries,)producing)tensile)stresses)and)cracking)within)the)layer.))Curvilinear)cracks)form)during)both)directional)and)noncdirectional)drying.))Occasionally)the)angle)between)cracks)measures)120˚,)producing)triple)junctions)like)those)seen)in)hexagonal)columns,)but)90˚)spacing)is)the)most)common)by)far,)producing)4)sided)polygons.))Though)few)6)sided)polygons)are)formed,)the)authors)do)make)interesting)observations)relating)the)thickness)of)their)dried)alumina)material)to)the)spacing)of)jointing.))In)one)experiment,)they)found)that)when)there)was)a)step)down)in)the)bottom)of)the)drying)tank,)and)subsequently)an)increase)in)about)50%)of)the)thickness)of)their)dried)alumina)material,)the)spacing)of)the)cracks)approximately)doubled.))This)clearly)demonstrates)that)there)are)consistent)links)between)crack)spacing)and)the)thickness)of)the)material.))This)is)true)in)cooling)lava)flows)as)well)(e.g.,)Tomkeieff,)1940).)) Allain)and)Limat)(1995))studied)regular)cracking)patterns)in)colloidal)suspensions.))They)found)that)a)series)of)regular)cracks)formed)perpendicular)to)the)drying)surface,)and)parallel)to)the)direction)of)evaporation.))Shortly)after)these)findings,)Müller)(1998))reintroduced)the)idea)of)analog)modeling)of)cooling)lava)flows)on)the)basis)that)cooling)of)basalt)and)starch)desiccation)are)both)diffusion)processes,)and)both)must)obey)similar)diffusion)equations.))Previous)authors)using)analog)modeling)techniques)include)Huxley)(1881))and)French)(1922),)as)stated)by)Goehring)and)Morris)(2005).))Other)authors)to)use)starch)desiccation)as)an)analog)for)cooling)lava)flows)include)Toramaru)and)Matsumoto)(2004))and)Lodge)and)Lescinsky)(2009),)and)their)findings)are)similar)to)those)of)Goehring)and)Morris)(2005))and)Goehring)et)al.)(2006),)as)detailed)below.) ) 16) ) Goehring)and)Morris)(2005))use)the)drying)of)corn)starch)and)water)slurries)as)a)proxy)for)the)cooling)of)a)lava)flow.))In)their)models,)the)evaporation)of)water)from)the)corn)starch)slurry)is)analogous)to)the)loss)of)heat)from)a)lava)flow.))Just)as)basalt)decreases)in)volume)and)increases)in)viscosity)with)a)decrease)in)temperature,)the)corn)starch)slurry)decreases)in)volume)and)increases)in)viscosity)due)to)water)loss)until)it)can)deform)only)under)brittle)conditions.)) As)the)corn)starch)slurry)solidifies)and)it)begins)to)decrease)in)volume,)the)contractional)stresses)begin)to)exceed)the)tensile)strength)of)the)material,)and)it)fails)brittlely,)forming)tension)cracks.))As)the)drying)front)propagates)downward,)the)cracks)follow,)forming)joints)that)organize)into)columns,)much)like)those)seen)in)basalts.)) With)this)type)of)easily)reproducible)analog)model,)it)is)possible)to)conduct)a)multitude)of)experiments)examining)properties)such)as)column)cross)sectional)area)as)compared)to)drying)time)and)initial)thickness)of)corn)starch)slurry.))Goehring)and)Morris)(2005))find)that)the)mean)cross)sectional)area)of)columns)decreases)with)increasing)drying)rates,)and)that)it)also)increases)with)increasing)model)depth.))These)findings)are)similar)to)those)found)in)basaltic)lava)flows)(Goehring)and)Morris,)2008).) 2.4.2.! Numerical!Modeling!of!Columns!) Field)observations)and)analog)modeling)have)both)helped)expand)the)horizon)of)knowledge)with)regard)to)columnar)joints,)but)numerical)modeling)is)a)very)useful)tool)as)well,)and)numerical)modeling)techniques)have)existed)for)over)50)years.))Crank)and)Nicolson)(1947))published)a)seminal)paper)on)numerical)solutions)for)partial)differential)equations)related)to)heat)conduction)that)has)been)used)by)others)(e.g.,)Carslaw)and)Jaeger,)1986).))Crank)and)Nicolson)(1947))described)an)implicit)spaceccentered)forward)model)that)was)unconditionally)stable,)and)faster)than)other)models)of)the)time.)) Jaeger)(1961))used)numerical)techniques)to)model)the)evolution)of)isotherms)within)a)cooling)lava)flow,)given)a)set)of)boundary)conditions.))Starting)with)simple)cross)sections)of)slabs,)he)then)moves)on)to)model)more)complex)shapes,)such)as)an)infilled)valley.))Numerical)models)have)also)been)used)to)describe)the)influx)of)water)into)joints,)helping)drive)joint)propagation)(Lister,)1974;)Long)and)Wood,)1986))and)as) ) 17) an)explanation)for)the)presence)of)entablature)in)the)Columbia)River)flood)basalts)(Long)and)Wood,)1986).)) Grossenbacher)and)McDuffie)(1995))use)numerical)analysis)techniques)to)model)not)only)temperature)profiles)and)thermal)gradients)within)cooling)flows,)but)also)to)investigate)the)relationship)between)chisel)mark)width)and)column)diameter,)finding)a)direct)relationship)between)the)two.))They)also)find)an)inverse)correlation)between)the)cooling)rate)and)columnar)joint)spacing,)as)well)as)between)the)thermal)gradient)and)the)chisel)mark)width.)) Constructing)a)model)that)accounts)for)viscoelastic)relaxation)in)addition)to)elastic)stress)release,)Lore)et)al.)(2000))show)that)relaxation)by)viscous)flow)does)have)an)effect)on)elastic)stress.))They)also)find)that)higher)cooling)and)strain)rates)correlate)with)higher)effective)glass)transition)temperatures.))The)glass)transition)temperature)is)the)temperature)at)which)strain)rate)exceeds)the)relaxation)timescale,)and)the)cooling)material)deforms)brittlely,)in)addition)causing)the)cooling)material)to)undergo)several)physical)parameter)changes)(thermal)expansivity,)heat)capacity,)etc.))(e.g.,)Dingwell)and)Webb,)1989;)Dingwell)and)Webb,)1990;)Webb)et)al.,)1992;)Webb,)1997).))Faster)cooling)rates)produce)higher)percentages)of)strain)that)is)elastic,)which)then)translates)to)stress)within)the)system.) 2.4.3! Field!Studies!of!Active!Lavas!) Peck)and)Minakami)(1968))use)the)cooling)of)the)1963)Alae)lava)lake,)as)well)as)the)1965)Makaopuhi)lava)lake,)to)observe)the)active)formation)of)columnar)joints.))Several)drill)cores)into)the)cooling)Alae)lava)lake)enabled)an)accurate)temperature)profile)to)be)constructed)for)the)top)half)of)the)lava)lake)throughout)the)entire)cooling)history,)and)for)the)entire)lava)lake)after)it)had)completely)cooled)below)the)glass)transition)temperature.)) They)were)able)to)observe)cracks)forming)on)the)surface)of)the)cooling)lava)lake,)which)would)initiate)at)temperatures)as)high)as)900˚C,)and)propagate)down)to)temperatures)up)to)1000˚C.))Using)a)highcgain)seismograph,)Peck)and)Minakami)(1968))could)record)each)increment)of)column)growth,)as)it)would)appear)as)a)short,)low)amplitude)vibration.) ) 18) ) Through)analog)and)numerical)modeling,)as)well)as)field)studies)of)both)current)and)past)systems,)understanding)of)columnar)joints)has)improved)markedly.))However,)there)remain)several)unanswered)questions)which)are)described)in)the)next)section,)and)which)this)thesis)attempts)to)answer.)) 2.5.! Unresolved!Issues!) Though)the)thermal)contraction)hypothesis)is)the)accepted)formation)mechanism)for)columnar)joints,)there)are)some)aspects)that)have)not)been)fully)explained,)such)as)curving)columns)and)the)relative)thicknesses)of)the)upper)and)lower)colonnades.)) Curving)columns)have)been)described)by)previous)authors)(e.g.,)Iddings,)1886;)Spry,)1962),)and)following)the)theory)that)columnar)joints)propagate)parallel)to)heat)flow,)joints)(and)therefore)columns))will)curve)following)heat)flow)vectors.))However,)curving)columns)have)never)before)been)described)by)numerical)models.))Using)heat)flow)vectors)as)a)proxy)for)columnar)joint)formation)direction,)and)heat)flow)magnitude)as)a)proxy)for)columnar)joint)spacing,)models)which)more)accurately)depict)curving)columns)within)a)lava)flow)are)presented)in)this)thesis.)) Previous)authors)have)invoked)various)cooling)mediums,)including)water,)to)explain)the)apparently)accelerated)cooling)rate)of)the)entablature)(e.g.,)Long)and)Wood,)1986;)Degraff)and)Aydin,)1987;)Degraff)et)al.,)1989).))Others,)such)as)Tomkeieff)(1940))and)Swanson)(1967),)observe)that)the)upper)colonnade)and)entablature)can)be)up)to)six)times)as)thick)as)the)lower)colonnade.))However,)the)relative)amount)of)heat)flow)from)one)boundary)as)compared)to)the)other)has)never)been)investigated)in)outcrops)such)as)these.))By)modeling)a)variety)of)the)outcrops)in)the)Whistler)field)area,)this)thesis)more)accurately)describes)the)relative)amounts)of)heat)lost)through)the)upper,)as)compared)to)the)lower,)boundaries.) ) 19) 3. Field!Examples! ) There)are)many)excellent)examples)of)columnar)joints)in)basaltic)lava)flows)throughout)the)northwest)of)the)United)States)and)the)southwest)of)British)Columbia,)Canada.))These)include)jointing)in)the)Columbia)River)flood)basalts))(e.g.,)Long)and)Wood,)1986;)Mangan)et)al.,)1986))and)the)Cheakamus)Valley)basalts)near)Whistler,)BC,)which)are)part)of)the)larger)Garibaldi)Group)(Mathews,)1958;)Lee,)1988;)Green,)2006).))The)Cheakamus)Valley)basalts)were)chosen)for)this)field)study)due)to)their)proximity,)ease)of)access,)their)excellent)exposure)due)to)both)erosion)and)road)cuts,)and)their)young)age.))Green)et)al.)(1988))sampled)and)dated)two)of)the)outcrops)in)this)study.))They)place)the)Railroad)Quarry)outcrops)at)34)Ka)(based)on)radiocarbon)dates)from)wood)in)lacustrine)sediments)of)the)same)age),)and)the)Daisy)Lake)outcrops)at)50)Ka)(based)on)KcAr)analysis).))The)young)age)ensures)minimal)weathering)and)alteration)of)the)column)surfaces.))Additionally,)these)basalt)lavas)were)erupted)while)there)was)ice)in)the)valleys,)or)possibly)while)glaciers)were)present)(Mathews,)1958).))The)highly)variable)cooling)environments)give)the)flows)interesting)and)dynamic)cooling)histories)that)vary)greatly)depending)on)the)outcrop.)) Mathews)(1958))observes)lava)flows)with)eskerclike)forms,)and)hypothesizes)that)these)flows)could)have)erupted)into)subglacial)meltwater)passages)during)the)waning)stages)of)the)Wisconsin)ice)sheet.))These)lava)flows)have)a)much)higher)aspect)ratio)than)is)typical)for)basaltic)lavas,)and)also)contain)radial)columnar)joints.))This)evidence)leads)him)to)the)conclusion)that)there)was)ice)in)the)valleys)for)at)least)some)of)the)time)during)the)eruption)of)the)Cheakamus)Valley)basalts.))However,)the)outcrops)in)this)study)do)not)have)the)same)eskerclike)structural)form,)and)thus)the)location)and)extent)of)the)ice)is)not)as)easily)determined.)) This)section)examines)four)outcrops)from)the)Whistler)field)area)(Fig.)3.1).))Columnar)structures,)including)the)column)interface,)are)described,)along)with)surface)features.))Both)colonnade)proportions)and)average)diameters)of)columns)are)qualitatively)analyzed.) ) 20) 3.1.! Location!and!Extent!of!Flows!) The)Cheakamus)Valley)basalts)are)part)of)the)Garibaldi)Group)(Mathews,)1958).))The)four)outcrops)this)study)focuses)on)are)located)along)Highway)99)between)Whistler)and)Squamish,)BC.))The)outcrops)are)named,)from)north)to)south,)Railroad)Quarry,)Brandywine)Falls,)Pinecrest,)and)Daisy)Lake)(Figs.)3.1)and)3.2).)) The)Railroad)Quarry)outcrops)are)approximately)10)km)SW)of)Whistler,)BC,)along)Highway)99)(see)Table)3.1)for)a)list)of)outcrop)locations).))These)outcrops)are)composed)of)at)least)two)different)flows,)all)originating)from)an)unknown)source)higher)in)elevation)(Kelman,)2005).))There)are)areas)near)the)highway)where)the)contact)between)the)underlying)intrusive)bedrock)and)the)overlying)basalts)is)visible,)but)this)contact)is)only)exposed)in)the)road)cut.))At)the)road,)the)basalts)are)5c8)m)thick,)but)increase)in)thickness)as)the)topography)drops)away)to)the)east.))The)eastern)exposure)of)the)basalts)is)a)large,)subvertical)cliffcface)of)both)vertical)and)horizontal)columns,)at)least)20)m)high)in)coherent)outcrop,)and)with)a)large)talus)slope)at)the)bottom,)equal)or)greater)in)vertical)height,)which)leads)down)to)the)Cheakamus)River.))Though)the)bedrock)is)seen)at)the)road)cut)near)the)top)of)the)outcrops,)it)is)not)visible)anywhere)else)in)the)area,)including)at)the)river.)) There)are)several)“islands”)of)basalts,)which)have)been)eroded)in)such)a)way)that)they)are)all)isolated)from)each)other)currently,)even)if)they)were)joined)at)some)point)in)the)past.))These)“islands”)have)been)labeled)outcrops)1)through)7)(Fig.)3.2).))Though)these)outcrops)are)not)the)only)ones)in)the)Railroad)Quarry)area,)they)are)the)ones)with)the)best)exposure)and)most)interesting)geometries.)) The)Brandywine)Falls)outcrops)are)5)km)south)of)the)Railroad)Quarry.))The)flows)have)been)exposed)through)erosion)by)Brandywine)Creek.))At)the)falls,)tens)of)meters)of)subhorizontal,)laterally)continuous)flows)are)visible,)but)there)is)no)easy)way)to)access)the)flows)in)this)vertical)cliff)face,)and)they)are)not)described)here.))There)is)one)outcrop)visible)on)the)upper)side)of)the)falls,)and)it)was)this)outcrop)that)was)studied)(Fig.)3.2).))This)same)outcrop)has)been)described)by)Mathews)(1958).))He)refers)to)this)outcrop)as)eskerclike,)and)it)will)be)discussed)further)below.) ) 21) ) At)the)Pinecrest)field)area,)3)km)south)of)Brandywine)Falls,)two)extensive)outcrops)occur)on)either)side)of)the)highway,)and)have)very)different)outcrop)exposures.))The)western)outcrop)is)approximately)20)m)wide,)while)the)eastern)outcrop)is)approximately)150)m)wide)(Fig.)3.2).))While)the)eastern)outcrop)is)slightly)taller,)it)still)has)a)much)lower)aspect)ratio)than)the)western)side.))The)reason)for)the)discrepancy)between)the)two)outcrop)patterns)is)unclear.))Both)western)and)eastern)Pinecrest)outcrops)have)a)wellcdefined)column)interface.))) The)southernmost)field)area)is)Daisy)Lake,)4)km)south)of)Pinecrest.))Here,)the)road)cuts)through)two)flows,)with)a)flow)breccia)visible)between)the)two.))The)upper)surface)of)the)upper)flow)has)been)eroded)somewhat)by)the)Fraser)Glaciation)(Green,)1981b),)and)the)bottom)of)the)lower)flow)is)not)visible.))Both)western)and)eastern)Daisy)Lake)outcrops)have)a)wellcdeveloped)column)interface,)visible)in)the)upper)of)the)two)flows.)))Table)3.1.))List)of)outcrops)and)their)locations.)Outcrop) Latitude) Longitude) UTM)Zone) Easting) Northing)Railroad)Quarry) 50˚04.4’)N) 123˚05.5’)W) 10) 493441) 5546788)Brandywine)Falls) 50˚01.6’)N) 123˚07.2’)W) 10) 491405) 5541603)Pinecrest) 50˚00.3’)N) 123˚07.9’)W) 10) 490565) 5539195)Daisy)Lake) 49˚59.2’)N) 123˚08.7’)W) 10) 489605) 5537158))) Chemically,)the)Cheakamus)Valley)basalt)is)characterized)by)Green)(1981))as)an)olivine)basalt,)containing)varying)amounts)of)olivine)(7c16%),)plagioclase)(10c16%),)and)clinopyroxene)(1c11%),)with)between)64)and)72%)groundmass.))The)groundmass)consists)mostly)of)glass,)but)has)minor)magnetite,)pyroxene,)and)plagioclase)as)well.))Fig.)3.3)shows)photos)of)an)entire)thin)section)from)Railroad)Quarry)outcrop)1,)in)both)planecpolarized)and)crosscpolarized)light.))) ) 22) 0 1 2 3 4 km Daisy L ake 1 2 3 4 Georgia Strait 0 10 20 km Whistler Vancouver )Figure)3.1.))Regional)map)of)the)Lower)Mainland)in)the)upper)right)corner,)with)box)showing)field)area.))Center)map)is)of)the)Cheakamus)Valley,)with)outcrops)numbered)as)follows:)Railroad)Quarry)(1),)Brandywine)Falls)(2),)Pinecrest)(3),)Daisy)Lake)(4).))Small)scale)map)image)modified)from)Mathews)(1951).) ) 23) Daisy Lake Daisy Lake West Daisy Lake East Highway 99 Daisy Lake 50 m Railroad Quarry Pinecrest Brandywine Falls 1 3 45 67 Cheaka mus Rive rHighway  99 50 m 2 Highway  99 50 m Brandywine Creek Esker-like outcrop 50 m Highway 99 Daisy Lake Pinecrest  East Pinecrest West )Figure)3.2.))Schematic)diagrams)of)the)field)areas)in)this)study.))The)Railroad)Quarry)schematic)shows)outcrops)1)through)7,)while)the)Brandywine)Falls)schematic)shows)the)eskerclike)outcrop,)which)is)part)of)a)larger)flow)that)is)less)well)exposed.))The)eastern)and)western)sections)of)the)Daisy)Lake)and)Pinecrest)areas)are)labeled)as)well.) ) 24) A B )Figure)3.3.))Thin)sections)of)the)Cheakamus)Valley)basalt.))A)is)in)planecpolarized)light,)and)B)is)in)crosscpolarized)light.))Phenocrysts)of)brightly)colored)olivine)and)gray)plagioclase)are)present,)as)seen)in)B.))The)olivine)is)both)rounded)and)angular,)while)the)plagioclase)occurs)mostly)in)elongated)or)angular)shapes.))The)groundmass)is)composed)of)mostly)glass,)with)minor)magnetite,)pyroxene,)and)plagioclase.) ) 25) 3.2.! Columnar!Structures!in!Outcrop!) There)are)several)types)of)columnar)structures)observed)in)the)outcrops.))In)the)past,)authors)such)as)Spry)(1962))have)identified)columnar)structures)such)as)fans,)chevrons,)and)basins)(Fig.)3.4),)but)not)all)of)these)structures)are)present)in)the)field)area)of)this)study.))This)is)partially)due)to)the)lack)of)entablature)in)any)of)the)outcrops)studied,)as)Spry)(1962))found)many)of)his)structures)within)the)entablatures)of)his)outcrops.)) One)of)these)unclassified)structures)is)seen)on)the)eastern)side)of)the)Railroad)Quarry)outcrop)6,)where)the)basalt)contacts)the)Cheakamus)River.))At)this)subvertical)cliff)face,)there)are)large)(approximately)1)m)diameter),)vertical)columns)near)the)bottom)of)the)outcrop,)and)smaller)(approximately)30)cm)diameter),)horizontal)columns)near)the)top.))Where)they)meet)it)is)possible)to)see)the)curving)of)the)vertical)columns)over)towards)horizontal)(Fig.)2.3).))The)columns)change)orientation)and)size)quite)suddenly,)and)the)possible)reasons)for)this)are)detailed)below.)) There)is)a)section)of)Railroad)Quarry)outcrop)3)that)shows)a)structure)similar)to,)but)distinct)from,)the)fan)as)described)by)Spry)(1962).))Instead)of)columns)that)curve)into)parallelism)from)a)more)radial)pattern)below,)they)instead)pinch)in)to)a)single)point)near)the)top,)as)viewed)on)the)outcrop)surface)(Fig.)3.5).))In)three)dimensions,)the)columns)pinch)in)to)a)lineation)on)the)top)of)the)flow,)rather)than)a)single)point.))It)is)also)distinct)in)that)the)lower)columns)are)completely)vertical,)rather)than)fanning)outwards.)) Mathews)(1958))observes)an)“eskerclike)flow”)at)the)Brandywine)Falls)outcrop)(Fig.)3.6).))Eskers)are)long,)winding)ridges)composed)of)sediment)deposited)from)englacial)and)subglacial)water)flow)(Ritter)et)al.,)2002).))They)are)essentially)the)depositional)remnant)of)glacial)rivers.))When)Mathews)(1958))refers)to)the)flow)as)eskerclike)in)form,)he)means)that)the)flow)has)a)high)aspect)ratio)(for)basaltic)flows))similar)to)that)of)an)esker,)and)that)its)geographic)form)is)narrow)and)sinuous,)also)similar)to)an)esker.))Based)on)these)observations,)along)with)the)presence)of)radial)columnar)jointing)as)well)as)sideromelane,)he)makes)the)conclusion)that)the)flow)may)have)erupted)or)flowed)subglacially.))Based)on)the)subsequent)dating)of)the)rocks) ) 26) (Green)et)al.,)1988),)it)is)likely)that)there)were)glaciers)or)valley)ice)present)during)the)eruption)of)the)Cheakamus)Valley)basalts)(Armstrong)et)al.,)1965;)Clague)et)al.,)1989),)as)shown)by)this)outcrop.) Basin FanChevron )Figure)3.4.))Three)structures)of)columns)found)in)outcrops,)as)discussed)by)Spry)(1962).))The)chevron)and)basin)structures)are)not)seen)in)the)Whistler)Field)area,)but)outcrops)similar)to)the)fan)structure)are)seen,)particularly)in)Railroad)Quarry)outcrop)3)(Fig.)3.5).))These)differing)column)structures)result)from)outcrops)with)a)variety)of)geometries.))Figure)modified)from)Spry)(1962).) ) 27) )Figure)3.5.))Vertical)columns)pinching)upwards)at)Railroad)Quarry)outcrop)3.))Lower)columns)are)vertical,)then)pinch)towards)each)other)near)the)top.))On)the)right)side,)coalescing)columns)are)visible.))The)column)structure)seen)in)this)outcrop)is)similar)to,)but)still)distinct)from,)the)fan)structure)in)Fig.)3.4.))Hammer)for)scale.) ) 28) )Figure)3.6.))Eskerclike)outcrop)at)Brandywine)Falls.))Column)geometries)are)complex,)and)arrows)show)approximate)direction)of)column)formation,)though)the)propagation)direction)is)not)always)clear,)such)as)near)the)top)where)the)columns)are)parallel)to)the)outer)surface)of)the)flow.))Backpack)circled)for)scale.) 3.3.! Field!Observations! 3.3.1.! Lower!Colonnade!) Most)of)the)lower)colonnades)in)outcrops)in)the)Whistler)field)area)are)composed)of)columns)with)diameters)between)50)cm)and)1)m,)and)are)generally)equant)in)crosscsection,)subvertical)in)orientation,)and)are)composed)of)either)5)or)6)sides.))Many)of)the)columns)have)wellcdeveloped)chisel)marks)on)their)surfaces)(Fig.)3.7),)but)show)no)plumose)structure.))Some)of)the)columns)have)planar)or)curviplanar)cross)joints)as)well)(Fig.)3.8),)known)as)ball"and"socket"joints)(e.g.,)James,)1920;)Preston,)1930;)Symons,)1967),)but)they)are)not)found)in)all)outcrops.) 3.3.2.! Upper!Colonnade!) Generally)the)columns)in)the)upper)colonnades)of)observed)outcrops)are)far)less)organized)than)those)of)the)lower)colonnades.))Individual)columns)are)not)as)well)defined,)and)appear)to)break)into)blocky)rubble)more)easily.))They)also)have)a)smaller)mean)diameter,)as)shown)by)the)statistical)data)for)the)eastern)Pinecrest)outcrop)in) ) 29) Section)3.4.2.))Chisel)marks)are)not)nearly)as)prevalent,)and)there)are)no)outcrops)with)ball)and)socket)joints.) 3.3.3.! Colonnade!Interface!) The)interface)between)the)upper)and)lower)colonnade)is)prominent)on)several)outcrops)in)the)field)area,)including)the)Daisy)Lake)outcrops,)Pinecrest)outcrops,)and)the)western)side)of)Railroad)Quarry)outcrop)1.))The)interface)looks)different)depending)on)the)scale)at)which)it)is)viewed)(Fig.)3.9).))From)a)distance,)the)interface)appears)to)be)quite)sharp,)a)definitive)boundary)between)the)smaller)columns)of)the)upper)colonnade)and)the)larger)columns)of)the)lower)colonnade.))However,)when)viewed)up)close,)the)interface)is)much)more)gradual)and)indeterminate.)) As)shown)in)Fig.)3.9,)the)interface)between)colonnades)is)not)a)sharp)boundary)but)rather)a)zone)of)blocky,)equant,)somewhat)rubbleclike)columns.))Joints)do)not)seamlessly)grade)into)one)another)across)the)interface,)nor)do)they)stop)completely.))The)joints)from)the)upper)colonnade)will)often)angle)away)from)vertical)to)intersect)another)joint,)and)create)a)column)with)a)tapered)end.))In)some)cases)the)joints)in)the)upper)colonnade)appear)to)simply)stop)propagating)downwards,)however)the)vertical)joint)often)terminates)in)a)perpendicular)crossccutting)joint.))There)are)also)many)cracks)that)are)smaller)than)the)columncforming)joints,)and)are)often)curvilinear.))These)cracks)often)subdivide)the)larger)lower)colonnade)columns)as)they)approach)the)interface,)but)they)are)clearly)not)part)of)the)upper)colonnade.))They)are)visible)in)the)lower)right)side)of)the)bottom)image)in)Fig.)3.9.))These)cracks)abound)at)the)interface,)preventing)the)clear)delineation)between)upper)and)lower)colonnade.)) ) 30) 300 cm )Figure)3.7.))Surficial)chisel)marks)on)the)columns)in)the)lower)colonnade)of)the)eastern)Daisy)Lake)outcrop.))No)plumose)structures)are)visible)on)the)joint)surfaces.) ) 31) )Figure)3.8.))Ball)and)socket)joints)in)outcrop)7)of)the)Railroad)Quarry)field)site.))Convexity)of)cross)joints)points)in)both)ways)and)does)not)indicate)the)direction)of)column)formation.))Cross)joints)do)not)appear)to)be)continuous)across)columns,)and)so)formed)after)columnar)joints.))Hammer)is)90)cm)in)length.) ) 32) B A C m0 1 )Figure)3.9.))Set)of)images)from)the)eastern)face)of)the)Daisy)Lake)field)area.))A)shows)the)column)interface)as)a)clearly)visible)and)definite)line.))In)B)the)column)interface)is)still)quite)obvious,)but)more)diffuse.))In)C,)the)column)interface)very)gradual)and)not)well)defined.) ) 33) 3.4.! Colonnade!Proportions!and!Measurements! 3.4.1.! Colonnade!Thickness!) The)upper)and)lower)colonnades)are)not)always)of)equal)thickness)(e.g.,)Iddings,)1886;)Swanson,)1967;)Schaefer)and)Kattenhorn,)2004).))Fig.)3.10)shows)information)gathered)from)three)outcrops)in)the)Whistler)field)area,)along)with)information)gathered)from)diagrams)and)photos)of)outcrops)from)three)other)studies)(Iddings,)1886;)Swanson,)1967;)Schaefer)and)Kattenhorn,)2004).))The)measurements)for)the)Snake)River)Plain)outcrops)(Schaefer)and)Kattenhorn,)2004),)as)well)as)for)the)Watchung)Group)(Iddings,)1886),)were)taken)from)photos)of)the)outcrops,)with)several)measurements)taken)to)show)the)range)within)the)outcrop.))The)Yakima)Group)measurements)were)taken)from)schematic)diagrams)of)flows)from)Swanson)(1967).)) Because)the)diameter)of)the)columns)is)inversely)proportional)to)the)cooling)rate,)the)upper)colonnade)should)be)thicker)than)the)lower)colonnade,)assuming)the)columns)in)the)upper)colonnade)are)smaller)in)diameter.))Faster)cooling)rates)are)a)product)of)higher)heat)flow;)if)more)heat)is)released)through)the)top)of)the)lava)flow)than)through)the)bottom,)then)logically)the)upper)colonnade)will)compose)a)higher)proportion)of)the)flow,)as)the)columnar)joints)will)propagate)more)quickly)from)the)upper)boundary.))This)model)only)works)for)a)static)lava)flow)that)is)not)perturbed)during)cooling.))If)the)cooling)conditions)of)the)flow)are)changed,)such)as)through)inundation)of)water)into)the)already)formed)cracks)in)the)upper)surface,)this)will)upset)the)stable)cooling)regime)and)change)the)expected)proportions)of)the)upper)and)lower)colonnade.)) The)hypotheses)of)entablature)formation)(such)as)water)infiltration)into)cracks))posit)that)the)presence)of)entablature)indicates)that)the)lava)was)not)subject)to)a)stable)cooling)regime,)but)rather)a)transient)one.))Because)the)cooling)history)of)outcrops)with)entablature)cannot)be)easily)quantified,)these)outcrops)are)not)used)in)determining)the)physicality)of)column)size)and)colonnade)proportions.)) The)Yakima)Group)outcrops)(Fig.)3.10))all)have)thicker)lower)colonnades)than)upper)colonnades,)when)entablature)is)present.))This)can)be)explained)by)the)fact)that)these)outcrops)have)extremely)thick)entablatures.))Assuming)either)of)the)two) ) 34) entablature)formation)mechanisms)described)above)are)correct,)the)entablature)forms)from)increased)heat)loss)through)the)upper)boundary,)not)the)lower)boundary.))This)results)the)entablature)consisting)only)of)what)would)have)been)upper)colonnade,)had)the)entablature)not)formed.))Because)the)thickness)of)the)lower)colonnade)remains)the)same,)and)the)upper)colonnade)decreases)in)thickness)due)to)the)presence)of)entablature,)it)is)possible)for)the)lower)colonnade)to)be)thicker)than)the)upper)colonnade)in)outcrops)with)large)proportions)of)entablature,)such)as)the)Yakima)Group.)) Fig.)3.10)shows)that)almost)all)outcrops)(without)entablature))measured)have)greater)than)50%)upper)colonnade.))The)only)outcrop)in)the)Whistler)Field)area)that)is)proportionally)greater)than)50%)lower)colonnade)is)outcrop)1)at)the)Railroad)Quarry)site)(Fig.)3.11).))There)are)a)couple)possible)explanations)for)this.))First,)the)lower)boundary)of)the)lava)flow)is)very)irregular,)but)the)thickness)of)the)upper)colonnade)is)constant,)and)the)colonnade)interface)boundary)is)horizontal.))This)means)that)the)lower)colonnade)varies)in)thickness,)and)in)some)places)is)thinner)than)the)upper)colonnade.))This)irregularity)in)the)lower)boundary)may)have)created)more)surface)area,)increasing)heat)flow.))A)second)possible)explanation)is)that)the)entire)Whistler)area)has)been)glaciated)since)these)flows)were)emplaced)(Green)1981b),)and)this)could)have)eroded)some)of)the)upper)colonnade)away.))However,)there)is)no)reason)for)there)to)be)more)erosion)here)than)elsewhere.) ) 35) 0%25%50%75%00.10 0.200.30 0.400.50 0.60 0.700.80 0.901 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1Lower Colonnade / Total Upper Colonn ade / T otal Railroad Quarry Outcrop 1 Whistler Field AreaSnake River PlainWatchung GroupYakima Group% Entablature A B C )Figure)3.10.)Basaltic)flow)colonnade)proportions)from)this)and)previous)studies.))Most)outcrops)have)a)larger)percentage)of)upper)colonnade)compared)to)lower)colonnade.))The)two)blue)lines)demarcate)three)different)zones)in)the)figure,)A,)B,)and)C.))A)includes)outcrops)with)high)ratios)of)upper)to)lower)colonnade.))These)outcrops)likely)experienced)extreme)cooling)on)the)upper)colonnade,)possibly)due)to)subglacial)emplacement)or)extreme)inundation)of)water)(flooding).))B)includes)outcrops)with)more)than)half)upper)colonnade,)but)not)extreme)amounts.))These)likely)experienced)high)rates)of)convection)on)the)upper)surface,)or)possibly)heavy)rain.))The)BcC)boundary)line)is)the)1:1)ratio)line,)and)below)this)the)outcrops)have)more)lower)than)upper)colonnade.))This)could)be)due)to)emplacement)on)a)wet)ground)surface,)enhancing)cooling)via)the)lower)boundary.))Outcrops)that)plot)off)the)0%)entablature)line)have)some)component)of)entablature)in)addition)to)the)colonnades,)regardless)of)whether)the)upper)or)lower)colonnade)is)thicker.))) ) 36) bedrock3 2 1 )Figure)3.11.))Western)face)of)Outcrop)1)of)the)Railroad)Quarry)area.))Line)1)shows)upper)surface)of)flow,)and)line)3)shows)the)lower)surface)of)the)flow.))Below)line)3)is)a)flowcbase)breccia)and)bedrock.))The)column)interface)is)represented)by)line)2,)situated)between)the)upper)and)lower)surfaces.))On)average,)the)upper)and)lower)colonnades)are)nearly)equal)in)thickness,)and)the)arrows)show)three)locations)in)particular)where)the)colonnades)are)equal)in)thickness.))The)noncplanar)upper)and)lower)surfaces)of)the)outcrop)may)contribute)to)the)thicker)than)average)lower)colonnade.) 3.4.2.! Column!Width!Variation!) Looking)at)outcrops)with)both)lower)and)upper)colonnades,)the)most)prominent)difference)is)the)sizes)of)columns;)the)columns)of)the)upper)colonnade)are)usually)noticeably)narrower)than)those)of)the)lower)colonnade.))This)is)due)to)the)difference)in)the)heat)transfer)coefficients)of)the)different)boundaries.))Air)is)a)more)efficient)medium)for)transferring)heat)than)the)ground)material,)partly)because)the)air)can)cool)via)convection,)and)partly)because)the)underlying)rock)is)a)very)poor)heat)conductor)(Touloukian)et)al.,)1989).)) Though)the)size)difference)is)qualitatively)noticeable,)a)quantitative)approach)was)deemed)necessary)to)assess)the)numerical)difference)in)column)widths)between)the)lower)and)upper)colonnades)of)a)typical)lava)flow)in)the)Whistler)field)area.)) Field)photos)were)taken)of)the)eastern)face)of)the)Pinecrest)outcrop,)because)it)has)a)clear)upper)and)lower)colonnade)with)different)widths)of)columns)in)each)colonnade.))The)individual)columns)are)also)readily)visible)to)make)measurements)easy)as)well)as)accurate.))These)were)then)traced)in)Adobe)Illustrator)CS5)(Fig.)3.12),)and)the)outlines)were)imported)into)ImageJ.))A)best)fit)ellipsoid)was)fit)to)the)columns,)and)the)long)and)short)axes)of)the)ellipses)were)computed.))In)order)to)account)for)columns)whose)exposure)was)greater)in)width)than)in)length)(and)thus)ImageJ)computed)the)) ) 37) A B 2 3 1 separate ϐŽ‘™m0 2 )Figure)3.12.))A)section)of)the)eastern)face)of)the)Pinecrest)outcrop.)A)is)the)original,)while)B)shows)the)columns)after)they)have)been)traced)in)Adobe)Illustrator)CS5,)and)these)outlines)were)imported)into)ImageJ)for)analysis.))Line)1)outlines)the)upper)boundary,)while)line)2)traces)the)column)interface,)and)line)3)shows)the)flowcbase)breccia)and)lower)boundary.))A)separate)lava)flow)lies)beneath)line)3.) ) 38) 0 20 40 60 80 100 120 <30 <60 <90 <120 <150 <180 <210 <240 <270 <300 <330 <360 <390 <420 Width (cm) Upper Colonnade Column Widths 0 2 4 6 8 10 12 14 16 18 20 <30 <60 <90 <120 <150 <180 <210 <240 <270 <300 <330 <360 <390 <420 Width (cm) Lower Colonnade Column Widths Numbe r of Col umns Numbe r of Col umns Mean:     223 cmMedian:  213 cm Mean:     143 cmMedian:  135 cm A B )Figure)3.13.))Histograms)of)the)northern)end)of)the)upper)colonnade)(A),)and)the)entire)lower)colonnade)(B),)of)the)eastern)Pinecrest)outcrop.))The)xcaxis)shows)the)range)of)widths)of)each)column,)with)“<30”)representing)the)range)from)0)to)30)cm,)“<60”)representing)the)range)from)30)to)60,)etc.))The)ycaxis)shows)the)number)of)columns)within)each)size)range.))The)histogram)of)the)upper)colonnade)is)more)similar)to)a)normal)distribution)due)to)the)larger)sample)size.))There)is)a)difference)of)approximately)80)cm)in)average)and)median)size)between)the)upper)and)lower)colonnades. ) 39) width)as)the)long)axis)instead)of)the)short)axis),)for)any)ellipse)with)an)angle)of)greater)than)45˚)from)horizontal,)the)long)axis)was)used)for)the)width)instead)of)the)short)axis.)) Histograms)show)the)relative)widths)of)the)columns)in)the)upper)and)lower)colonnades)(Fig.)3.13).))Both)upper)and)lower)colonnades)show)a)somewhat)normal)distribution)of)widths)(the)upper)colonnade)shows)a)more)regular)normal)distribution.))The)columns)in)the)upper)colonnade)range)in)width)from)less)than)30)cm)up)to)approximately)360)cm,)with)an)average)of)143)cm.))Columns)in)the)lower)colonnade)range)from)35)cm)up)to)approximately)420)cm)in)width,)with)an)average)width)of)225)cm.) ) 40) 4. A!Forward!Model! ) Many)workers)have)employed)forward)numerical)modeling)in)their)research)of)cooling)igneous)bodies,)both)extrusive)and)intrusive)(e.g.,)Jaeger,)1961;)Lister,)1974;)Long)and)Wood,)1986;)Grossenbacher)and)McDuffie,)1995).))Because)of)the)nature)of)lava)flows)and)inaccessibility)of)intrusions,)numerical)models)are)an)excellent)proxy)for)direct)measurements.))There)have)been)some)cases)where)measurement)of)large)cooling)extrusive)igneous)bodies)has)been)possible,)such)as)Hawaiian)lava)lakes)(Peck)and)Minakami,)1968),)but)this)is)not)common.)) Past)authors,)such)as)Grossenbacher)and)McDuffie)(1995),)have)used)numerical)models)to)evaluate)temperature)profiles)within)simple)onecdimensional)cooling)bodies.))This)thesis)expands)on)these)past)authors’)work)and)examines)twocdimensional)flows,)which)are)directly)comparable)to)outcrops)found)in)the)field.)) The)question)this)thesis)addresses)focuses)on)the)propagation)of)columnar)joints)within)a)cooling)lava)flow.))The)models)help)constrain)the)rate)at)which)they)propagate,)and)how)the)boundary)conditions)affect)the)direction)of)propagation)at)various)times)and)locations)within)the)flow.))The)models)also)address)the)sizes)of)the)columns,)and)how)the)size)of)the)columns)changes)with)respect)to)the)boundary)conditions.))The)boundary)conditions)change)for)each)model,)but)all)are)within)the)range)of)natural)materials)that)could)exist)on)various)boundaries,)such)as)rock,)ice,)and)water.)) Modeling)the)physics)of)crack)propagation)is)a)difficult)process,)and)beyond)the)scope)of)this)thesis.))However,)joint)formation)is)closely)related)to)heat)flow)and)thus)the)models)use)heat)flow)as)a)proxy)for)modeling)the)propagation)of)columnar)joints.))Multiple)models)with)both)identical)and)edgecdependent)boundary)conditions)are)computed,)and)the)results)are)compared)to)each)other)and)to)results)from)actual)cooling)rock)bodies.)) The)aim)of)the)modeling)is)1))to)show)the)transient)temperature)distribution)and)how)it)changes)with)various)boundary)conditions;)2))to)show)the)magnitude)and)direction)of)the)heat)flow,)and)from)that,)to)infer)the)propagation)direction)and)relative)size)of)columns)within)a)lava)flow;)3))to)show)where)columns)must)change)direction) ) 41) and)interact)with)one)another,)based)on)the)direction)of)heat)flow;)4))to)show)the)temperature)gradients)and)heat)flow)at)a)specified)column)formation)temperature,)which)can)be)directly)related)to)the)high)temperature)experiments)discussed)Chapter)5.) 4.1.! Methodology! 4.1.1.! Finite!Element!Method!) The)Partial)Differential)Equations)Toolbox,)an)addcon)to)Matlab,)is)used)to)model)an)instantaneously)emplaced)cooling)basalt)flow.))This)addcon)allows)the)user)access)to)many)highclevel)Matlab)functions)employing)partial)differential)equations.))These)functions,)and)the)associated)graphical)user)interface)(GUI),)let)the)user)model)elliptic,)parabolic,)and)hyperbolic)equations)for)the)purposes)of)modeling)wave)and)heat)equations.)) The)models)presented)below)use)the)parabolic)equation)to)model)conductive)heat)diffusion)through)a)solid)bounded)by)Neumann)boundary)conditions,)which)give)the)boundary)a)fixed)heat)transfer)coefficient,)rather)than)a)fixed)temperature)or)fixed)amount)of)heat)flow.))This)coefficient)can)be)tweaked)to)accurately)model)each)boundary)between)the)flow)and)the)cooling)environment.))To)accomplish)this,)the)PDE)Toolbox)employs)a)finite)element)method)to)solve)the)equation)numerically.))Depending)on)the)size)of)the)model,)the)spacing)between)each)element)node)along)the)boundaries)ranges)from)0.0125)m)to)0.125)m,)and)the)models)range)in)size)from)1)m2)to)30)m2.) 4.1.2.! Equations!) The)parabolic)partial)differential)equation)is)used)(terms)defined)in)Table)4.1):) € ρ⋅ Cp ⋅ ∂u ∂t = c⋅ ∇ 2u ) or)expanded)and)rearranged)(in)two)dimensions)) € ∂u ∂t = c ρCp ⋅ ∂ 2u ∂x 2 + ∂ 2u ∂y 2 % & ' ( ) * ) For)a)complete)list)of)variables)used)in)these)equations,)see)Table)4.1.) ) 42) ) The)equation)for)the)generalized)Neumann)boundary)condition)is) € n⋅ (c∇u) + qu = g )where)n)is)the)vector)normal)to)the)boundary,)c)is)a)constant)equal)to)the)thermal)conductivity)of)the)material,)grad(u))is)the)temperature)gradient,)q)is)the)heat)source)amount,)and)g)is)the)total)heat)flux)through)the)boundary.))If)q)is)defined)such)that) € q = h )and) € g = hu∞)where)h)is)the)heat)transfer)coefficient)(higher)for)quicker)transfer,)lower)for)slower)transfer))and)u∞"is)the)external)temperature,)then)the)equation)can)be)rearranged)such)that) € n⋅ (c∇u) = h(u − u∞) )This)form)of)the)equation)facilitates)entering)the)h)and)u∞"values)into)Matlab.) 4.1.3.! Constants!Used!Table)4.1.))Physical)parameters)and)variables)used)in)the)numerical)modeling.))Value)ranges)and)units)are)shown.))See)text)for)more)detail)and)conditions)in)which)the)variables)below)are)used.) Physical!Parameter! or!Variable! Symbol! Value! Source!Thermal)conductivity) c" 2)W)mc1)˚Cc1)) Touloukian)et)al.)(1989))Heat)transfer)coefficient) h" 1c6000)W)mc2)˚Cc1) Recktenwald)(2006),)Keszthelyi)and)Denlinger)(1996))Heat)capacity) Cp" 850)J)kgc1)˚Cc1) Bouhifd)et)al.)(2007))Density) ρ" 2900)kg)mc3) wet/dry)measurements)Boundary)temperature) u∞" 1c25)˚C) ))Emplacement)temperature) ui" 1100)˚C) )Boundary)normal)vector) € n ) )) ))Temperature) u" )) ))Temperature)gradient) ∇u" )) ))Volume) V" )) ))Heat) Q" )) ))Length) L" )) ))Height) z" )) ))Time) t" )) )) ) 43) )) The)density)of)field)samples)is)around)2810)kg)mc3,)though)the)value)used)in)the)calculations)is)2900)kg)mc3,)for)the)sake)of)simplicity.))The)variable)u∞)changes)depending)on)the)boundary)considered,)but)ranges)between)1˚C)for)the)iceccontact)edge)and)25˚C)for)the)airccontact)edge.))The)variable)h)also)changes,)and)ranges)from)1)to)6,000)W)mc2)˚Cc1.))Recktenwald)(2006))uses)6,000)W)mc2)˚Cc1)as)the)h)value)for)cooling)of)a)metal)sphere)in)50˚C)water,)and)this)value)was)initially)deemed)appropriate)for)the)most)extreme)examples)of)iceclava)contact.))After)running)several)model)trials)(Appendix)A),)it)was)shown)that)there)is)a)negligible)difference)in)temperature)distribution)or)magnitude)between)h)values)of)6,000)and)100.))Because)of)this,)the)highest)h)value)used)in)the)models)is)100)W)mc2)˚Cc1.))Keszthelyi)and)Denlinger)(1996))use)70)W)mc2)˚Cc1)for)the)h)value)between)a)pahoehoe)flow)and)the)convective)atmosphere)above)it,)based)on)field)experiments.))The)wind)speed)measured)in)their)experiments)ranges)between)3)and)4)m)sc1.))They)find)that)the)hforced)value)(the)h)value)due)to)forced)convection)of)atmospheric)wind))did)not)change)significantly)with)temperature,)but)hypothesized)that)it)would)change)with)wind)speed.))The)atmospheric)conditions)present)during)these)measurements)are)considered)acceptable)for)the)models)in)this)thesis.))An)h)value)of)between)1)and)10)W)mc2)˚Cc1)is)used)for)the)groundclava)interface,)because)the)groundclava)interface)is)not)a)convective)boundary,)but)the)equation)used)models)a)convective)boundary.))Thus)a)very)low)h)value)is)used)to)mitigate)the)effect)of)the)modeled)convective)cooling.))There)are)no)published)experimental)values)on)what)this)h)value)is,)so)these)are)estimated)values.)) The)range)of)h)is)so)large)because)of)the)difference)in)ability)to)transfer)heat)between)the)various)substances)against)which)lava)cools.))While)the)ability)to)transfer)heat)between)lava)and)the)ground)is)very)low,)the)heat)transfer)between)lava)and)air)or)especially)melted)ice)is)much)higher,)and)the)range)in)h)reflects)that.)) According)to)Griffiths)and)Fink)(1992))radiative)cooling)accounts)for)very)little)of)the)heat)lost)from)the)lava,)and)so)it)is)neglected)and)believed)to)have)no)influence)on)the)outcomes)of)this)model,)especially)over)the)long)time)scales)on)which)this)model)runs).) ) 44) 4.1.4.! Double!Checking!Integrity!of!the!Code!) Although)the)Partial)Differential)Equations)Toolbox)for)Matlab)is)a)professionally)constructed)GUI,)it)was)prudent)to)check)that)there)were)no)“holes”)in)the)model;)nowhere)that)heat)was)escaping)or)being)created)that)was)not)accounted)for)by)the)physical)elements)of)the)model.)) To)do)this,)the)total)heat)loss)of)the)lava)flow)was)calculated)in)two)independent)ways.))First,)the)heat)loss)was)calculated)simply)by)the)difference)in)temperature)from)the)beginning)of)the)model)to)the)end.))This)was)done)using)the)following)equation:) € ΔQtotal = Cp ⋅ ρ⋅ V ⋅ Δu)This)simply)gives)the)total)heat)lost)from)the)lava)flow)in)Joules.)) The)second)and)independent)way)to)calculate)the)heat)loss)was)to)measure)the)heat)flow)through)the)boundaries)exclusively,)and)add)the)heat)flow)per)time)for)the)entire)run)time)of)the)model.))To)do)this,)the)temperature)was)first)calculated)at)a)node)point)i,)and)subtracted)from)the)external)temperature)T∞.))This)was)then)multiplied)by)the)heat)transfer)coefficient)h,)the)change)in)time)between)node)points,)the)thickness)of)the)lava)flow,)and)the)length)between)node)points)along)the)boundary.))Qboundary""i"has)units)of)Joules.) € Qboundary i = ΔL⋅ z⋅ Δt⋅ h(ui − u∞) )This)gives)a)matrix)of)heat)flow)through)the)area)between)two)adjacent)node)points)for)each)time)interval.))Summing)the)entire)matrix)gives)the)total)heat)flow)through)the)boundaries)over)the)time)length)of)the)model.) € Qboundary i i=1 n ∑ = Total heat through boundary ) This)is)equivalent)to)the)total)heat)lost)from)the)modeled)lava)flow,)and)provides)a)check)against)the)total)heat)loss)calculated)earlier)from)simple)temperature)change.)) The)code)was)checked)using)both)identical)and)edgecdependent)boundary)conditions,)and)the)results)are)discussed)after)each)section)below.) ) 45) 4.2.! Model!Testing!) The)following)models)are)examples)of)sections)of)lava)flows)that)can)be)found)in)the)field.))Rather)than)trying)to)tackle)the)entire)lava)flow)all)at)once,)sections)of)the)flow)are)analyzed)in)increasing)complexity,)with)various)boundary)conditions.))The)emplacement)temperature)for)all)models)is)1100˚C.))This)temperature)was)chosen)because)it)is)below)the)calculated)liquidus)of)1213˚C)for)the)Cheakamus)Basalts,)based)on)data)from)Green)(1981))and)calculated)using)the)program)rhyolitecMELTS)(Gualda)et)al.,)2012),)and)it)is)likely)that)these)flows)were)erupted)slightly)subcliquidus.)) The)models)are)all)shown)with)symbology)from)Matlab’s)Partial)Differential)Equation)Toolbox.))The)color)maps)range)from)cool)to)warm)colors,)with)warmer)colors)representing)higher)temperatures.))The)thin)dark)lines)within)the)models)represent)isotherms.))Matlab)takes)the)entire)temperature)range)in)the)model)at)any)one)time,)creates)20)equal)bins,)and)draws)the)isotherms)at)those)specified)temperatures.)) The)arrows)in)some)of)the)models)show)the)formation)direction)and)size)of)columns.))The)arrow)vectors)quantitatively)represent)the)heat)flow)direction)and)magnitude)at)specific)points)in)time.))To)construct)these)arrows,)the)temperature)gradients)are)first)calculated)at)every)time)step)throughout)the)model.))The)heat)flow)vector)is)then)calculated)at)specific)points.))While)columnar)joints)form)parallel)to)the)direction)of)heat)flow,)joints)propagate)towards)the)higher)temperatures,)and)so)the)arrows)point)in)the)opposite)direction)of)the)heat)flow.))Column)size)is)also)inversely)proportional)to)the)magnitude)of)heat)flow;)large)columns)are)formed)by)low)heat)flows,)while)small)columns)are)formed)by)high)heat)flows.))Thus)the)direction)and)magnitude)of)the)arrows)is)calculated)quantitatively)from)the)thermal)gradients,)and)they)are)used)in)the)models)to)qualitatively)show)the)direction)of)column)formation,)and)the)relative)sizes)of)the)columns)(large)arrows)indicate)small)columns,)and)vice)versa).)) In)some)of)the)models)isograds)are)used)instead)of)(or)in)conjunction)with))arrows)to)represent)the)thermal)gradient)(Figs.)4.10)&)4.11).))The)gradient)is)calculated)in)the)same)way,)but)the)contours)show)lines)of)equal)heat)flow.))Columnar)joints)form)perpendicular)to)these)isograds,)and)these)isograds)show)the)same)data)in)a)different) ) 46) form.))Closely)spaced)isograds)show)high)thermal)gradients,)while)widely)spaced)isograds)show)low)thermal)gradients.))The)difference)in)spacing)between)the)isograds)is)also)often)easier)to)see)than)the)difference)in)size)between)the)arrows,)and)so)provides)a)better)representation)of)the)magnitude)of)heat)flow)and)thermal)gradients.)) While)the)temperature)profile)shown)in)the)models)is)the)temperature)at)the)time)given)(the)end)of)the)model)run),)the)arrows)represent)column)formation,)and)because)column)formation)is)a)transient)process,)the)arrow)vectors)are)not)all)calculated)at)the)same)time.))A)column)formation)temperature,)close)to)the)glass)transition)temperature)of)the)basalt)(in)this)case)Tcolumn)is)800˚C),)is)used,)and)the)heat)flow)direction)and)magnitude)is)calculated)when)each)modeled)cell)cools)to)that)temperature.))Thus)the)arrows)represent)the)correct)size)and)orientation)of)the)columns)as)they)formed)in)discrete)time)steps.))The)same)is)true)for)the)heat)flow)isograds.))The)gradient)is)calculated)at)Tcolumn,)and)therefore)the)spacing)of)the)contours)represents)the)transient)thermal)gradient)at)the)time)of)column)formation.) 4.3.! Identical!Boundary!Conditions!) These)models)all)have)boundaries)with)equal)boundary)conditions,)with)the)exception)of)boundaries)that)are)treated)as)perfect)insulators)so)as)to)isolate)sections)of)possible)flows)for)simpler)analysis.))These)models)serve)as)an)introduction)to)the)modeling)section,)introducing)several)ideas,)such)as)the)column)interface,)before)adding)additional)variables)to)the)models.))These)models)all)have)h)factor)values)of)100)W)mc2)˚Cc1))on)the)boundaries)that)transmit)heat.) 4.3.1.! Semi]Infinite!Slab!) This)model)has)two)cooling)surfaces,)one)on)the)top)and)bottom)of)the)modeled)lava)flow)(Fig.)4.1).))In)this)way)a)semicinfinite)slab)is)modeled,)so)that)any)side)boundaries)are)arbitrarily)far)away)and)have)no)effect)on)the)cooling)history)of)the)model.))This)is)accomplished)by)making)the)side)boundaries)of)the)model)perfect)insulators.)) Because)the)boundary)conditions)of)the)two)cooling)surfaces)are)equal,)any)joints)that)form)will)nucleate)on)the)boundary)and)propagate)inwards.))In)the)exact) ) 47) middle)of)the)flow,)these)joints)will)meet)at)the)column"interface.))Though)simple)in)these)models,)this)interface)is)rather)complex)in)natural)rocks,)and)has)been)covered)in)Chapter)3.)) The)arrows)indicate)that)the)columns)that)form)on)the)exterior)of)the)flow)will)be)much)narrower)than)those)that)form)on)the)interior)of)the)flow,)since)the)heat)flow)magnitude)is)much)larger)on)the)edge.)) Though)this)is)a)simple)model,)basalt)flows)have)such)low)viscosities)that)outcrops)often)do)have)geometries)such)as)this)in)the)middle,)with)only)the)top)and)bottom)boundaries)influencing)the)cooling)history)of)the)lava.))In)most)cases)the)top)and)bottom)boundaries)are)not)equal,)and)the)outcrop)is)more)like)the)semicinfinite)slab)model)with)edgecdependent)boundary)conditions.) 4.3.2.! Slab!Corner!) This)model)also)has)two)cooling)surfaces,)but)they)are)adjacent)surfaces,)not)opposite)surfaces)as)in)the)previous)model.))In)this)way)the)model)represents)the)corner)of)a)cooling)lava)flow,)where)two)cooling)surfaces)come)into)contact)(Fig.)4.2).)) The)main)difference)between)the)slab"corner)model)and)the)semiAinfinite"slab)model)is)that)there)is)no)column)interface)present.))The)isotherms)do)not)repeat)within)the)model,)but)rather)curve)around)from)one)boundary)to)the)adjacent)one.))Because)the)isotherms)curve,)the)columns)formed)by)columnar)joints)will)curve)as)well,)since)columnar)joints)form)perpendicular)to)isotherms.))Due)to)this)nonlinearity,)the)columnar)joints)will)meet)and)likely)coalesce,)because)as)the)joints)propagate)inward,)there)is)less)space)(and)less)total)thermal)stress))for)the)same)number)of)joints,)and)they)will)decrease)in)number.))There)is)still)melt)for)the)joints)to)propagate)into,)but)the)joints)will)not)meet)straight)on)as)in)the)semiAinfinite"slab)model.)) 4.3.3.! Slab!Side!) This)model)is)the)most)complex)of)the)three)identical)boundary)models)detailed)(Fig.)4.3).))It)contains)both)curving)columns)as)well)as)a)column)interface.))Unlike)the) semiAinfinite"slab)model,)the)column)interface)does)not)extend)across)the)entire)outcrop,)but)rather)stops)as)it)approaches)the)lateral)boundary.))As)seen)in)Fig.)4.3,)columnar) ) 48) joints)propagating)from)the)lateral)boundary)interfere)with)the)column)interface.))Fig.)4.3)also)shows)the)density)distribution)of)columnar)joints)within)an)outcrop)as)it)relates)to)heat)flow.))Heat)flow)arrows)show)large)magnitudes)of)heat)flow)near)the)edge)of)the)flow,)while)the)heat)flow)decreases)rapidly)on)the)interior)of)the)flow.))This)is)represented)in)the)distribution)of)the)joints)–)there)is)a)higher)joint)density)near)the)boundaries,)and)a)lower)density)further)from)the)boundaries.))The)cessation)of)a)columnar)joint)results)in)the)two)adjacent)columns)coalescing.) 4.3.4.! Identical!Boundary!Code!Integrity!) Several)models)were)run)with)the)total)change)in)heat)compared)to)the)heat)lost)through)the)boundaries.))In)these)cases,)all)the)boundaries)for)each)model)had)equal)T∞"values)and)equal)h)factor)values,)though)they)change)in)value)for)different)models.))The)results)are)summarized)in)Table)4.2)and)Fig.)4.4.))The)main)point)is)that)there)is)very)little)difference)between)the)two)heat)measurements,)and)this)difference)is)small)enough)to)be)considered)insignificant.)) ! 49! X (m) Y (m) Ǐ -0.4-0.8-1-0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.6 0-0.2 0.2 10.80.60.4 700 100 200 300 400 500 600 !Figure!4.1.!!Semi.infinite!slab!model!with!identical!boundary!conditions!on!top!and!bottom!surface.!!Sides!are!perfect!insulators.!!Color!represents!temperature,!with!warmer!colors!representing!higher!temperatures.!!Thin!lines!within!the!model!are!isotherms.!!Arrows!represent!column!formation!direction!and!size.!!The!arrows!near!the!center!of!the!flow!are!very!small,!and!may!appear!as!dots,!rather!than!arrows.!!Midpoint!of!flow!and!column!interface!is!shown!by!dashed!line.!!Model!ran!for!72000!s.!!See!text!for!further!explanation.! ! 50! X (m) Y (m) Ǐ -0.8-1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.6 -0.4 0.20-0.2 700 100 200 300 400 500 600 0.5 0.4 -0.5 -0.4 -1 !Figure!4.2.!!Slab!corner!model.!!In!this!model,!there!is!no!column!interface.!!Instead,!the!curving!temperature!isotherms!produce!curving!columns.!!Because!of!the!space!issue!associated!with!all!the!columns!propagating!towards!a!common!point!in!the!upper!right!corner,!!the!propagation!of!some!joints!ceases,!causing!columns!to!coalesce.!!Model!ran!for!180000!s.!!Symbology!same!as!previous!figure. ! 51! Ǐ 700 100 200 300 400 500 600 Ǐ 700 100 200 300 400 500 600 A B X (m) Y (m) -1 -0.5 0 0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.5 0.4 -0.5 -0.4 X (m) Y (m) -1 -0.5 0 0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.5 0.4 -0.5 -0.4 !Figure!4.3.!!Slab!side!model.!!A!shows!the!slab!side!model!with!heat!flow!arrows,!and!the!dashed!line!shows!to!where!the!column!interface!extends.!!It!is!not!continuous!across!the!flow!because!the!lateral!cooling!boundary!creates!coalescing!columns.!!B!shows!hypothetical!joints!drawn!perpendicular!to!the!isotherms,!and!column!diameters!are!relative!to!heat!flow!gradients!at!the!column!formation!temperature.!!Models!ran!for!72000!s.!!Other!symbology!same!as!previous!figure.! ! 52! Table!4.2.!!A!summary!of!numerical!models!1!through!9!with!identical!boundary!conditions,!with!the!various!dimensions!of!the!models!and!h!factor!values!listed.!!The!two!values!compared!for!each!model!are!the!Q1$Qend!value!and!the!Q(through(boundaries!value,!both!of!which!have!units!of!Joules.! Trial& Boundary&1&(Top)& Boundary&2&(Right)& Boundary&3&(Bottom)& Boundary&4&(Left)& & h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& h&factor& T∞&(˚C)&1! 20! 1! 20! 1! 20! 1! 20! 1!2! 20! 1! 20! 1! 20! 1! 20! 1!3! 5! 1! 5! 1! 5! 1! 5! 1!4! 5! 1! 5! 1! 5! 1! 5! 1!5! 5! 1! 5! 1! 5! 1! 5! 1!6! 20! 1! 20! 1! 20! 1! 20! 1!7! 20! 1! 20! 1! 20! 1! 20! 1!8! 20! 1! 20! 1! 20! 1! 20! 1!9! 5! 1! 5! 1! 5! 1! 5! 1! Trial& time& step&(s)& total& time&(s)& x&size&(m)& y&size& (m)& total&area& (m2)& Q1DQend& (J)& Q&through& boundaries&(J)&1! 600! 720000! 4! 4! 16! 2.44E+10! 2.45E+10!2! 2000! 3600000! 8! 8! 64! 1.10E+11! 1.11E+11!3! 600! 1080000! 4! 4! 16! 2.39E+10! 2.41E+10!4! 2000! 3600000! 8! 8! 64! 9.89E+10! 1.00E+11!5! 1000! 1800000! 16! 4! 64! 9.10E+10! 9.10E+10!6! 1000! 1440000! 16! 4! 64! 9.79E+10! 9.76E+10!7! 1000! 3600000! 16! 4! 64! 1.38E+11! 1.37E+11!8! 500! 1800000! 6! 6! 36! 5.84E+10! 5.90E+10!9! 600! 2160000! 6! 6! 36! 5.47E+10! 5.54E+10!!! ! 53! 1010 1011 1012 1010 1011 1012 Identical Boundary Condition Heat Change ‘–ƒŽ‡ƒ–Šƒ‰‡ȏɏ’ȋ—i Ǧ—ȌȐȋ
Ȍ ‘ –ƒ Ž ‡ƒ – Š” ‘— ‰Š  ‘— † ƒ” ‹‡ •ȋ 
 Ȍ !Figure!4.4.!!Comparison!of!the!total!heat!through!boundaries!vs.!the!total!heat!change!of!the!system!between!the!beginning!and!end!of!the!model.!!The!dashed!line!shows!parity!between!the!two!independent!measurements!of!total!heat!change!within!the!system,!and!all!the!models!tested!fall!almost!exactly!on!the!dashed!line.! 4.4.& EdgeDDependent&Boundary&Conditions&! Identical!boundary!conditions!are!the!simplest!to!model,!but!very!rarely!in!nature!are!boundary!conditions!identical!on!all!sides!of!a!cooling!lava!flow.!!EdgeQdependent!boundary!conditions!(models!with!different!boundary!conditions!on!each!side!of!the!modeled!flow)!are!a!more!accurate!depiction!of!the!processes!occurring!in!the!natural!world.!!This!also!enables!a!more!direct!comparison!of!models!and!field!outcrops,!which!makes!understanding!the!thermal!history!of!these!outcrops!easier!and!increases!the!accuracy!of!the!comparisons!as!well.! 4.4.1.& SemiDInfinite&Slab&! In!this!model!(Fig.!4.5)!the!upper!boundary!has!been!given!an!h!factor!value!of!70!W!mQ2!˚CQ1,!while!the!lower!boundary!h!value!is!10!W!mQ2!˚CQ1.!!Convecting!air!is!more!efficient!at!heat!dissipation!than!the!soil!or!rock!that!typically!underlies!most!lava!flows.!! ! 54! The!column!interface!is!not!in!the!middle!of!the!flow,!but!shifted!downwards,!closer!to!the!lower!boundary.!!This!is!due!to!higher!heat!flow!through!the!upper!boundary,!causing!quicker!propagation!of!joints.!!This!shift!in!the!position!of!the!column!interface!is!observed!often!in!the!field!area!of!this!study!as!well.! 4.4.2.& Slab&Corner&! This!model!(Fig.!4.6)!shows!similar!temperature!distributions!as!the!slab!corner!with!identical!boundary!conditions,!but!both!boundaries!do!not!cool!to!the!same!temperature.!!This!changes!the!geometry!of!the!isotherms!within!the!model!from!the!identical!boundary!model,!but!not!drastically.!!The!left!boundary!has!an!h!factor!value!of!70,!while!the!bottom!has!a!value!of!10.! 4.4.3.& Slab&Side&! Fig.!4.7!shows!both!the!first!two!models!combined,!and!all!three!nonQinsulating!boundaries!have!different!heat!transfer!coefficients.!!This!changes!both!the!location!of!the!column!interface!and!the!isotherms!near!the!sides!of!the!flow,!as!described!below.!!The!upper!and!lower!boundaries!have!h!factor!values!of!70!and!10!respectively,!while!the!left!boundary!has!a!value!of!100.!! Fig.!4.7!also!shows!representative!columnar!joints!drawn!in,!similar!to!those!in!Fig.!4.3.!!In!Fig.!4.7!the!distribution!of!the!joints!is!more!complex,!due!to!the!edgeQdependent!boundary!conditions.!!With!higher!heat!flow!magnitudes!on!the!upper!boundary!than!on!the!lower!boundary,!the!joints!are!more!closely!spaced!on!the!upper!boundary.! 4.4.4.& Finite&Slab&! This!last!model!(Fig.!4.8)!represents!an!actual,!finite!lava!flow!with!different!boundary!conditions!on!the!top,!bottom,!and!sides.!!The!sides!have!identical!boundary!conditions!of!100!W!mQ2!˚CQ1,!because!it!is!likely!that!most!actual!lava!flows!were!bounded!on!both!sides!by!similar!mediums,!whether!they!were!confined!by!ice!or!a!valley.!!If!they!were!confined!only!by!air,!the!aspect!ratio!of!the!flow!would!be!much!lower,!but!the!boundaries!would!be!very!similar,!and!the!inferences!made!the!same.!! ! 55! ! The!top!has!an!h(factor!of!70,!and!thus!can!transfer!heat!away!from!the!boundary!at!a!higher!rate.!!This,!along!with!the!smaller!h!factor!value!of!10!on!the!bottom!boundary,!causes!the!column!interface!to!be!located!below!the!midpoint!of!the!flow,!similar!to!many!outcrops!seen!in!the!Whistler!field!area.!!The!higher!h!factor!value!of!100!on!the!side!boundaries!creates!more!crossQsectional!area!in!which!the!isotherms!curve!between!the!top!and!bottom!boundaries!and!the!side!boundaries,!which!affects!the!direction!of!propagation!of!the!columnar!joints.! 4.4.5.& EdgeDDependent&Boundary&Conditions&Integrity&! Several!models!were!run!with!the!total!change!in!heat!compared!to!the!heat!lost!through!the!boundaries.!!In!these!cases,!the!boundaries!had!unequal!T∞(values!and!in!some!cases!unequal!h!factor!values.!!The!results!are!summarized!in!Table!4.3!and!Fig.!4.9!below.!!The!two!models!with!the!highest!heat!output!(Trials!16!and!17)!had!the!most!difference!between!the!two!heat!change!measurements,!but!this!difference!is!not!large.!!Again,!the!main!point!is!that!there!is!very!little!difference!between!the!two!heat!measurements,!and!this!difference!is!small!enough!to!be!considered!insignificant.!! ! 56! X (m) Y (m) Ǐ -0.4-0.8-1-0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.6 0-0.2 0.2 10.80.60.4 700 200 300 400 500 600 !Figure!4.5.!!Semi.infinite!slab!model!with!edge.dependent!boundary!conditions!on!top!and!bottom!surface.!!Sides!are!perfect!insulators.!!Color!represents!temperature,!with!warmer!colors!representing!higher!temperatures.!!Thin!lines!within!the!model!are!isotherms.!!Arrows!represent!column!formation!direction!and!magnitude!of!heat!flow!at!the!time!of!column!formation.!!Column!interface!is!shown!by!dashed!line,!and!is!below!the!midpoint!of!the!flow.!!Model!ran!for!90000!s.!!See!text!for!further!explanation.! ! 57! X (m) Y (m) Ǐ -0.8-1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.6 -0.4 0.20-0.2 700 100 200 300 400 500 600 0.5 0.4 -0.5 -0.4 -1 !Figure!4.6.!!Slab!corner!model.!!In!this!model,!similar!to!Fig.!4.2,!there!is!no!column!interface.!!The!unequal!boundary!conditions!produce!curving!temperature!isotherms.!!These!in!turn!produce!curving!columns!of!varying!diameters!propagating!from!the!lower!and!left!lateral!boundaries.!!Because!of!the!space!issue!associated!with!all!the!columns!propagating!towards!a!common!point!in!the!upper!right!corner,!!the!propagation!of!some!joints!ceases,!causing!columns!to!coalesce.!!Model!ran!for!216000!s.!!Symbology!same!as!previous!figures.! ! 58! A B X (m) Y (m) -1 -0.5 0 0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.5 0.4 -0.5 -0.4 X (m) Y (m) -1 -0.5 0 0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.5 0.4 -0.5 -0.4 Ǐ 700 100 200 300 400 500 600 Ǐ 700 100 200 300 400 500 600 !Figure!4.7.!!Slab!side!model.!!A!shows!the!slab!side!model!with!heat!flow!arrows,!and!the!dashed!line!shows!where!the!column!interface!extends!to.!!It!is!not!continuous!across!the!flow!because!the!lateral!cooling!boundary!creates!coalescing!columns.!!B!shows!hypothetical!joints!drawn!perpendicular!to!the!isotherms,!and!column!diameters!are!relative!to!heat!flow!gradients!at!the!column!formation!temperature.!!Joint!density!is!less!on!the!bottom!because!of!the!lower!relative!heat!flow!through!the!lower!boundary.!!Models!ran!for!90000!s.!!Other!symbology!same!as!previous!figures.! !! 59! X (m) Y (m) Ǐ -1-1.5 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.5 0 1.510.5 700 100 200 300 400 500 600 1 0.8 -1 -0.8 !Figure!4.8.!!Finite!slab!model.!!Column!interface!occurs!below!middle!of!flow!due!to!unequal!boundary!conditions.!!As!in!Fig.!4.7,!the!column!interface!does!not!extend!to!the!lateral!boundaries,!but!rather!is!confined!within!the!center!of!the!flow.!!Model!ran!for!108000!s.!!Symbology!same!as!previous!figures. !! 60! Table!4.3.!!A!summary!of!numerical!models!10!through!19!with!edge>dependent!boundary!conditions,!with!the!various!dimensions!of!the!models!and!h!factor!values!listed.!!The!two!values!compared!for!each!model!are!the!Q1$Qend!value!and!the!Q(through(boundaries!value,!both!of!which!have!units!of!Joules.! Trial& Boundary&1&(Top)& Boundary&2&(Right)& Boundary&3&(Bottom)& Boundary&4&(Left)& & h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& h&factor& T@∞&(˚C)&10! 70! 1! 500! 1! 3! 1! 500! 1!11! 70! 1! 500! 1! 3! 1! 500! 1!12! 70! 1! 500! 1! 3! 1! 500! 1!13! 70! 25! 500! 1! 3! 25! 500! 1!14! 7! 25! 40! 1! 1! 25! 7! 1!15! 7! 25! 40! 1! 1! 25! 7! 1!16! 7! 25! 40! 1! 1! 25! 7! 1!17! 70! 25! 500! 1! 3! 25! 500! 1!18! 70! 25! 500! 1! 3! 25! 500! 1!19! 7! 25! 40! 1! 1! 25! 7! 1! Trial& time& step&(s)& total& time&(s)& x&size&(m)& y&size&(m)& total&area& (m2)& Q1@Qend&(J)& Q&through& boundaries&(J)&10! 600! 1800000! 6! 6! 36! 5.75E+10! 5.76E+10!11! 600! 1800000! 16! 4! 64! 9.88E+10! 9.81E+10!12! 600! 900000! 4! 4! 16! 2.62E+10! 2.62E+10!13! 600! 900000! 4! 4! 16! 2.60E+10! 2.59E+10!14! 1000! 1080000! 4! 4! 16! 2.51E+10! 2.52E+10!15! 600! 720000! 10! 2! 20! 2.60E+10! 2.54E+10!16! 2000! 7920000! 40! 10! 400! 5.01E+11! 4.83E+11!17! 2000! 7200000! 40! 10! 400! 5.53E+11! 5.33E+11!18! 1000! 3600000! 8! 8! 64! 1.07E+11! 1.08E+11!19! 1000! 3600000! 8! 8! 64! 9.89E+10! 9.99E+10!! !! 61! 1012 1010 1011 1010 1011 1012 Edge-Dependent Boundary Condition Heat Change ‘–ƒŽ‡ƒ–Šƒ‰‡ȏɏ’ȋ—i Ǧ—ȌȐȋ
Ȍ ‘ –ƒ Ž ‡ƒ – Š” ‘— ‰Š  ‘— † ƒ” ‹‡ •ȋ 
 Ȍ !Figure!4.9.!!Comparison!of!the!total!heat!through!boundaries!vs.!the!total!heat!change!of!the!system!between!the!beginning!and!end!of!the!model.!!The!dashed!line!shows!parity!between!the!two!independent!measurements!of!total!heat!change!within!the!system,!and!all!the!models!tested!fall!almost!exactly!on!the!dashed!line.!!The!two!models!with!the!most!heat!loss!are!very!slightly!off!the!dashed!line,!but!the!difference!is!insignificant.! 4.5.& Modeling&Results& 4.5.1.& Temperature&Profiles&! All!of!the!above!models!assume!instantaneous!emplacement!of!the!flow!into!the!cooling!environment.!!As!the!model!starts!its!first!time!step,!the!difference!in!temperatures!between!the!environment!and!the!lava!flow,!as!well!as!the!high!h!factor!values!used!for!some!of!the!boundaries,!creates!a!very!large!heat!flow!and!very!high!thermal!gradient!at!the!edge!of!the!flow.!!Because!both!lava!and!solid!basalt!have!such!high!heat!capacities!and!low!thermal!diffusivities,!a!large!temperature!difference!between!the!interior!and!exterior!of!the!flow!is!maintained!for!the!majority!of!the!cooling!history.! !! 62! ! As!the!model!progresses,!the!temperature!differences!between!the!boundaries!and!interior!of!the!flow!decrease.!!However,!while!parts!of!the!flow!are!above!Tcolumn,!there!is!always!a!large!temperature!difference!present.!!The!greatest!difference!occurs!immediately!after!emplacement!when!the!edges!of!the!flow!have!cooled!to!near!T∞,!and!when!the!center!of!the!flow!has!not!yet!lost!any!heat.!!The!exact!amount!of!time!the!center!stays!above!Tcolumn!depends!completely!on!the!size!of!the!flow,!but!in!the!two>dimensional!models!that!measure!1!m!by!3!m,!the!interior!can!stay!above!Tcolumn!for!over!24!hours.!! The!finite(slab!model!shown!has!edge>dependent!boundary!conditions!on!all!four!sides!of!the!model,!and!most!accurately!depicts!the!temperature!profile!present!within!an!actual!lava!flow.!!The!unequal!boundaries!have!two!distinct!effects!on!the!temperature!profile!of!the!model.!!First,!they!cause!the!column!interface!between!the!upper!and!lower!colonnade!to!be!located!below!the!midpoint!of!the!flow!cross!section.!!Second,!they!cause!much!higher!heat!flows!near!the!sides!of!the!model!where!the!h(factor!is!highest,!with!a!value!of!100.!!Not!only!is!this!visible!in!the!heat!flow!arrow!magnitudes,!but!also!in!the!temperature!profile!contours.!!The!temperature!n!meters!in!from!the!edge!of!the!side!of!the!flow!is!significantly!less!than!the!temperature!n!meters!in!from!the!top!or!bottom!of!the!flow.! 4.5.2.& Heat&Flow&Gradients&at&Tcolumn&! As!mentioned!above,!the!large!heat!capacity!of!both!molten!lava!and!solid!basalt,!along!with!the!small!thermal!diffusivity!values!allow!large!temperature!differences!between!the!interior!and!exterior!of!a!cooling!lava!flow.!!The!modeled!lava!flows!are!also!instantaneously!emplaced,!placing!1100˚C!lava!against!material!that!ranges!from!1>25˚C.!!This!large!temperature!difference!creates!very!large!thermal!gradients!on!the!edge!of!the!modeled!flows,!with!the!gradients!decreasing!as!the!critical!column!formation!temperature!propagates!inward.!!Fig.!4.10!shows!thermal!gradients!for!one!of!the!models!with!identical!boundary!conditions.!! The!spacing!of!the!heat!flow!isograds!represents!the!gradient!when!the!model!is!at!a!specific!temperature:!the!column!formation!temperature!(Tcolumn).!!The! !! 63! resulting!gradient!is!transient!from!emplacement!until!the!entire!flow!is!below! Tcolumn.!!The!closer!the!contours!are!together,!the!greater!the!heat!flow!at!Tcolumn.!! The!range!of!boundary!conditions!used!in!the!forward!models!creates!a!large!range!of!cooling!rates!and!thermal!gradients!at!the!column!formation!temperature.!!Where!two!boundaries!interact,!the!heat!flow!isograds!curve!in!response.!!Based!on!previous!assumptions!that!columns!follow!the!direction!of!heat!flow,!the!columns!will!curve!within!the!flow.!!The!magnitude!of!heat!flow!changes!dramatically!from!the!outside!of!the!flow!to!the!inside!as!well,!and!again!based!on!previous!assumptions,!the!size!of!the!columns!produced!will!vary.!!As!the!section!of!the!flow!in!question!is!at!the!column!formation!temperature,!smaller!columns!form!where!the!heat!flow!is!greatest,!and!larger!columns!where!the!heat!flow!is!least.!!Because!the!magnitude!of!heat!flow!is!directly!proportional!to!the!h!factor!value!at!a!particular!boundary,!boundaries!with!large!h!factor!values!will!have!columns!with!smaller!diameters!propagating!away!from!them,!while!boundaries!with!small!h!factor!values!will!create!large!diameter!columns.!! The!models!show!that!the!geometry!of!the!columns,!including!the!size!and!distribution,!is!dependent!upon!the!boundary!conditions.!!Because!the!diameter!of!the!columns!is!inversely!proportional!to!the!cooling!rate,!the!more!effective!at!cooling!a!boundary!is,!the!smaller!the!diameter!of!the!columns!that!will!be!formed.!! The!models!predict!that!high!heat!flow!and!cooling!rates!are!present!at!boundaries!with!high!h!factors,!while!lower!heat!flow!and!smaller!thermal!gradients!are!present!at!boundaries!with!low!h!factors.!!Any!boundary!with!a!low!h!factor!will!necessarily!have!larger!diameter!columns!propagating!away!from!it!than!will!a!boundary!with!a!high!h!factor.!!The!models!also!dictate!that!as!the!columnar!joints!propagate!inwards,!the!cooling!rate!and!thermal!gradient!will!decrease!as!well.!!This!leads!to!a!decrease!in!the!formation!of!tensile!stresses,!and!thus!a!decrease!in!the!number!of!columnar!joints!per!square!meter.!!Reduction!in!the!number!of!joints!per!square!meter!is!accomplished!by!the!termination!of!some!columnar!joints,!and!thus!an!increase!in!average!column!diameter,!in!addition!to!the!differences!in!column!diameter!already!present!from!the!various!boundary!conditions.! !! 64! ! Near!the!corners!of!a!lava!flow,!there!will!necessarily!be!curving!columnar!joints.!!Joints!propagate!parallel!to!heat!flow,!which!is!perpendicular!to!the!thermal!gradient!isograds!in!Fig.!4.10.!!If!one!were!to!trace!a!line!perpendicular!to!the!isograds!that!originates!from!somewhere!near!one!of!the!corners!of!the!lava!flow!(as!shown!in!Fig.!4.12),!that!line!(joint)!will!necessarily!have!to!curve!to!maintain!orthogonality!to!the!isograds.!!This!is!assuming!that!the!lava!flow!in!question!has!a!high!enough!aspect!ratio!at!the!lateral!boundaries!of!the!flow,!and!that!these!are!affected!by!the!side!boundaries.!!Curving!columns!are!visible!in!outcrop!setting!in!Figs.!3.5!and!6.3.&! The!location!of!the!column!interface!is!also!dependent!on!the!boundary!conditions.!!The!more!effective!at!cooling!a!boundary!is,!the!further!from!it!the!colonnade!interface!will!be.!!This!is!because!the!cooling!rate!is!higher!at!that!boundary,!and!the!columnar!joints!propagate!further!in!the!same!amount!of!time.!!This!is!visible!in!Figs.!4.8!and!4.11.!! The!models!accurately!predict!the!amount!of!relative!heat!flow!and!relative!sizes!of!cooling!gradients!within!cooling!lava!masses,!as!well!as!accurately!predict!the!direction!and!relative!sizes!of!columns!within!the!outcrop.!!With!this!determined,!the!models!can!be!used!in!conjunction!with!the!high!temperature!experiments!outlined!in!Chapter!5!to!later!reconstruct!the!cooling!history!of!lava!flows!in!the!field!based!on!the!geometry!of!the!columns!in!outcrop.! 4.5.3.& Predictions&! Larger!diameter!columns!are!observed!in!the!field!most!often!in!lower!colonnades!and!especially!near!the!center!of!flows!(Grossenbacher!and!McDuffie,!1995),!where!the!models!show!the!cooling!rates!are!the!lowest.!!For!the!experiments!in!Chapter!5,!we!know!that!lower!cooling!rates!produce!larger!diameter!columns,!and!higher!cooling!rates!produce!smaller!diameter!columns.!!From!this,!we!can!predict!that!there!will!be!a!certain!cooling!rate,!at!the!column!formation!temperature,!that!produces!columnar!joints.!!We!can!also!predict!that!if!the!cooling!rate!is!too!low!for!the!physical!dimensions!of!the!experimental!sample,!(i.e.!if!the!cooling!rate!is!lower!and!the!sample!is!small)!columns!will!not!form.!!It!is! !! 65! also!important!that!this!cooling!rate!is!present!at!the!column!formation!temperature!(Tcolumn).!!If!it!is!present!at!some!other!temperature,!columnar!joints!may!not!form. !! 66! -5 -4 -3 -2 -1 0 1 2 3 4 5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5   1000 2000 3000 4000 5000 6000 7000 8000 9000 X (m) Y (m) ǏȀο !Figure!4.10.!!Heat!flow!contour!map.!!All!edges!have!h!factor!values!of!60.!!The!heat!flow!isograds!are!symmetric!about!all!the!boundary!surfaces.!!The!isograds!show!lines!of!equal!magnitude!of!heat!flow!at!Tcolumn.!!The!spacing!of!the!isograds!is!proportional!to!the!thermal!gradient.!!The!isograds!are!close!together!near!the!edge!of!the!flow,!and!show!high!gradients!at!Tcolumn,!while!the!isograds!become!more!spaced!out!in!the!interior,!showing!lower!gradients!at!Tcolumn.!!Midpoint!of!flow!is!shown!by!dashed!line.!!Gradient!units!are!in!˚C!/!∆L,!where!∆L!is!the!node!spacing.!!These!units!are!directly!proportional!to!heat!flow.!!Arrows!show!heat!flow!as!well,!and!arrows!in!the!center!of!the!model!may!appear!as!dots!due!to!small!size.!!Model!was!run!until!below!Tcolumn,!approximately!800000!s.! -5 -4 -3 -2 -1 0 1 2 3 4 5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5   2000 4000 6000 8000 10000 12000 X (m) Y (m) ǏȀο !Figure!4.11.!!Heat!flow!contour!map.!!This!model!has!edge>dependent!boundary!conditions.!!The!bottom!boundary!has!the!lowest!h!factor,!with!a!value!of!8,!while!the!side!boundaries!have!high!h!factors,!with!values!of!100,!and!the!top!boundary!has!an!h!factor!value!of!60.!!Column!interface!location!is!shown!by!the!dashed!line.!!Note!that!it!is!below!the!midpoint!of!the!flow.!Model!was!run!until!below!Tcolumn,!approximately!800000!s.!!Other!symbology!same!as!Fig.!4.10.! !! 67! -5 -4 -3 -2-2 -1 0 1 2 X (m) Y (m) 2000 4000 6000 8000 10000 12000 !Figure!4.12.!!Line!drawing!of!hypothetical!columnar!joints!superimposed!upon!model!with!heat!flow!isograds.!!Joints!propagate!normal!to!isograds,!and!column!diameter!is!inversely!proportional!to!cooling!rate.!!Both!curving!and!coalescing!columns!are!shown,!as!is!the!column!interface.!!Other!symbology!same!as!previous!figures.!! !! 68! 5. High&Temperature&Experiments& ! High!temperature!experiments!are!used!extensively!in!petrological!studies.!!However,!they!are!not!commonly!used!for!heat!flow,!melt,!and!brittle!deformation!studies!and!have!not!been!used!to!study!column!formation.!!Only!analog!experiments,!as!well!as!some!field!experiments,!have!been!conducted!with!the!aim!of!increasing!understanding!of!the!mechanisms!of!formation!and!the!geometrical!expression!of!columnar!joints.!! Ryan!and!Sammis!(1981)!infer!the!glass!transition!temperature!of!basalt!to!be!725˚C,!based!on!dilatometry,!stress!relaxation,!and!acoustic!spectroscopy!measurements!of!basalts!at!various!temperatures.!!Taking!this!as!the!approximate!“columnar!formation!temperature,”!the!rate!of!cooling!through!this!temperature!is!what!determines!the!spacing!of!the!joints,!and!thus!the!diameter!of!the!columns!formed.!! Peck!and!Minakami!(1968)!observed!the!cooling!of!Kilauean!lava!lakes!and!the!formation!of!jointing!in!those!lavas.!!They!recorded!jointing!starting!at!temperatures!as!high!at!900˚C,!and!propagating!down!to!temperatures!up!to!1000˚C.!!Based!on!the!work!of!both!Ryan!and!Sammis!(1981)!and!Peck!and!Minakami!(1968),!the!“column!formation!temperature”!ranges!from!725>900˚C.!! The!experiments!outlined!below!were!carried!out!using!powdered!basalt,!a!high!temperature!furnace,!and!various!cooling!mediums.!!The!purpose!is!to!1)!see!if!columnar!joints!can!be!synthesized!in!a!laboratory!setting!to!document!joint!morphology!and!texture;!2)!to!determine!the!thermal!gradients!and!cooling!rates!that!are!required!to!form!columnar!joints!in!these!samples.!! The!powdered!basalt!used!in!these!experiments!is!from!the!Cheakamus!Valley!basalts,!which!are!fairly!typical!olivine!basalts.!!The!chemistry!and!petrology!of!the!basalts!is!described!briefly!in!Section!3.1,!and!for!an!in>depth!chemical!and!mineralogical!analysis,!see!Green!(1981).!!!! !! 69! 5.1.& Methodology& 5.1.1.& Designing&the&Experiments&! Lithium!metaborate!flux!was!added!to!the!powdered!basalt!prior!to!melting,!in!order!to!lower!both!the!liquidus!and!the!viscosity!of!the!melt.!!For!these!experiments,!a!lower!liquidus!is!desired!to!prevent!undue!wear!and!tear!on!the!Nabertherm!high!temperature!furnace.!!Lithium!metaborate!fluxes!are!typically!used!in!the!fusion!of!samples!for!x>ray!fluorescence,!often!with!flux!to!sample!ratios!of!5:1!or!higher.!!The!flux!is!only!needed!to!ensure!glass!formation,!and!there!are!no!good!data!describing!the!effects!of!much!smaller!flux!to!sample!ratios,!such!as!those!used!in!this!study,!which!are!near!1:5,!rather!than!5:1.!!Mastin!et!al.!(2009)!mention!that!the!5!wt.!%!dilithium!tetraborate!flux!they!used!in!their!experiments!decreased!the!viscosity!by!several!times,!and!also!decreased!the!liquidus!to!below!their!experimental!temperature!of!1200˚C.!!However,!they!performed!no!quantitative!measurements!on!the!viscosity!and!liquidus!of!the!fluxed!melt.!! The!way!in!which!the!flux!would!alter!the!ideal!starting!temperature!for!the!experiments!was!another!unknown.!!The!exact!mineralogy!of!the!crystals!present!in!the!experiments!was!not!a!concern,!but!the!amount!of!crystals!present!in!the!melt!was,!since!this!will!affect!the!tensile!strength!and!the!heterogeneity!of!the!samples,!as!well!as!the!volume!change!available!due!to!the!phase!changes!in!the!crystallizing!samples.!! Initially,!1000˚C!was!picked!as!the!starting!temperature!for!the!experiments.!!However,!upon!removing!the!samples!from!the!furnace!and!cooling!either!by!partial!or!complete!submersion!in!water,!or!even!simply!by!free!air!convection,!!the!cooling!material!would!simply!become!glass.!!An!additional!observation!was!that!the!material!would!accommodate!any!volume!loss!due!to!a!decrease!in!temperature!via!viscous!flow,!but!only!in!the!center!of!the!sample.!!Where!the!sample!met!the!crucible!on!the!perimeter,!the!material!would!solidify!extremely!quickly!and!be!unable!to!flow.!!Thus,!with!all!the!viscous!deformation!occurring!in!the!center!of!the!samples,!a!“cone!of!depression”!was!formed!(Fig.!6.9).!!If!thermocouples!were!to!be!used!in!these!experiments,!this!“cone!of!depression”!may!expose!the!thermocouples! !! 70! to!the!atmosphere!and!interfere!with!the!readings.!!Between!the!viscous!flow!and!complete!glassification!of!the!samples,!it!was!obvious!that!a!lower!starting!temperature!was!needed,!so!the!cooling!material!would!have!a!higher!viscosity,!and!be!less!able!to!accommodate!volume!loss!through!viscous!flow.!! To!decide!a!starting!temperature!for!the!main!experiments,!a!set!of!preliminary!experiments!was!carried!out.!!Two!crucibles!were!filled!with!a!basalt>flux!mixture,!one!with!10!wt.!%!flux,!and!the!other!with!15!wt.!%!flux.!!It!was!necessary!to!lower!the!liquidus!below!the!1000˚C!starting!temperature!to!ensure!a!homogenous!starting!melt,!but!it!was!also!undesirable!for!the!flux!to!influence!the!experiments!to!a!large!degree.!!Unsure!of!what!exact!weight!percentage!of!flux!to!use,!the!preliminary!experiments!were!carried!out!with!two!different!percentages!of!flux.!!The!thermocouples!were!inserted!into!the!middle!of!each!crucible,!and!were!attached!to!a!computer!program!that!recorded!the!temperature!once!every!second.!! For!these!and!subsequent!experiments,!a!Nabertherm!high>temperature!chamber!furnace!with!SiC!rod!heating!was!used,!model!HTC!08/15.!!The!Nabertherm!furnace!was!set!at!1000˚C,!and!when!the!thermocouples!reported!that!the!center!of!the!samples!was!at!equilibrium!with!the!furnace,!a!small!aliquot!of!melt!was!sampled!with!a!glass!rod!and!immediately!quenched.!!The!furnace!was!then!set!to!900˚C,!and!when!the!sample!was!at!equilibrium,!another!aliquot!of!melt!was!taken!and!quenched.!!Below!900˚C,!the!10!weight!percent!flux!melt!became!too!viscous!to!sample!without!disturbing!the!crucible.!!The!15!wt.!%!flux!melt!was!also!sampled!at!800˚C!and!750˚C.!!The!aliquots!of!melt!were!then!analyzed!and!the!crystal!fraction!of!the!various!samples!was!determined!(Fig.!5.1).!! The!purpose!of!these!preliminary!experiments!was!two>fold.!!First,!by!measuring!the!time!it!takes!the!samples!to!reach!equilibrium!temperature!with!the!furnace,!the!dwell!time!was!determined!to!ensure!homogeneous!temperature!distribution!within!the!samples.!!Second,!taking!aliquots!of!the!melt!at!various!temperatures!enabled!plotting!of!the!change!in!crystal!fraction!against!the!change!in!temperature!and!finding!an!ideal!starting!temperature!for!the!main!experiments!(Fig.!5.1).!!The!purpose!of!two!different!flux!concentrations!was!to!ascertain!that!at!1000˚C,!the!quenched!aliquot!is!entirely!glass.!!A!homogenous!starting!material!is! !! 71! required!before!cooling!the!samples!down!to!the!starting!temperature,!to!ensure!that!they!are!in!equilibrium.!!It!was!not!clear!if!10!or!15!wt.!%!flux!was!needed!to!reach!liquidus!at!1000˚C,!so!both!were!used!in!the!preliminary!experiments.!! Starting!temperatures!ranging!from!800>700˚C!were!chosen!because!the!large!percentage!of!crystals!within!the!samples!ensures!little!viscous!flow!will!accommodate!volume!change!during!cooling,!but!the!samples!are!not!yet!entirely!solid,!and!there!is!still!a!difference!in!crystal!fraction!between!experiments.!!! As!shown!in!Fig.!5.2,!the!experimental!setup!for!the!forced!air!convection!experiments!consisted!of!a!cut!rock!slab!cooling!surface!and!a!household!fan.!!The!samples!were!placed!on!the!rock!slab,!and!the!fan!was!turned!on!to!the!highest!setting.!!The!air!temperature!was!approximately!20!˚C!for!all!experiments.!!For!the!water!cooled!experiments,!convecting!water!was!necessary!to!prevent!the!samples!from!heating!the!nearby!water,!and!possibly!reducing!heat!transfer!to!the!cooling!material.!!This!was!accomplished!by!placing!a!large!beaker!filled!with!1!L!of!water!at!approximately!3!˚C!on!a!magnetic!stirrer.!!The!stirrer!was!adjusted!so!that!the!water!was!circulating!quite!quickly,!but!was!slow!enough!that!the!insertion!of!the!sample!into!the!water!did!not!cause!undue!disturbance!of!the!circulation.!!The!samples!were!placed!midway!between!the!center!and!edge!of!the!beaker,!since!the!circulation!of!the!water!would!be!minimal!in!the!center!of!the!beaker.! !! 72! 100 60 20 80 40 0 1000 900 800 7501100 700 Crystal  Percen tage ‡’‡”ƒ–—”‡ȋǏȌ !Figure!5.1.!!Four!aliquots!of!sample!were!taken!from!a!single!experiment!of!15!wt.!%!flux,!one!each!at!1000,!900,!800,!and!750˚C,!as!represented!by!the!stars.!!These!samples!were!smear!mounted!and!crystal!percentages!were!estimated!visually!using!a!percent!abundance!estimation!chart,!in!conjunction!with!analysis!from!X>ray!diffraction!and!subsequent!Rietveld!refinement,!to!determine!percent!crystallinity.!!The!dashed!line!shows!the!inferred!crystal!percentage!between!samples.!!The!box!on!the!right!side!of!the!chart!outlines!the!temperature!range!chosen!as!starting!temperatures!for!the!experiments.!!These!temperatures!were!chosen!because!the!large!proportion!of!crystals!ensures!little!viscous!flow!during!cooling,!but!differences!in!crystal!percentages!still!remain!between!experiments.! !! 73! 5.1.2.& Textural&Experimental&Grid&! All!of!the!experiments,!both!textural!and!gradient!focused,!are!performed!using!cylindrical!alumina!crucibles,!with!a!radius!and!height!of!25!mm,!and!an!approximate!volume!of!10!mL.!! Starting!at!three!initial!temperatures!(700˚C,!750˚C,!and!800˚C),!an!experimental!grid!was!created!(Table!5.1),!using!different!cooling!mechanisms,!producing!a!variety!of!thermal!gradients.!!While!liquid!nitrogen!was!originally!thought!to!produce!the!highest!gradient,!it!in!fact!does!not,!most!likely!due!to!the!Leidenfrost!effect.!!The!Leidenfrost!effect!occurs!when!a!liquid!and!a!much!hotter!solid!come!into!contact!with!each!other.!!The!liquid!immediately!boils!and!forms!a!layer!of!gas!between!the!liquid!and!the!solid.!!The!thermal!conductivity!of!the!gas!is!so!low!that!it!actually!acts!as!an!insulator,!preventing!the!solid!from!cooling!quickly!(Gottfried!et!al.,!1966;!Leidenfrost,!1966).!!Thus!the!fastest!cooling!rates!occurred!when!the!samples!were!cooled!in!water.!!The!slowest!cooling!occurred!while!cooling!in!the!oven,!at!a!temperature!decrease!of!5˚C!per!minute.!!Table!5.1.!!Experimental!grid!for!textural!experiments.!!The!numbers!2012>XX!represent!a!single!experiment.!!For!some!experimental!conditions,!no!experiments!were!performed.!!Two!experiments!per!temperature!value!were!performed!for!the!partially!submerged,!water!cooled!experiments.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Temperature!(˚C)!Cooling!Medium! 800! 750! 700!Oven!(5˚C!per!minute)! 2012>21! >! 2012>22!Rock!Slab!(with!forced!air!convection)! 2012>05! 2012>03! >!Liquid!Nitrogen!(3!sides)! 2012>06! 2012>07! >!Water!(partially!submerged)! 2012>04!2012>16! 2012>15!2012>17! 2012>13!2012>18!Water!(fully!submerged)! 2012>11! 2012>12! 2012>14!! 5.1.3.& Gradient&Experimental&Grid&! To!measure!the!thermal!gradients!and!cooling!rates,!samples!were!subjected!to!the!same!cooling!conditions!as!the!textural!experiments,!but!had!two!thermocouples!in!the!samples!(Fig.!5.2).!!These!experiments!are!separate!from!the! !! 74! textural!experiments,!because!the!presence!of!thermocouples!in!the!sample!would!obscure!any!textures!created!by!the!cooling.!! For!each!experiment,!the!samples!were!heated!to!1000˚C!to!ensure!homogeneous!melting,!and!then!the!thermocouples!were!inserted.!!The!thermocouples!were!spaced!9.5!mm!apart!from!each!other,!and!they!were!inserted!so!one!of!the!ends!touched!the!bottom!of!the!crucible.!!Because!the!crucibles!measure!25!mm!tall,!and!the!crucibles!were!not!completely!filled,!9.5!mm!spacing!between!crucibles!was!determined!to!produce!a!substantial!difference!in!cooling!rate,!and!return!accurate!results.!! Two!experiments!were!conducted!for!each!set!of!cooling!conditions,!with!either!a!starting!temperature!of!800˚C!or!700˚C,!or!as!close!as!was!possible!to!these!temperatures.!!Because!the!thermocouples!could!not!be!in!the!sample!while!it!was!in!the!high!temperature!furnace,!for!all!the!experiments!where!the!sample!was!cooled!outside!of!the!oven,!the!thermocouples!had!to!be!inserted!in!the!samples!while!they!were!outside!the!furnace.!!This!was!done!when!the!samples!were!at!higher!temperatures!(around!1000˚C)!since!they!would!be!too!viscous!at!800˚C!or!700˚C.!!Once!the!thermocouples!were!inserted!into!the!samples,!the!samples!were!slowly!cooled!outside!the!furnace!with!the!help!of!a!blowtorch!to!prevent!any!significant!temperature!gradient!from!forming!prematurely!in!the!sample!as!it!cools!to!the!starting!temperature!for!the!experiment.!!Due!to!the!error!associated!with!this!method,!small!temperature!differences!of!approximately!20>25!˚C!did!develop.!!The!largest!starting!temperature!difference!occurred!in!experiment!2012>20,!with!a!difference!of!40!˚C!between!the!thermocouples.!!Once!the!samples!were!cooled!to!approximately!the!correct!starting!conditions,!and!the!difference!in!temperature!between!thermocouples!was!at!a!minimum,!the!samples!were!exposed!to!the!specified!cooling!conditions.!!Table!5.2!shows!the!experimental!grid!for!the!thermal!gradient!experiments.!!Figs.!5.7!through!5.10!show!the!thermocouple!readings!of!the!thermal!gradient!experiments.!!!! !! 75! Table!5.2.!!Thermal!gradient!experiments!with!cooling!medium!and!starting!temperature!shown.!!Though!no!thermal!gradient!experiments!were!carried!out!using!750˚C!as!a!starting!temperature,!the!column!is!present!because!textural!experiments!were!conducted!starting!at!this!temperature.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Temperature!(˚C)!Cooling!Medium! 700! 750! 800!!Oven!(5˚C!per!minute)! 2012>21! >! 2012>22!!Rock!Slab!(with!forced!air!convection)! 2012>23! >! 2012>24!!Water!(partially!submerged)! 2012>19! >! 2012>20!!Water!(fully!submerged)! 2012>25! >! 2012>26!! !! 76! legend melt cooling           material mm cooling surface thermocouples forced airconvection 0 10 A B !Figure!5.2.!!A!shows!the!experimental!setup!for!samples!cooled!via!forced!air!convection.!!The!sample!sits!on!a!room!temperature!rock!slab!and!has!air!blown!across!it!by!a!household>style!fan,!set!on!its!highest!setting.!!B!shows!the!experimental!setup!for!samples!cooled!via!partial!submersion!in!water.!!The!container!holding!the!water!is!much!larger!than!pictured!in!this!figure,!and!contains!ice!as!well,!so!the!temperature!of!the!water!does!not!change!by!an!appreciable!amount.!!For!samples!completely!submerged!in!water,!the!setup!is!the!same,!but!the!sample!is!cooled!on!all!sides!by!water,!including!the!upper!surface.! !! 77! 5.2.& Results& 5.2.1.& Internal&Structures&and&Textures&! Joints!are!found!within!some!of!the!experimental!products,!but!not!all!samples!contain!joints.!!Overall,!experiments!cooled!via!either!partial!or!complete!submersion!in!water!developed!jointing,!while!experiments!cooled!in!the!oven!or!via!forced!air!convection!did!not!form!joints.!!The!specific!textures!found!in!the!experiments!vary!from!sample!to!sample,!but!this!division!holds!true!for!all!the!experiments.!! Some!of!the!samples!are!not!jointed,!but!do!have!fractured!surfaces,!such!as!experiments!2012>21!and!2012>03!(Figs.!5.3!and!5.4).!!Fracture!surfaces!form!only!where!the!sample!was!broken!to!expose!the!interior!for!observation,!and!they!are!not!present!elsewhere!within!the!sample.!!If!cooling!joints!are!present!within!the!sample,!they!will!be!visible!as!joints!intersecting!the!main!broken!surface!(Figs.!5.5!and!5.6).!!! Fig.!5.3!shows!experiment!2012>21,!which!was!cooled!in!the!furnace!from!700˚C!down!to!400˚C!(well!below!the!solidus!and!glass!transition)!at!5˚C!per!minute.!!This!sample!cooled!slowly!enough!to!form!small!crystals,!visible!in!the!lower!right!of!Fig.!5.3.!!As!is!evident!from!the!photo,!experiment!2012>21!does!not!have!any!joints!bisecting!it,!though!fracture!surfaces!are!visible.!!This!is!true!for!both!oven>cooled!samples.!! Experiment!2012>03!was!cooled!via!forced!air!convection!from!a!temperature!of!750!˚C!(Fig.!5.4).!!No!joints!exist!within!the!sample,!though!texturally!it!is!distinct!from!experiment!2012>21!(Fig.!5.3).!!The!air!cooled!experiment!is!rougher!in!surface!texture,!and!did!not!form!many!of!the!fracture!surfaces!that!are!present!in!experiment!2012>21.!!Experiment!2012>03!did!not!form!any!visible!crystals.!! In!Figs.!5.5!and!5.6,!jointing!can!be!seen!throughout!the!samples.!!Much!of!this!jointing!is!perpendicular!to!the!cooling!surfaces,!though!cross!joints!are!seen!as!well.!!Both!these!samples!were!cooled!in!convecting!water,!with!experiment!2012>12!(Fig.!5.5)!fully!submerged!in!water,!while!experiment!2012>15!(Fig.!5.6)!was! !! 78! partially!submerged!(cooled!by!water!on!the!bottom!and!the!sides,!with!the!top!open!to!the!atmosphere).!! The!joints!formed!in!these!two!samples!are!not!well!organized!or!ordered!like!those!found!in!outcrops.!!However,!well!organized!joints!were!not!expected!to!be!found,!owing!to!the!rapid!cooling!and!small!size!(approximately!10!mL)!of!the!samples.!!Regardless,!the!presence!of!joints!within!these!samples!sets!them!apart!from!experiments!with!slower!cooling!rates,!such!as!experiment!2012>21!(Fig.!5.3).!!! The!difference!in!textures!and!presence!of!joints!between!the!experiments!shows!that!the!cooling!rate!does!have!a!direct!impact!on!the!presence!or!absence!of!cooling!joints!within!the!samples.!!See!Appendix!C!for!photos!of!all!the!experiments. !! 79! 50 mm !Figure!5.3.!!Photo!of!experiment!2012>21.!!This!sample!was!cooled!from!700˚C!down!to!400˚C!in!the!Nabertherm!furnace!at!5˚C!per!minute.!!It!cooled!slowly!enough!that!small!white!crystals!formed!during!the!process,!visible!in!the!lower!right!corner!of!the!sample.!!The!planar!surfaces!facing!the!viewer!are!not!joints,!but!are!rather!the!fracture!surfaces!formed!when!the!crucible!was!broken!off!the!sample.!!The!sample!does!not!have!any!joints!in!its!interior,!and!so!the!sample!fractured!near!the!crucible,!rather!than!through!the!center.!!These!fractures!are!all!parallel!to!the!crucible!walls,!rather!than!perpendicular!to!those!cooling!surfaces.!!The!sample!extends!towards!the!viewer!in!this!photo!by!approximately!8!mm.!!The!fractures!are!not!considered!cooling!joints,!but!rather!a!sample!preparation!artifact.!!They!do!not!propagate!into!the!interior!of!the!sample,!and!this!experiment!cooled!as!one!mass.!!This!is!in!contrast!to!experiments!2012>12!and!2012>15,!which!cooled!much!more!quickly!than!this!sample,!and!are!extensively!jointed.! !! 80! 50 mm !Figure!5.4.!!Photo!of!experiment!2012>03.!!This!sample!was!cooled!from!750˚C!via!forced!air!convection.!!There!is!much!more!variability!in!the!texture!of!the!sample!than!in!the!oven!cooled!experiment!(Fig.!5.3),!however!cooling!joints!are!not!present.!!There!are!one!or!two!planar!surfaces!that!could!be!considered!fracture!surfaces,!but!these!are!only!present!on!the!large!broken!face!created!to!view!the!cross!section!of!the!sample.!!There!are!no!joints!present!that!are!not!associated!with!and!created!by!the!breaking!of!the!sample!after!cooling.! !! 81! 50 mm A B !Figure!5.5.!!A!shows!experiment!2012>12.!!This!sample!was!fully!submerged!in!water!and!cooled!by!forced!convection.!!B!shows!a!schematic!drawing!of!the!above!sample.!!Dark!lines!outline!joints!in!sample.!!In!some!cases!these!have!organized!to!form!columns!within!the!sample.!!Timing!relationships!can!be!determined!by!joint!geometry.!!Later!joints!perpendicularly!intersect!earlier,!continuous!joints.!!Almost!all!the!joints!have!formed!perpendicular!to!the!cooling!surfaces.! !! 82! 50 mm A B !Figure!5.6.!!A!shows!experiment!2012>15.!!Sample!was!cooled!on!the!sides!and!lower!boundary!in!water!by!forced!convection,!while!the!upper!surface!was!cooled!by!freely!convecting!air.!!In!B,!dark!lines!outline!joints!within!sample.!!Joints!form!subperpendicular!to!cooling!surface,!and!later!joints!perpendicularly!intersect!earlier!joints.! !! 83! 5.2.2& Cooling&Rates&and&Gradients&! Each!cooling!method!produced!a!distinct!set!of!cooling!rates!and!thermal!gradients,!which!are!reported!here.!!The!results!are!outlined!in!Figs.!5.7!through!5.10.!!Fig.!5.11!shows!the!maximum!difference!in!temperatures!between!the!two!thermocouples!during!the!experiments.!!The!maximum!difference!happened!at!different!times!for!each!of!the!experiments,!but!as!a!general!rule,!the!maximum!difference!occurred!very!early!for!the!quickly!cooled!experiments,!such!as!the!water!cooled!ones,!and!somewhat!further!into!the!experiment!for!the!slowly!cooled!experiments,!such!as!those!cooled!in!the!oven.!! There!is!one!outlier!within!the!experimental!results!–!experiment!2012>19.!!The!maximum!temperature!difference!is!far!greater!for!this!experiment!than!for!the!rest!of!the!experiments.!!It!is!not!entirely!clear!why!this!is!the!case,!since!the!cooling!rate!for!experiment!2012>19!is!very!similar!to!the!other!partially!submerged!experiment,!2012>20!(Table!5.5,!Fig.!5.12).!!It!is!possible!that!the!middle!thermocouple!happened!to!be!located!in!the!exact!center!of!the!sample,!where!it!was!most!insulated,!whereas!in!the!other!experiments!the!middle!thermocouple!was!slightly!off>center,!but!this!is!merely!speculation.!!The!cooling!rates!for!this!experiment!are!still!valid,!and!it!is!those!data!that!are!analyzed!below.!! The!oven!cooled!experiments!had!very!low!thermal!gradients,!as!judged!by!the!maximum!temperature!difference,!and!that!is!to!be!expected.!!The!samples!took!over!an!hour!to!cool!from!either!700!or!800˚C!down!to!400˚C,!so!the!variation!in!temperature!within!the!sample!was!minimal,!and!generally!fairly!constant!for!the!duration!of!the!experiment.!!As!shown!by!Fig.!5.3,!the!slow!cooling!rate!and!negligible!thermal!gradient!does!not!produce!columnar!joints!within!the!sample.!! The!air!conduction!cooled!experiment!gave!comparatively!intermediate!values!for!the!maximum!temperature!difference.!!Though!the!atmosphere!was!much!cooler!than!the!sample!at!the!time!of!the!experiment,!air!does!not!the!ability!to!absorb!large!amounts!of!heat!effectively,!and!so!was!not!the!most!effective!refrigerant.!!Fig.!5.4!shows!that!the!air!cooled!experiments!did!not!form!cooling!joints.! !! 84! ! Excepting!experiment!2012>19,!all!the!water!cooled!experiments!had!similar!maximum!differences!in!temperature.!!Surprisingly,!the!experiment!with!a!starting!temperature!of!700˚C!(2012>25)!had!a!larger!temperature!difference!than!the!experiment!with!a!starting!temperature!of!800˚C!(2012>26).!!This!could!be!from!some!small!difference!between!the!experiments,!such!as!an!enhanced!surface!crack!network!in!the!700˚C!sample.!!Regardless,!both!samples!that!were!completely!submerged!had!higher!temperature!differences!than!the!sample!that!was!cooled!from!only!the!bottom!and!sides.!!Table!5.3.!!Shows!the!maximum!temperature!difference!between!the!two!thermocouples,!and!converts!this!into!the!maximum!thermal!gradient!experienced!by!the!sample!based!on!the!9.5!mm!distance!between!the!thermocouples.!Experiment! Cooling!Mechanism! Max!Temp!Difference!(˚C)! Thermal!Gradient!(˚C/mm)!2012>21! oven! 6.32! 0.66!2012>22! oven! 6.16! 0.65!2012>23! air! 26.83! 2.82!2012>19! partial!sub.!in!water! 206.46! 21.68!2012>20! partial!sub.!in!water! 58.53! 6.14!2012>25! full!sub.!in!water! 66.06! 6.94!2012>26! full!sub.!in!water! 61.41! 6.45!!!!!!!!!!!!!! !! 85! Table!5.4.!!This!table!shows!each!experiment,!the!thermocouple!that!made!the!reading,!and!the!maximum!averaged!heat!flow.!!This!number!was!calculated!by!finding!the!maximum!change!in!temperature!per!second!in!each!thermocouple,!averaging!that!value!with!the!previous!and!next!change!in!temperature!values,!and!then!accounting!for!heat!capacity!and!mass!to!arrive!at!the!J!s>1,!or!heat!flow,!of!the!experiments.! Experiment! Thermocouple! Cooling!Mechanism! Maximum!Averaged!˚C!s>1!(∂T/∂t(Cooling!Rate)! Maximum!Averaged!J!s>1!(Heat!Flow)!1! oven! >0.08! >0.83!2012>21! 2! oven! >0.08! >0.81!1! oven! >0.61! >6.11!2012>22! 2! oven! >0.08! >0.80!1! air! >2.6! >26.54!2012>23! 2! air! >2.4! >24.70!2012>24! 2! air! >6.2! >62.52!1! partial!sub.! >14.5! >145.51!2012>19! 2! partial!sub.! >12.9! >129.84!1! partial!sub.! >15.3! >154.78!2012>20! 2! partial!sub.! >20.5! >207.05!1! full!sub.! >18.0! >181.21!2012>25! 2! full!sub.! >24.3! >245.25!1! full!sub.! >17.3! >172.64!2012>26! 2! full!sub.! >32.8! >327.83!! !! 86! 0 1000 2000 3000 4000 5000 6000 70000 100200 300400 500600 700800 Time (seconds) Tempe rature (C) Experiment 2012-21 ‘˜‡…‘‘Ž‡†ˆ”‘͹ͲͲǏ 0 1000 2000 3000 4000 5000 6000 70000 100200 300400 500600 700800 Time (seconds) Tempe rature (C) Experiment 2012-22 ‘˜‡…‘‘Ž‡†ˆ”‘ͺͲͲǏ Max πȀπ– Š‡”ǤͳǣǦͲǤͲͺǏ•-1Therm. 2: -0.08Ǐ•-1 Max πȀπ– Š‡”ǤͳǣǦͲǤ͸ͳǏ•-1Therm. 2: -0.08Ǐ•-1 12 2 1 A B 2 1 2 1 !Figure!5.7.!!A!shows!experiment!2012>21,!with!a!starting!temperature!of!700˚C.!!B!shows!experiment!2012>22,!with!a!starting!temperature!of!800˚C.!!Both!samples!were!cooled!at!a!rate!of!approximately!5˚C!per!minute!down!to!400˚C.!!The!cooling!rate!was!not!perfectly!constant,!as!shown!by!the!small!inflection!points!in!both!graphs,!but!was!close!enough!for!the!purposes!of!these!experiments.!!The!maximum!cooling!rate!is!shown!for!each!thermocouple,!with!the!numbers!1!and!2!labeling!each!thermocouple,!and!showing!approximately!where!the!maximum!cooling!rate!occurred!during!the!experiment.!!As!shown!by!these!two!experiments,!with!a!sufficiently!slow!cooling!rate,!the!temperature!difference!between!the!center!and!edge!of!the!samples!is!negligible.!!Neither!of!these!experiments!produced!columnar!joints.!!Inset!shows!location!of!thermocouples.! !! 87! 0 50 100 150 200 250 300 350 400 450 5000 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-23 …‘‘Ž‡†˜‹ƒˆ‘”…‡†ƒ‹”…‘˜‡…–‹‘ˆ”‘͹ͲͲǏ 0 50 100 150 200 250 300 350 400 450 5000 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-24 …‘‘Ž‡†˜‹ƒˆ‘”…‡†ƒ‹”…‘˜‡…–‹‘ˆ”‘ͺͲͲǏ Max πȀπ–Therm. 2: -20.5Ǐ•-1 12 2 A B Max πȀπ– Š‡”ǤͳǣǦʹǤ͸Ǐ•-1Therm. 2: -2.4Ǐ•-1 1 2 1 2 !Figure!5.8.!!A!shows!experiment!2012>23,!with!a!starting!temperature!of!700˚C.!!B!shows!experiment!2012>24,!with!a!starting!temperature!of!800˚C.!!Both!samples!were!cooled!via!forced!air!convection,!with!a!household!fan!on!its!highest!setting!blowing!air!past!the!sample!as!it!sits!on!a!cut!rock!slab.!!The!numbers!1!and!2!label!each!thermocouple,!and!show!approximately!where!the!maximum!cooling!rate!occurred!during!the!experiment.!!A!shows!that!the!cooling!did!not!start!from!exactly!700˚C,!but!was!close!enough!that!the!results!are!still!valid.!!In!B,!Thermocouple!1!was!exposed!to!the!atmosphere!and!did!not!produce!viable!results,!so!was!excluded.!!Inset!shows!location!of!thermocouples.! !! 88! 0 20 40 60 80 100 120 1400 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-19 …‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹™ƒ–‡”ˆ”‘͹ͲͲǏ 0 20 40 60 80 100 120 1400 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-20 …‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹™ƒ–‡”ˆ”‘ͺͲͲǏ Max πȀπ– Š‡”ǤͳǣǦͳͶǤͷǏ•-1Therm. 2: -12.9Ǐ•-11 2 Max πȀπ– Š‡”ǤͳǣǦͳͷǤ͵Ǐ•-1Therm. 2: -20.5Ǐ•-1 21 A B 2 1 1 2 !Figure!5.9.!!A!shows!experiment!2012>19,!with!a!starting!temperature!of!approximately!700˚C.!!B!shows!experiment!2012>20,!with!a!starting!temperature!of!approximately!800˚C.!!Neither!of!these!samples!started!at!exactly!the!specified!temperature,!but!the!difference!in!both!cases!is!negligible.!!Both!samples!were!cooled!via!partial!submersion!in!convecting!water!with!a!temperature!of!approximately!3˚C.!!The!numbers!1!and!2!label!each!thermocouple,!and!show!approximately!where!the!maximum!cooling!rate!occurred!during!the!experiment.!!Inset!shows!location!of!thermocouples.!!Thermocouple!1!was!closer!to!the!edge!of!the!sample!in!experiment!2012>19,!but!this!thermocouple!broke!after!the!experiment,!and!as!it!was!replaced!the!relative!locations!of!the!thermocouples!changed,!which!is!why!thermocouple!2!experienced!a!higher!cooling!rate!in!experiment!2012>20.! !! 89! 0 20 40 60 80 100 120 1400 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-25 …‘‘Ž‡†˜‹ƒˆ—ŽŽ•—„‡”•‹‘‹™ƒ–‡”ˆ”‘͹ͲͲǏ 0 20 40 60 80 100 120 1400 100200 300400 500600 700800 time (seconds) temper ature ( C) Experiment 2012-26 …‘‘Ž‡†˜‹ƒˆ—ŽŽ•—„‡”•‹‘‹™ƒ–‡”ˆ”‘ͺͲͲǏ Max πȀπ– Š‡”ǤͳǣǦͳͺǤͲǏ•-1Therm. 2: -24.3Ǐ•-1 Max πȀπ– Š‡”ǤͳǣǦͳ͹Ǥ͵Ǐ•-1Therm. 2: -32.8Ǐ•-1 1 2 12 A B 1 2 1 2 !Figure!5.10.!!A!shows!experiment!2012>25,!with!a!starting!temperature!of!700˚C.!!B!shows!experiment!2012>26,!with!a!starting!temperature!of!800˚C.!!Both!samples!were!cooled!via!complete!submersion!in!convecting!water!with!a!temperature!of!approximately!3˚C.!!The!numbers!1!and!2!label!each!thermocouple,!and!show!approximately!where!the!maximum!cooling!rate!occurred!during!the!experiment.!!Inset!shows!location!of!thermocouples.!!Thermocouple!2!was!closer!to!the!edge!of!the!sample,!and!experienced!a!higher!cooling!rate!in!both!experiments.!!! Subtracting!each!temperature!reading!from!the!previous!temperature!reading,!a!crude!derivative!of!the!temperature!can!be!taken.!!The!thermocouples!take!temperature!readings!once!per!second,!so!this!produces!the!change!in!temperature!per!second.!!There!was!a!large!difference!in!the!change!in!temperature! !! 90! values!from!reading!to!reading.!!Because!of!this,!the!maximum!˚C!s>1!values!were!averaged!with!the!previous!and!next!value.!!Once!the!heat!capacity!and!mass!of!each!sample!(the!heat!capacity!and!mass!of!the!crucible!is!ignored)!is!taken!into!account,!the!resulting!units!are!in!J!s>1,!also!called!heat!flux!(Table!5.4).!! According!to!the!thermocouple!readings,!the!forced!air!convection!cooled!experiments!all!had!approximately!25!times!higher!heat!flow!than!the!furnace!cooled!experiments.!!The!water!cooled!experiments,!both!partially!and!fully!submerged,!had!heat!flows!between!6!and!13!times!as!large!as!the!forced!air!experiments.!! Oven cooledAir/convection cooledWater cooled (sides and bottom)Water cooled (fully submerged) 0 50 100 150 200 250 2012-21 2012-22 2012-23 2012-19 2012-20 2012-25 2012-26 Maximum Temperature Difference Experiment  ƒš ‹ — ‡  ’‡ ”ƒ –— ”‡  ‹ˆˆ ‡” ‡ …‡ ȋ Ǐ Ȍ !Figure!5.11.!!Maximum!difference!in!temperature!between!two!thermocouples!within!the!samples!during!cooling.!!Legend!shows!the!different!means!by!which!the!samples!were!cooled.!!With!the!exception!of!Experiment!2012>19,!which!experienced!an!anomalously!large!temperature!difference!between!the!two!thermocouples!for!reasons!unknown,!there!is!a!correlation!between!cooling!medium!and!maximum!temperature!difference.!!Oven!and!air!cooled!experiments!had!lower!temperature!differences,!while!water!cooled!experiments!had!higher!temperature!differences.! !! 91! 2012-21 2012-22 2012-23 2012-19 2012-20 2012-25 2012-260 5 10 15 20 25 30 35 Negativ e Degre es C pe r secon d oven cooled partially submerged fully submergedair cooled Thermocouple 1Thermocouple 2 !Figure!5.12.!!Maximum!averaged!cooling!rate.!!The!chart!shows!the!change!in!temperature!in!seconds!of!each!experiment.!!Colors!match!those!in!previous!figures,!with!blue!representing!thermocouple!1!and!green!thermocouple!2.!!Oven!cooled!samples!experienced!the!least!temperature!change!per!second,!with!partially!and!fully!submerged!samples!experiencing!the!greatest.!!There!is!less!difference!between!the!partially!and!fully!submerged!samples!as!there!is!between!the!other!samples,!but!there!is!still!a!slight!increase!from!partially!to!fully!submerged.!!Dashed!line!shows!general!increase!in!rate!of!temperature!loss!for!the!different!cooling!methods.! 5.3.& Discussion& 5.3.1.& Joint&Formation&! The!major!findings!of!these!experiments!are!first,!that!it!is!possible!to!synthesize!columnar!joints,!and!second,!to!narrow!down!the!possible!conditions!under!which!joints!form.!!Experiments!like!these,!on!this!small!scale,!have!never!been!attempted!before,!and!the!results!are!promising.!!Though!perfectly!formed!hexagonal!columns!are!not!produced!from!the!experiments,!the!formation!of!columnar!joints!is!an!excellent!starting!point!for!further!experiments.!! Many!of!the!joints!formed,!propagate!perpendicular!to!the!cooling!surface!(the!crucible!wall).!!This!matches!with!what!others!have!hypothesized!about!the!formation!of!columnar!joints,!and!matches!with!numerous!field!observations!as!well.!!Not!all!joints!propagate!in!this!way,!and!this!is!most!likely!due!to!two!reasons.!!The!effects!of!the!small!size!of!the!samples!and!the!high!thermal!gradients!and! !! 92! cooling!rates!within!the!samples!are!one!possibility.!!With!gradients!on!the!order!of!7!˚C!mm>1!and!cooling!rates!up!to!approximately!32.8!˚C!s>1!in!the!water!cooled!samples,!it!is!expected!that!the!joints!are!not!perfectly!organized.!!The!other!possibility!is!that!because!joints!propagate!such!that!they!commonly!intersect!free!surfaces!perpendicularly!(e.g.,!Dyer,!1988;!Rawnsley!et!al.,!1992;!Gross,!1993),!later!joints!are!influenced!by!earlier!joints,!and!may!cause!the!later!joints!to!curve!during!propagation!and!intersect!the!earlier!joints.!! Columnar!joints!do!not!form!in!all!of!the!experiments.!!This!is!because!joints!only!form!within!a!certain!range!of!cooling!conditions!and!thermal!gradients.!!In!the!textural!experiments!conducted,!joints!only!form!within!the!water!cooled!experiments!(in!both!partially!and!fully!submerged!samples).!!From!the!gradient!experiments,!this!is!equivalent!to!a!thermal!gradient!of!between!approximately!6!and!7!˚C!mm>1!and!cooling!rates!of!between!approximately!12.9!to!32.8!˚C!s>1.!!When!exposed!to!these!cooling!conditions,!columnar!joints!are!able!to!nucleate!and!propagate.!!When!the!cooling!rate!is!below!approximately!12!˚C!s>1!(Fig.!5.13),!or!when!these!cooling!rates!do!not!occur!through!the!column!formation!temperature,!joints!do!not!form.!! With!regard!to!an!upper!limit!on!the!thermal!gradient!or!cooling!rate,!the!data!from!these!experiments!are!inconclusive.!!As!mentioned!above,!preliminary!experiments!in!which!samples!cooled!immediately!from!1000˚C!to!room!temperature!turned!completely!to!glass!and!did!not!create!any!joints.!!However,!it!is!not!clear!whether!this!was!because!the!thermal!gradient!and!cooling!rate!of!these!experiments!was!too!high,!or!simply!because!the!synthetic!basalt!was!still!too!low!in!viscosity,!and!the!appropriate!amount!of!tensile!stress!was!not!generated.!!It!is!also!possible!that!some!degree!of!heterogeneity,!achieved!through!crystallization,!was!required!to!nucleate!jointing.!!However,!because!of!the!“cone!of!depression”!that!formed!in!these!samples!(Fig.!6.9)!it!is!likely!due!to!the!lack!of!tensile!stress,!rather!than!too!high!cooling!rates!or!lack!of!crystals,!that!the!samples!did!not!form!joints.!!Because!of!this,!these!experiments!cannot!define!an!upper!limit!of!thermal!gradients!or!cooling!rates!that!produce!columnar!joints.!!However,!they!do!show!that!for!samples!of!this!size!(cylinders!25!mm!high!with!25!mm!diameter),!the!lower! !! 93! boundaries!for!columnar!joint!formation!are!between!3!and!6!˚C!mm>1!for!thermal!gradients,!and!between!approximately!25!and!130!J!s>1.!! 0 5 10 15 20 25 0 5 10 15 20 25 30 35 UnjointedJointed Non-JointForming  ƒš ‹ —  Š‡ ” ƒŽ   ”ƒ †‹ ‡ –ȋ Ǐ   -1 ) ƒš‹—˜‡”ƒ‰‡†‘‘Ž‹‰ƒ–‡ȋǏ•-1 ) ‘••‹„Ž‡
‘‹–Forming Joint Forming !Figure!5.13.!!Joint!formation!conditions.!!All!experiments!plotted!in!cooling!rate!vs.!thermal!gradient!space.!!Experiments!are!split!into!two!groups,!joint!forming!and!non>joint!forming.!!The!exact!contact!between!the!joint!forming!and!non>joint!forming!conditions!cannot!be!exactly!specified,!because!there!is!a!range!of!parameters!that!the!experiments!did!not!investigate,!due!to!limitations!of!the!experimental!setup.!!Thus!there!is!a!section!where!joint!formation!is!possible,!but!the!exact!conditions!defining!the!boundary!are!unknown.!!It!is!also!unknown!exactly!how!the!thermal!gradient!and!cooling!rate!relate!to!each!other,!and!how!the!thermal!gradient!relates!to!joint!formation,!so!the!boundaries!between!the!groups!are!drawn!only!with!respect!to!the!cooling!rate.! 5.3.2.& Comparison&of&Experimental&and&Modeled&Temperature&Profiles&! The!small!sample!size!of!the!experiments!makes!direct!comparison!of!the!models!and!experiments!difficult,!but!some!comparisons!can!still!be!made.!! The!experiments!do!not!show!many!curving!columnar!joints,!and!the!ones!present!do!not!extend!continuously!very!far.!!This!is!again!a!limitation!due!to!the!small!sample!size.!!Since!the!crucibles!are!only!25!mm!in!diameter,!the!joints!do!not!have!enough!time!during!cooling!to!be!influenced!by!more!than!one!boundary.! !! 94! ! Despite!these!limitations,!the!thermal!gradients!of!the!experiments!can!still!be!compared!to!those!of!the!forward!models.!!By!finding!the!temperatures!on!the!edge!and!in!the!center!of!a!model!that!is!19!mm!high!by!25!mm!wide!(the!average!cross!sectional!dimensions!of!the!experiments),!thermal!gradients!can!be!calculated!and!compared!to!those!experimentally!determined.!! Two!different!h!factor!values!were!used!for!the!models.!!70!W!m>2!˚C>1!!(from!Keszthelyi!and!Denlinger!(1996))!and!1000!W!m>2!˚C>1!!(modified!from!Recktenwald!(2006))!were!used!to!represent!cooling!via!forced!air!convection!and!complete!submersion!in!water,!respectively.!!Each!of!these!models!was!evaluated!at!15,!30,!and!60!seconds!after!emplacement!for!the!temperature!at!the!edge!of!the!cooling!surface!and!in!the!middle!of!the!model.!!These!temperature!differences!were!then!divided!by!the!distance!between!the!two!points!to!calculate!the!thermal!gradient.!!Table!5.5!shows!the!results!of!the!models.!! The!modeled!thermal!gradients!are!much!higher!than!those!measured!in!the!experiments.!!The!only!experiment!that!comes!remotely!close!to!any!of!the!models!is!experiment!2012>25,!a!fully!submerged!sample,!with!a!thermal!gradient!of!!!!!!!!!!!!!!!!!!6.94!˚C!mm>1.!!However!this!model!was!supposed!to!represent!the!forced!air!convection!experiments,!so!none!of!the!models!can!be!validly!compared!to!the!experiments.!! There!are!two!definite!and!several!possible!reasons!for!the!differences!between!the!experimental!thermal!gradients!and!the!modeled!thermal!gradients.!!The!models!use!the!exact!center!and!the!extreme!edge!temperatures!to!create!the!gradients,!while!the!thermocouples!use!the!bottom!edge!(which!is!still!bounded!by!the!crucible)!and!a!point!9.5!mm!away!from!that!edge,!which!should!be!in!the!center!of!the!sample,!but!it!is!not!guaranteed!to!be!in!the!exact!center.!!Both!of!these!issues!cause!the!experimental!gradients!to!be!lower!than!the!modeled!gradients.!!Other!possible!reasons!include!various!operator!errors!due!to!the!small!sample!size,!and!enhanced!heat!dissipation!due!to!cracking!or!a!permeability!network!within!the!experimental!samples!that!homogenizes!the!temperature!profile!of!the!samples.!! Table!5.6!shows!the!thermal!gradients!calculated!from!an!outcrop>sized!flow,!3!meters!thick.!!Again,!the!temperatures!at!the!edge!and!the!center!of!the!flow!were! !! 95! taken!at!two!different!times!during!the!cooling!history.!!One!is!from!the!early!history!of!the!flow,!while!the!second!is!after!the!entire!flow!is!below!the!column!formation!temperature.!!Though!no!experiments!of!comparable!size!were!undertaken!in!this!study,!the!furnace!cooled!experiments!have!similar!thermal!gradients,!at!.66!and!.65!˚C!mm>1,!to!two!of!the!modeled!thermal!gradients!from!the!180,000!second!mark,!.69!and!.71!˚C!mm>1.!! Though!no!conclusive!interpretations!can!be!made!using!the!comparison!of!experimental!versus!modeled!thermal!gradients,!better!techniques!in!the!future!may!enable!better!agreement!between!models!and!experiments.!!Table!5.5.!!Two!forward!models!were!evaluated!at!three!different!times!throughout!the!cooling!process.!!The!two!models!had!two!different!h!factor!values,!70!W!m>2!˚C>1!!and!1000!W!m>2!˚C>1,!representing!cooling!by!forced!air!convection!and!complete!submersion!in!water,!respectively.!!The!difference!in!temperature!between!the!edge!and!the!center!of!the!models!was!then!divided!by!the!distance!between!the!points!to!solve!the!thermal!gradient!at!that!time.! h!factor!!(W!m>2!˚C>1)( T∞!(˚C)! Time!(s)! Gradient!(˚C!mm>1)!70! 25! 15! 9.58!70! 25! 30! 10.95!70! 25! 60! 10.74!1000! 1! 15! 56.00!1000! 1! 30! 48.21!1000! 1! 60! 30.63!!!Table!5.6.!!Two!forward!models!of!outcrop>sized!flows!were!evaluated!at!two!times!during!the!cooling!period,!one!close!to!the!beginning!of!the!cooling,!and!one!after!the!entire!flow!had!cooled!past!the!column!formation!temperature,!specified!as!800˚C!for!these!models.! h!factor!!(W!m>2!˚C>1)( T∞!(˚C)! Time!(s)! Gradient!(˚C!mm>1)!70! 25! 180,000! 0.69!70! 25! 900,000! 0.41!1000! 25! 180,000! 0.71!1000! 25! 900,000! 0.41!!! 5.3.3.& Limitations&of&Experimental&Setup&! Though!the!high!temperature!experiments!display!excellent!examples!of!Mode!I!tension!cracks!within!synthesized!basalts,!there!are!some!limitations!to!the!setup.!!One!of!these!limitations!is!the!size!of!the!samples.!!The!small!size!of!the! !! 96! samples!necessitated!small!columns.!!High!cooling!rates!were!necessary!to!form!the!small!columns.!!With!such!high!cooling!rates,!the!cooling!mediums!available!were!limited.!!In!the!future,!using!larger!crucibles!and!different!cooling!mediums!to!explore!a!larger!range!of!thermal!gradients!and!cooling!rates!could!lead!to!new!insights!into!the!formation!of!columnar!joints.! !! 97! 6. Discussion& &Conclusion& 6.1.& Fit&of&Models&to&Outcrops&! The!comparison!of!the!forward!models!with!the!observations!gathered!from!the!four!outcrop!areas!provides!insights!into!the!mechanisms!for!heat!dissipation!and!the!unique!cooling!histories!of!the!outcrops.!! Immediately!after!emplacement!of!the!lava!flow,!the!difference!in!temperature!between!the!flow!and!the!surrounding!environment!creates!extremely!high!cooling!rates!and!thermal!gradients.!!The!large!cooling!rates!cause!the!lava!to!cool!past!the!glass!transition!temperature!extremely!quickly,!too!quickly!for!any!crystallization!to!occur.!! The!transition!from!liquid!to!glass!is!a!second>order!phase!transition,!and!there!is!no!volume!change!associated!(Turnbull!and!Cohen,!1961).!!Physical!properties!change!during!the!liquid!to!glass!transition,!including!the!thermal!expansion!and!specific!heat!values!(Turnbull!and!Cohen,!1961),!but!there!is!no!volume!change!associated!with!the!phase!transition!itself.!!The!only!volume!change!that!occurs!is!due!to!the!specific!volume>temperature!relationship;!a!decrease!in!temperature!causes!a!decrease!in!volume,!as!is!true!with!most!materials.!!Because!of!this!second>order!phase!transition,!quenching!of!the!exterior!shell!of!the!lava!flow!produces!glass,!but!no!tensile!stresses!due!to!phase!transition.!! Once!glass!forms!on!the!exterior!of!the!flow,!the!interior!slowly!crystallizes!and!decreases!in!temperature,!both!of!which!cause!the!volume!to!decrease.!!Lacking!a!viscous,!free!surface!on!the!upper!boundary!of!the!lava!flow!to!help!accommodate!viscous!flow!and!volume!decrease,!tensile!stress!builds!up,!eventually!exceeding!the!tensile!strength!of!the!material,!at!which!point!columnar!joints!form!in!response.!!Since!the!cooling!flow!is!a!mixture!of!both!crystals!and!melt,!the!formation!of!the!columnar!joints!is!still!contingent!upon!the!stresses!from!the!volume!decrease!of!the!material!exceeding!the!viscous!relaxation!timescale!of!the!cooling!melt.!!Only!through!this!mechanism!will!tensile!stresses!increase!until!the!tensile!strength!of!the!material!is!exceeded.! !! 98! ! This!explanation!is!supported!by!earlier!high!temperature!experiments.!!The!rapid!cooling!of!high!temperature!lava!does!not!form!columnar!joints,!but!simply!forms!glass.!!As!described!by!other!workers!(e.g.,!Peck!and!Minakami,!1968;!Long!and!Wood,!1986),!cooling!basaltic!flows!often!form!a!glassy!carapace!on!the!outer!edge!of!the!flow.!!Columnar!jointing,!though!sometimes!present!on!the!surface,!is!not!organized!into!columns!until!further!into!the!interior!of!the!flow!(Peck!and!Minakami,!1968).!! The!outcrops!studied!clearly!show!that!columns!are!affected!by!the!boundary!conditions!present!during!the!emplacement!and!cooling!of!the!flow.!!The!characteristics!most!affected!are!the!location!of!the!column!interface,!the!width!of!the!columns,!and!the!direction!of!column!propagation.!! Macroscopic!structures,!including!the!column!interface,!as!well!as!curving!and!coalescing!columns,!predicted!by!the!numerical!models!are!observed!in!the!Whistler!field!area!outcrops.!!The!column!interface!is!present!in!several!outcrops,!including!Railroad!Quarry!outcrop!1!(Fig.!6.1)!as!well!as!the!western!Daisy!Lake!outcrop!(Fig.!6.2).!!The!outcrops,!unlike!the!numerical!models,!are!not!perfectly!rectangular!in!cross!section,!so!the!interface!is!not!completely!horizontal!along!the!entire!outcrop,!but!it!is!roughly!parallel!to!the!upper!and!lower!boundaries!in!both!outcrops.!! The!same!western!Daisy!Lake!outcrop!and!Railroad!Quarry!outcrop!1!show!a!difference!in!column!diameter!due!to!cooling!rate,!also!in!agreement!with!the!models.!!In!both!outcrops,!the!columns!in!the!upper!colonnade!have!a!smaller!diameter!than!those!in!the!lower!colonnade.!!This!stems!from!the!different!boundary!conditions!on!the!top!and!bottom!of!the!flows.!!With!lower!heat!flow!and!a!lower!cooling!rate,!the!lower!colonnade!produced!columns!with!larger!diameters.!!High!heat!flow!and!a!higher!cooling!rate!on!the!upper!boundary!produced!narrower!columns!in!the!upper!colonnade.!! Curving!and!coalescing!columns!are!seen!particularly!well!on!the!eastern!side!of!Railroad!Quarry!outcrop!6!(Fig.!6.3).!!The!columns!change!from!vertical!to!nearly!horizontal!within!a!short!distance.!!This!is!predicted!in!the!models,!and!the!changing!geometry!of!the!columns!is!depicted!in!Figs.!4.3!and!4.7.!!Also!predicted!in! !! 99! the!models,!and!depicted!schematically!in!the!same!figures,!is!the!coalescing!of!columns.!!Not!all!columnar!joints!are!continuous!from!the!edge!of!the!flow!to!the!center,!and!cessation!of!some!of!these!joints!causes!multiple!columns!to!merge!together.!!This!is!visible!in!the!foreground!of!Fig.!6.3.! bedrock !Figure!6.1.!!Western!face!of!outcrop!1!of!the!Railroad!Quarry!area.!!The!non>planar!upper!and!lower!surfaces!of!the!outcrop!are!visible,!and!may!contribute!to!the!thicker!than!average!lower!colonnade.! upper colonnade lower colonnade m0 1 !Figure!6.2.!!Daisy!Lake!West!outcrop!showing!upper!and!lower!colonnade,!along!with!column!interface!zone!(bounded!by!dashed!lines).! !! 100! m0 1 !Figure!6.3.!!Eastern!side!of!Railroad!Quarry!outcrop!6.!!Curving!columns!visible!in!both!foreground!and!background,!and!coalescing!columns!visible!in!foreground.!!Scale!accurate!for!foreground.!!Background!column!diameters!~80!cm.!! All!the!columnar!structures!that!involve!curving!columns!are!due!to!the!interaction!of!more!than!one!boundary!condition.!!A!completely!linear!column!is!influenced!only!by!a!single!boundary.!!This!is!seen!in!outcrops!modeled!as!an!infinite!slab!near!the!center!–!the!lateral!edges!have!no!effect!on!the!columns,!and!all!the!jointing!is!due!only!to!either!the!top!or!bottom!boundaries.!!Whenever!more!than!one!boundary!influences!the!formation!of!a!column,!that!column!will!curve.!!Any!curved!column!within!an!outcrop!is!due!to!the!interaction!of!multiple!boundaries!during!the!formation!of!that!column.!! An!important!point!related!to!reconstructing!the!boundary!conditions!is!that!columns!can!coalesce,!but!they!can!never!diverge.!!As!the!cooling!rate!decreases!on! !! 101! the!interior!of!the!flow,!tensile!stresses!decrease!and!columnar!joints!cease!propagation.!!In!order!for!divergence!to!occur,!the!interior!of!the!flow!would!have!to!suddenly!cool!without!changing!the!direction!of!heat!flow,!which!is!impossible.!!Thus,!the!direction!of!column!coalescence!will!always!be!towards!the!interior!of!the!flow,!and!is!the!same!as!the!propagation!direction.!! Using!the!above!characteristics!and!rules,!it!is!possible!to!qualitatively!reconstruct!the!boundary!locations!and!cooling!conditions!at!those!boundaries!from!the!column!geometries.!!Relative!rates!of!cooling!and!general!locations!of!boundaries!can!be!inferred!on!an!outcrop!scale,!increasing!the!understanding!of!the!flow!in!question.!! Many!of!the!outcrops!have!thicker!upper!colonnades!compared!to!their!lower!colonnades.!!Cooling!starts!through!both!boundaries!simultaneously,!as!does!columnar!jointing.!!If!heat!flow!is!higher!through!one!boundary!than!the!other,!this!causes!the!jointing!front!to!propagate!more!rapidly!towards!the!center!of!the!flow.!!When!both!jointing!fronts!(one!propagating!up!from!the!lower!boundary,!one!down!from!the!upper!boundary)!meet!at!the!column!interface,!the!vertical!location!of!the!interface!within!the!flow!(assuming!an!infinite!or!semi>infinite!slab!geometry)!indicates!the!relative!heat!flow!through!the!two!boundaries.!! However,!since!the!temperatures!within!the!flow!are!constantly!in!flux,!and!basalt!(and!all!rocks!in!general)!has!a!fairly!high!heat!capacity!of!850!J!kg>1!˚C>1!(Bouhifd!et!al.,!2007),!and!a!low!thermal!conductivity!of!2!W!m>1!˚C>1!(Touloukian!et!al.,!1989),!the!relationship!between!heat!flow!and!location!of!column!interface!is!not!linear.!!Changing!the!boundary!conditions!on!the!forward!models!shows!that!in!order!to!have!the!upper!colonnade!twice!as!thick!as!the!lower,!the!upper!boundary!must!have!25!times!more!effective!heat!loss!than!the!lower!boundary.!!As!seen!in!Fig.!3.12,!the!upper!colonnade!of!the!eastern!face!of!the!Pinecrest!outcrop!is,!on!average,!twice!as!thick!as!the!lower!colonnade.!!The!numerical!model!in!Fig.!6.4!has!a!convective!heat!transfer!coefficient!on!the!upper!surface!that!is!25!times!as!great!as!that!of!the!lower!surface,!and!it!matches!well!with!the!Pinecrest!outcrop.!!The!model!cannot!predict!the!exact!h!factor!value!for!the!outcrop,!only!the!relative!values!of!the!two!boundaries.!!But!even!without!the!model,!looking!at!the!relative! !! 102! diameters!of!the!columns!in!the!upper!and!lower!colonnades!it!is!obvious!that!there!was!a!great!discrepancy!in!cooling!rates.!! In!other!outcrops,!such!as!the!western!face!of!the!Daisy!Lake!outcrop!(Fig.!6.5),!the!column!interface!is!40%!up!from!the!lower!boundary!(it!would!be!50%!for!equal!amounts!of!heat!flow).!!The!semi>infinite!slab!model!in!Fig.!6.5!shows!an!example!of!this!type!of!outcrop,!with!two!different!h!factor!values.!!The!value!for!the!lower!boundary!is!3,!while!the!value!for!the!upper!boundary!is!25,!which!is!8.3!times!that!of!the!lower!boundary.!!The!column!interface!for!this!model!is!located!42%!up!from!the!lower!boundary.!!This!shows!that!the!amount!of!heat!lost!through!the!upper!boundary!of!a!flow!must!be!significantly!greater,!approximately!8!to!9!times!greater,!than!the!heat!lost!through!the!lower!boundary!in!order!to!have!a!significant!effect!on!the!location!of!the!column!interface.!! Another!influence!of!this!non>linear!relationship!between!heat!and!change!in!flow!structure!is!seen!in!the!relationship!between!the!planarity!of!the!flow!base!and!the!column!interface.!!The!western!face!of!the!Railroad!Quarry!outcrop!1!shows!a!very!planar!column!interface!despite!an!undulating!flow!bottom,!with!one!particularly!high!amplitude!change!in!the!flow!bottom!geometry!(Fig.!6.6).!!However,!this!change!in!flow!bottom!geometry!does!not!have!an!effect!on!the!location!of!the!column!interface!within!the!outcrop.!!A!model!of!similar!geometry!to!this!outcrop!(Fig.!6.6)!shows!that!a!modeled!change!in!flow!bottom!geometry!also!has!very!little!effect!on!the!location!of!the!column!interface.!!This!is!partially!due!to!averaging!effects!of!the!overall!lower!boundary,!but!also!likely!due!to!the!large!heat!capacity!and!low!thermal!conductivity!of!rock.!!Any!deviations!from!a!planar!surface!have!minimal!impact!on!the!column!interface,!simply!because!the!effects!are!quickly!reduced!by!the!surrounding!material.!This!reduces!the!effect!that!small!wavelength!changes!in!the!boundaries!have!on!the!column!interface,!even!if!these!changes!are!quite!large!in!amplitude.!!This!further!shows!that!the!models!accurately!represent!the!cooling!lava!flows.!! There!is!a!limit!to!the!effective!amount!of!heat!that!a!flow!can!lose!during!a!given!time.!!Beyond!a!certain!h!factor!value,!there!is!no!additional!cooling!effect!on!the!flow.!!This!is!because!the!thermal!diffusivity!of!the!flow!is!the!limiting!factor,! !! 103! rather!than!the!cooling!efficiency!of!the!bounding!medium.!!Fig.!6.7!shows!that!for!h!factors!of!6000!and!1000,!there!is!no!appreciable!change!in!lava!temperature.!!Fig.!6.8!shows!that!below!an!h!factor!of!70!is!when!changing!h!factor!values!start!to!affect!the!internal!temperature!of!the!flow!over!a!given!time!of!900,000!seconds,!or!10.4!days.!!The!difference!is!slight,!but!measureable.!!See!Appendix!A!for!comparison!of!all!h!factor!values!for!a!single!model!with!identical!boundary!conditions.!! One!possibility!for!the!large!disparity!between!the!heat!flow!from!the!top!and!bottom!colonnades!could!be!due!to!a!“permeability!network”!on!the!top!surface.!!As!the!surface!cools!and!forms!cracks!within!the!upper!surface,!fluids!are!able!to!penetrate!the!sub>millimeter!vacancies!and!accelerate!cooling!via!convection.!!Even!with!only!air!present!the!cooling!will!be!accelerated,!but!if!water!is!present,!the!cooling!of!the!flow!will!increase!dramatically.!!As!the!flow!continues!to!cool!and!the!cracks!propagate!further,!the!fluids!also!extend!deeper!into!the!flow!and!continue!to!accelerate!cooling.!!This!produces!a!positive!feedback!loop,!which!continues!until!the!quickly!cooling!upper!colonnade!intersects!the!lower!colonnade.!!Thus!the!top!surface!is!able!to!release!a!much!greater!amount!of!heat!than!the!lower!surface,!partly!due!to!the!boundary!conditions,!but!also!due!to!the!convective!cooling!through!this!permeability!network.! 6.1.1& Paleoenvironmental&Conditions&Based&on&Column&Geometries&! The!difference!in!column!diameters!in!the!upper!and!lower!colonnade,!as!well!as!the!unequal!proportions!of!upper!and!lower!colonnades!in!many!of!the!outcrops,!definitively!show!that!the!boundary!conditions!are!not!identical!for!all!sides!of!the!outcrops.!!However,!they!do!not!define!exactly!what!the!boundary!conditions!are.!!The!relative!size!and!orientation!of!columns!within!the!outcrops!give!clues!to!the!boundary!and!paleoenvironmental!conditions!into!which!these!flows!erupted.!! For!both!the!eastern!Pinecrest!outcrop!(Fig.!3.10)!and!the!western!face!of!the!Daisy!Lake!outcrop!(Fig.!6.2),!the!upper!colonnade!is!much!thicker,!up!to!twice!as!thick,!as!the!lower!colonnade.!!Based!on!numerical!modeling,!the!heat!flow!through!the!upper!boundary!may!have!to!be!as!high!as!25!times!the!heat!flow!through!the! !! 104! lower!boundary!in!order!to!create!such!differences!in!colonnade!thicknesses.!!While!lower!differences!in!heat!flow!may!be!explained!simply!by!convective!atmospheric!cooling!on!the!upper!boundary,!a!difference!of!25!times!is!more!likely!due!to!additional!factors,!such!as!water!infiltration!along!joint!surfaces.!!This!implies!that!either!there!was!ice!that!was!melted!and!flowed!along!the!top,!but!not!the!bottom,!of!the!lava!flow,!or!that!the!flow!was!precipitated!upon.!! Railroad!Quarry!outcrop!6!is!unique!among!the!outcrops!in!this!study,!in!that!it!forms!a!cliff!tens!of!meters!high,!and!while!the!lower!section!of!the!outcrop!is!composed!of!large,!vertical!columns,!the!upper!section!is!composed!of!narrow,!horizontal!columns!(Fig.!6.3).!!No!colonnade!interface!is!seen!in!this!outcrop,!as!the!lower!columns!simply!seem!to!change!propagation!direction!from!vertical!to!horizontal.!!The!most!likely!explanation!for!the!formation!of!this!outcrop!is!that!the!flow!was!impounded!against!ice!in!the!valley.!!This!could!give!extremely!high!cooling!rates!on!the!lateral!flow!boundary,!due!to!meltwater,!while!conceivably!the!lower!boundary!of!the!flow!experienced!more!typical!slow,!conductive!cooling!into!the!ground!surface.!!If!the!original!contact!with!the!valley!ice!eroded!away!(which!it!likely!would,!since!most!rapidly!cooled!flow!boundaries!are!brittle,!glassy,!and!fragile),!this!could!leave!an!outcrop!where!the!columns!propagating!upwards!from!the!lower!boundary!meet!columns!propagating!inwards!from!the!lateral!boundary,!similar!to!a!section!of!the!slab(corner!forward!model!(Figs.!4.2!&!4.6).!!The!curving!columns!are!certainly!due!to!the!interaction!of!two!boundaries,!but!the!difference!in!diameter!of!the!columns!involved!points!to!boundaries!with!vastly!different!cooling!rates.! 6.1.2& Rules&for&Columns&! All!these!observations!lead!to!a!set!of!“rules”!for!column!formation.!!These!are!a!set!list!of!principles!that,!based!on!the!above!evidence!and!previous!work,!columnar!joints!“follow.”!!!! !! 105! 1.( Columns(form(parallel(to(heat(flow(! As!lava!flows!cool,!they!decrease!in!volume.!!In!an!infinite!slab!model,!the!vertical!aspect!of!this!volume!change!can!be!accommodated!by!viscous!flow!of!the!still!warm!interior.!!However,!the!horizontal!aspect!of!the!volume!change!cannot!be!accommodated!by!viscous!flow,!since!all!the!surrounding!material!is!brittle!as!well.!!Thus!tensile!joints!form,!and!as!the!cooling!front!propagates!into!the!interior!of!the!flow,!so!do!the!columnar!joints.!!Thus!columnar!joints!propagate!parallel!to!heat!flow.!!This!rule!is!often!misstated!as!“columns!form!perpendicular!to!the!cooling!surface.”!!While!this!is!often!true!near!the!boundaries!of!flows,!the!presence!of!curving!columns!within!both!the!models!and!outcrops,!which!form!parallel!to!heat!flow!and!not!perpendicular!to!the!cooling!surface,!shows!that!this!statement!is!not!true.!! 2.( Column(diameter(is(inversely(proportional(to(cooling(rate(! As!covered!in!Chapter!2,!quicker!cooling!creates!columns!with!smaller!diameters.!!Though!quantitative!data!are!not!available!for!prescribing!an!exact!cooling!environment!based!on!a!specific!column!diameter,!columns!under!10!cm!in!diameter!generally!indicate!extremely!rapid!cooling,!perhaps!by!water,!while!columns!over!a!meter!in!diameter!generally!indicate!slow!cooling,!possibly!through!a!non>convective!boundary,!such!as!underlying!rock.!! 3.( Extremely(rapid(cooling(forms(poorly$organized(columns(! During!high!rates!of!cooling,!abundant!thermal!stresses!keep!columns!from!becoming!well>organized.!!With!high!thermal!stresses,!the!joints!propagate!so!quickly!that!there!is!no!need!to!conserve!energy,!and!the!joints!remain!four>sided!and!somewhat!chaotic.!!This!was!evident!in!the!high!temperature!experiments!in!Chapter!5,!and!the!lack!of!organized!columns.!!With!slower!cooling!rates!and!slightly!less!thermal!stress,!there!is!more!time!between!increments!of!joint!formation,!and!the!system!finds!the!most!energetically!effective!direction!in!which!to!fracture.!Because!hexagons!necessitate!the!least!amount!of!energy!to!form,!slower!cooling!rates!form!hexagonal!columns.! !! 106! 4.( Columns(form(in(discrete(time(steps(! It!is!important!to!remember!that!columnar!joints!do!not!all!form!simultaneously;!they!form!over!a!period!of!time.!!This!gives!the!environment!time!to!change!during!the!formation!of!the!columns.!!An!example!of!this!would!be!if!a!flow!starts!cooling!and!forming!columnar!joints,!and!at!some!later!time,!the!surface!of!the!flow!is!inundated!with!water,!which!travels!down!already!formed!joints.!!This!would!cause!a!drastic!change!in!both!the!cooling!rate!and!cooling!boundaries!of!the!flow,!forming!a!set!of!columns!with!different!diameter!and!trends!in!the!interior!of!the!flow.!!The!only!way!to!explain!this!is!through!the!transient!nature!of!columnar!jointing.!! 5.( Columns(only(coalesce,(never(bifurcate(! Column!diameter!is!inversely!proportional!to!the!cooling!rate,!as!mentioned!above,!and!a!consequence!of!this!rule!is!that!columns!can!only!coalesce.!!As!the!cooling!rate!decreases!within!the!interior!of!a!flow,!columns!begin!to!increase!in!diameter,!and!thus!joints!will!terminate,!and!cause!columns!to!coalesce.!!In!order!to!have!columns!that!bifurcate,!the!cooling!rate!would!need!to!increase!on!the!interior!of!the!flow,!without!changing!the!cooling!boundaries.!!This!is!not!possible,!so!the!idea!of!bifurcating!columns!can!be!ruled!out.!!The!cooling!rate!can!be!increased!in!an!already!cooling!flow,!but!this!necessarily!changes!the!cooling!boundaries.!!For!example,!water!influx!can!occur!along!already!formed!columnar!joints!and!increase!the!cooling!rate!of!the!interior!of!the!lava!flow,!but!this!causes!the!cooling!boundary!to!change!from!the!top!of!the!flow!to!the!columnar!joint!surfaces.!!This!would!cause!new!joints!to!form,!and!though!they!would!be!smaller!in!diameter,!they!would!be!completely!different!joints.!!The!older!joints!still!would!not!bifurcate.!! 6.( Columns(curve(only(when(affected(by(multiple(boundaries(! If!only!one!boundary!defines!the!cooling!history!for!a!given!set!of!columns,!those!columns!will!all!have!perfectly!linear!geometries.!!This!is!because!the!heat!flow!will!be!perpendicular!to!the!cooling!boundary,!and!with!no!other!boundaries!affecting!the!direction!of!the!heat!flow,!the!columns!will!not!curve.! !! 107! ! If!more!than!one!boundary!is!present,!this!will!cause!the!thermal!gradient!isograds!to!curve.!!Since!the!heat!flow!is!perpendicular!to!the!isograds,!this!causes!the!heat!flow!vectors!to!curve,!and!thus!the!!columns!will!curve!as!well.!!Curving!columns!are!visible!in!outcrops!such!as!the!western!face!of!Railroad!Quarry!outcrop!1,!the!southeastern!face!of!Railroad!Quarry!outcrop!3,!and!the!eastern!face!of!Railroad!Quarry!outcrop!6.!!These!outcrops!all!indicate!multiple!cooling!boundaries!affecting!the!column!formation!geometry.!! Ǐ 700 200 300 400 500 600 100 30% 70% -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3 !Figure!6.4.!!The!upper!boundary!of!this!model!has!an!h!factor!value!of!25,!while!the!lower!boundary!has!an!h!factor!value!of!1.!!With!a!convective!heat!transfer!value!25!times!greater!on!top,!this!enables!the!upper!colonnade!to!be!more!than!twice!as!thick!as!the!lower!colonnade.!!Model!run!time!is!1260000!s.!! !! 108! X (m) Y (m) Ǐ -3-5 -1 0 1 2 3 -2 1 432 700 100 200 300 400 500 600 -3 -2 -4 0-1 5 A B !Figure!6.5.!!The!upper!photo!is!of!the!western!face!of!the!Daisy!Lake!outcrop.!!It!shows!a!section!of!that!face!where!the!upper!colonnade!is!approximately!60%!of!the!thickness!of!the!flow.!!This!locates!the!column!interface!40%!of!the!way!up!from!the!flow!bottom,!indicated!by!the!dashed!line.!!The!forward!model!is!based!on!this!outcrop,!and!has!differing!boundary!conditions!on!the!top!and!bottom!that!cause!the!column!interface!to!occur!42%!of!the!way!up!from!the!lower!boundary.!!The!h!factor!value!for!the!upper!boundary!is!25,!and!the!h!factor!value!for!the!lower!boundary!is!3.!!Model!run!time!is!900000!s.! !! 109! !Figure!6.6.!!Top!image!is!a!panorama!of!the!western!face!of!Railroad!Quarry!outcrop!1.!!Dashed!lines!show!the!bottom!flow!boundary!and!the!column!interface.!!The!black!arrow!shows!a!high!amplitude!change!in!the!flow!base!boundary!geometry,!but!there!is!no!change!in!the!column!interface!geometry!above!that!location.!!The!bottom!image!is!a!model!of!the!same!outcrop,!with!a!dashed!line!showing!the!location!of!the!column!interface.!!Despite!the!large!change!in!flow!bottom!geometry,!the!location!of!the!column!interface!does!not!change!significantly.!!The!boundary!conditions!for!the!model!were!h=20,!T=25˚C!on!top;!h=60,!T=1˚C!on!the!sides;!h=3,!T=25˚C!on!bottom.!!The!arrows!in!this!model!do!not!accurately!depict!the!heat!flow!at!the!column!formation!temperature,!so!the!size!of!the!arrows!should!be!disregarded,!but!they!do!still!show!the!column!formation!direction.!!Model!run!time!is!720000!s.!! !! 110! h facto r value  = 1000 h facto r value  = 6000 X (m) Y (m) Ǐ -3-5 -1 0 1 2 3 -2 1 432 100 200 300 400 500 600 -3 -2 -4 0-1 5 X (m) Y (m) Ǐ -3-5 -1 0 1 2 3 -2 1 432 100 200 300 400 500 600 -3 -2 -4 0-1 5 !Figure!6.7.!!The!top!model!has!an!h!factor!value!of!6000,!while!the!bottom!model!has!an!h!factor!value!of!1000.!!These!models!were!run!for!identical!times!(900,000!seconds,!or!10.4!days),!and!there!is!no!difference!in!temperature!profiles!between!the!two!(arrows),!despite!the!large!difference!in!h!factor!values.!!The!cooling!rate!is!limited!by!the!thermal!diffusivity!of!the!flow!itself.! !! 111! h facto r value  = 70 h facto r value  = 25 X (m) Y (m) Ǐ -3-5 -1 0 1 2 3 -2 1 432 100 200 300 400 500 600 -3 -2 -4 0-1 5 X (m) Y (m) Ǐ -3-5 -1 0 1 2 3 -2 1 432 100 200 300 400 500 600 -3 -2 -4 0-1 5 !Figure!6.8.!!Top!forward!model!has!h!values!of!70!on!all!sides,!whereas!the!bottom!forward!model!has!h!values!of!25!on!all!sides.!!The!models!were!run!for!identical!amounts!of!time!(900,000!seconds,!or!10.4!days),!and!there!is!a!small,!but!measureable!difference!in!the!maximum!temperature!of!the!models,!as!shown!by!the!location!of!the!600!˚C!marker!on!the!temperature!scale!on!the!right!of!the!models!(arrows).!!Comparing!models!with!h!values!above!approximately!100,!there!does!not!seem!to!be!a!difference!between!temperature!profiles!in!the!models.!! !! 112! 6.2.& Summary&of&Experiments&! The!textural!experiments!in!this!thesis!demonstrate!that!it!is!possible!to!synthesize!joints!within!laboratory!settings.!!These!joints!are!interpreted!as!thermal!contraction!joints,!directly!comparable!to!the!columnar!joints!found!in!flows!and!intrusions!of!various!compositions!around!the!world.!! The!joints!in!the!experiments!generally!form!perpendicular!to!the!cooling!surfaces,!but!the!joints!are!not!as!well!organized!as!those!usually!found!in!nature.!!The!best!explanation!for!this!is!that,!due!to!the!small!size!of!the!samples,!and!the!necessity!of!extremely!high!cooling!rates!in!order!to!produce!the!required!thermal!gradients,!the!heat!flow!vectors!within!the!samples!were!never!organized!into!a!regular!geometry.!!Rapid!temperature!changes!did!not!allow!the!samples!to!settle!into!organized!temperature!profiles!like!those!shown!in!the!forward!models.!!Instead,!the!thermal!stresses!inside!the!samples!were!so!large!and!poorly!organized!that!the!cooling!material!simply!jointed!in!the!direction!that!would!relieve!the!most!stress,!even!if!the!joint!did!not!break!parallel!to!the!heat!flow!direction!at!that!point.!! Despite!the!lack!of!well>organized!joints,!both!the!textural!and!thermal!gradient!experiments!allow!some!interesting!conclusions!to!be!made.!!As!shown!by!the!textural!experiments,!not!all!cooling!conditions!produce!columnar!joints.!!In!general,!high!cooling!rates!produce!joints,!while!low!cooling!rates!do!not,!especially!in!the!small!sample!sizes!used!in!this!study!(approximately!10!mL).!!This!is!corroborated!by!the!thermal!gradient!experiments.!!The!experiments!that!experienced!the!lowest!cooling!rates,!the!oven!and!air!cooled!experiments,!did!not!produce!columnar!joints,!while!the!water!cooled!experiments,!with!the!highest!cooling!rates,!did!produce!columnar!joints.!! According!to!the!thermocouple!experiments,!the!experiments!that!generally!formed!columnar!joints!(those!fully!and!partially!submerged!in!water)!had!internal!thermal!gradients!of!between!6.14!and!6.94˚C!mm>1,!and!cooling!rates!of!between!12.9!and!32.8!˚C!s>1.!!The!air>convection!and!oven!cooled!experiments!had!much!lower!thermal!gradients!and!cooling!rates,!on!the!order!of!less!than!1!up!to!3˚C!!!mm>1,!and!cooling!rates!ranging!from!.08!to!2.6!˚C!s>1.!!Thus,!of!the!experiments! !! 113! carried!out!in!this!study,!only!experiments!with!thermal!gradients!between!6!and!7˚C!mm>1!and!cooling!rates!between!12.9!to!32.8!˚C!s>1!were!able!to!form!columnar!joints.!!This!link!between!columnar!joint!formation!and!both!the!thermal!gradient!and!cooling!rate!is!obviously!dependant!on!the!size!of!the!sample,!since!jointed!flows!found!in!nature!must!have!experienced!less!extreme!thermal!gradients.!! Though!the!experiments!show!that!a!certain!thermal!gradient!is!required!during!cooling!to!produce!columnar!joints,!just!as!important!as!the!magnitude!of!the!gradient!is!the!temperature!at!which!it!occurs.!!As!mentioned!in!Chapter!4,!early!experiments!that!were!removed!from!the!furnace!at!1000˚C!and!immediately!quenched!did!not!produce!columnar!joints,!but!rather!turned!completely!to!glass,!and!accommodated!change!in!temperature!by!viscous!flow,!forming!a!“cone!of!depression”!(Fig.!6.9).!!Without!measurements,!the!thermal!gradients!in!these!early!experiments!cannot!be!quantified,!but!it!is!safe!to!assume!that!because!the!conditions!of!cooling!were!the!same,!the!gradients!are!similar!to!those!of!the!water>cooled!thermal!gradient!experiments.!!So!despite!the!fact!that!the!cooling!conditions!were!the!same,!because!the!starting!temperature!was!dissimilar,!columnar!joints!did!not!form.!! The!starting!temperature!for!the!experiments!had!to!be!at!a!subliquidus!temperature,!due!to!the!nature!of!the!relationship!between!the!rate!of!cooling!and!the!relaxation!timescale.!!High!temperature!lavas,!even!when!cooled!very!quickly,!remain!above!the!column!formation!temperature!(or!glass!transition!temperature!–!they!are!similar)!for!long!enough,!while!the!timescale!of!relaxation!is!still!short!enough,!that!most!of!the!volume!loss!is!accommodated!through!viscous!flow,!and!no!joints!form.!!Also,!since!it!is!a!second>order!phase!transition,!there!is!no!volume!loss!associated!with!the!transition!from!melt!to!glass.!! Even!though!at!lower!starting!temperatures!some!volume!loss!has!already!occurred,!when!the!melt!and!crystal!mixture!is!cooled!quickly!from!the!lower!temperatures,!the!relaxation!timescale!is!somewhat!longer.!!As!the!sample!cools,!there!is!no!low!viscosity!free!surface!to!accommodate!viscous!flow,!and!the!relaxation!rate!is!longer!than!the!cooling!rate.!!Thus,!tensile!stress!accumulates,!and!columnar!joints!form!in!response.! !! 114! ! Another!reason!for!the!lower!starting!temperature!for!the!experiments!is!to!have!a!non>zero!percentage!of!crystals!mixed!in!with!the!melt.!!Crystals!have!much!higher!thermal!expansion!values!than!glass!does,!so!while!glass!may!not!change!much!in!volume!with!a!decrease!in!temperature,!the!crystals!within!the!cooling!material!will.!!According!to!Austin!(1952),!quartz!has!a!thermal!expansion!coefficient!of!approximately!83!x!10>6!˚C>1!between!0!and!600˚C,!while!Arndt!and!Häberle!(1973)!show!that!synthetic!glasses!with!plagioclase>like!compositions!have!thermal!expansion!coefficients!of!between!6!and!7!x!10>6!˚C>1!given!temperatures!from!20!to!600˚C.!!These!measurements!are!below!the!glass!transition!temperature,!and!there!is!a!discontinuous!change!in!thermal!expansion!at!the!glass!transition!temperature.!!Though!quartz!is!not!found!in!abundance!in!the!synthetic!basalts!in!this!study,!these!values!show!that!minerals!can!contract!greater!than!10!times!as!much!as!the!non>crystal!matrix!of!the!material.!!This!could!have!a!large!effect!on!the!tensile!stress!buildup!in!the!experiments,!and!in!natural!lava!flows!in!the!field.!! The!best!explanation!for!this!temperature!dependency!is!that!column!formation!is!not!only!dependent!on!the!thermal!gradient!and!cooling!rate!of!the!material!at!the!column!formation!temperature,!but!is!also!dependent!on!the!viscosity!of!the!material!when!the!required!thermal!gradient!is!present.!!If,!in!these!experiments,!the!required!6>7˚C!mm>1!thermal!gradient!occurs!while!the!temperature!is!too!high,!around!1000˚C,!the!cooling!material!still!have!a!very!low!viscosity,!and!be!able!to!accommodate!much!of!the!change!in!volume!by!viscous!flow.!!If!the!thermal!gradient!remains!the!same!down!to!the!column!formation!temperature,!the!thermal!stresses!required!may!not!be!present,!since!much!of!the!stress!has!already!been!reduced!by!viscous!flow.!! The!conclusion!reached!from!the!experiments!is!that!a!specific!thermal!gradient!and!cooling!rate!is!required!for!columnar!joints!to!form,!and!in!the!case!of!these!samples!the!required!gradient!was!found!to!be!between!6!and!7˚C!mm>1,!and!the!required!cooling!rate!to!be!between!12.9!and!32.8!˚C!s>1.!!However,!this!gradient!also!needs!to!occur!within!a!specific!temperature!range!for!the!joints!to!form,!which!was!approximately!between!700!and!800˚C.!!Below!the!required!thermal!gradient,!or!outside!the!correct!temperature!range,!columnar!joints!will!not!form.! !! 115! 100 mm !Figure!6.9.!!The!photograph!on!the!right!shows!experiment!2012>26!with!the!so!called!“cone!of!depression,”!while!the!schematic!on!the!left!shows!a!cross!sectional!view!of!the!sample.!!The!glassy!surface!of!the!sample!makes!informative!photos!difficult!to!obtain.!!The!surface!of!the!sample!slopes!down!towards!the!center,!where!it!comes!to!a!blunted!point.!!The!schematic!is!drawn!to!scale,!and!there!is!no!vertical!exaggeration!of!the!slope!of!the!cone!in!the!figure.!!Experiment!2012>26!was!quenched!specifically!for!this!photograph,!and!did!not!have!this!form!during!the!actual!thermal!gradient!experiments.! 6.3.& Further&Work&! This!thesis!has!an!experimental!program!that!shows!what!thermal!gradients!and!cooling!rates!form!columnar!joints!in!a!certain!sample!size,!but!this!can!be!improved!upon!with!further!work.!!An!expanded!experimental!grid,!containing!a!range!of!larger!sample!sizes,!would!allow!slower!cooling!rates!to!be!used,!since!the!columns!would!not!need!to!be!created!on!such!a!small!scale.!!In!addition,!a!larger!range!of!starting!temperatures!would!better!define!the!upper!and!lower!limits!on!the!column!formation!temperature.!!This!would!give!a!better!indication!of!what!conditions!columnar!joints!form!under.!! The!forward!modeling!could!also!be!improved,!taking!more!variables!into!account,!such!as!the!heat!of!crystallization!and!tensile!stresses!in!the!cooling!flow.!!It!could!also!be!modified!to!model!a!three>dimensional!flow.!!However,!any!of!these!additions!would!require!an!enormous!amount!of!coding!and!a!high!degree!of!skill,!and!is!beyond!the!scope!of!this!thesis.! !! 116! ! Though!the!Whistler!field!area!has!a!range!of!well>preserved!columns!with!a!large!variety!of!flow!boundary!geometries,!a!different!field!area!may!give!more!insights.!!A!larger!number!of!outcrops,!with!perhaps!simpler!geometries,!could!allow!comparison!of!small!differences!within!the!outcrops,!and!perhaps!tease!out!smaller!scale!effects!of!boundary!conditions!on!columnar!joint!formation.! !! 117! 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Appendix&A&–&Forward&Models& ! This!appendix!has!a!number!of!forward!models!with!various!h!factors!on!the!boundaries.!!They!show!the!effects!the!different!h!factor!values!have!on!the!temperature!profiles.!!Each!model!in!this!section!was!run!for!900,000!seconds,!and!the!size!of!the!flow!and!all!physical!properties!remain!the!same!for!all!models.!!! -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 100 200 300 400 500 600 X (m) Y (m) !Figure!A.1.!!Model!has!h!factor!value!of!6000.! !! 123! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 100 200 300 400 500 600 X (m) !Figure!A.2.!!Model!has!h!factor!value!of!1000.! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 100 200 300 400 500 600 X (m) !Figure!A.3.!!Model!has!h!factor!value!of!100.! !! 124! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 100 200 300 400 500 600 X (m) !Figure!A.4.!!Model!has!h!factor!value!of!70.! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 100 200 300 400 500 600 X (m) !Figure!A.5.!!Model!has!h!factor!value!of!25.! !! 125! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3 Ǐ 200 300 400 500 600 700 X (m) 100 !Figure!A.6.!!Model!has!h!factor!value!of!10.! Y (m) -5 -4 -3 -2 -1 0 1 2 3 4 5-3 -2 -1 0 1 2 3  Ǐ 600650 700 750 800 950 X (m) 500 550 850 900 !Figure!A.7.!!Model!has!h!factor!value!of!1.! !! 126! Appendix&B&–&MATLAB&Code& ! Most!of!the!forward!models!used!a!Matlab!Toolbox!add>on,!called!the!Partial!Differential!Equation!Toolbox.!!This!is!a!GUI!interface!in!which!the!user!can!create!shapes,!set!boundary!conditions!and!PDE!coefficients!and!parameters,!and!solve!for!a!given!amount!of!time.!!The!entirety!of!this!code!will!not!be!presented!here,!but!the!specifics!used!for!the!majority!of!the!forward!models,!along!with!other!MATLAB!codes!used,!are!presented.! B.1.& Finite&Slab&! This!code,!when!used!in!conjunction!with!the!PDE!Toolbox,!creates!and!solves!the!finite!slab!forward!model,!with!unique!boundary!conditions!for!the!top,!bottom,!and!lateral!boundaries.!!For!the!semi>infinite!slab,!slab!corner,!and!slab!side!models,!one!or!more!of!the!boundary!conditions!is!changed!so!no!heat!escapes!from!that!boundary.!! function pdemodel [pde_fig,ax]=pdeinit; pdetool('appl_cb',9); set(ax,'DataAspectRatio',[1 1 1]); set(ax,'PlotBoxAspectRatio',[3 2 1]); set(ax,'XLimMode','auto'); set(ax,'YLimMode','auto'); set(ax,'XTickMode','auto'); set(ax,'YTickMode','auto');  % Geometry description: pderect([-5 5 1.5 -1.5],'R1'); set(findobj(get(pde_fig,'Children'),'Tag','PDEEval'), 'String','R1')  % Boundary conditions: pdetool('changemode',0) pdesetbd(4,... 'neu',... 1,... '100',... '100*1') pdesetbd(3,... 'neu',... 1,... '3',... '3*25') pdesetbd(2,... !! 127! 'neu',... 1,... '100',... '100*1') pdesetbd(1,... 'neu',... 1,... '25',... '25*25')  % Mesh generation: setappdata(pde_fig,'Hgrad',1.3); setappdata(pde_fig,'refinemethod','regular'); setappdata(pde_fig,'jiggle',char('on','mean','')); pdetool('initmesh') pdetool('refine') pdetool('refine') pdetool('refine')  % PDE coefficients: pdeseteq(2,... '2',... '0.0',... '(0)+(0.0).*(0.0)',... '(2900).*(850)',... '0:1000:25*36000',... '1100',... '0.0',... '[0 100]')   % Solve parameters: setappdata(pde_fig,'solveparam',... str2mat('0','1032','10','pdeadworst',... '0.5','longest','0','1E-4','','fixed','Inf'))  % Plotflags and user data strings: setappdata(pde_fig,'plotflags',[1 1 1 1 3 1 1 1 0 0 0 201 1 1 0 1 0 1]); setappdata(pde_fig,'colstring',''); setappdata(pde_fig,'arrowstring','[cux;cuy]'); setappdata(pde_fig,'deformstring',''); setappdata(pde_fig,'heightstring','');  % Solve PDE: pdetool('solve') ! B.2.& Thermal&Gradient&! To!show!the!thermal!gradient!isograds,!in!addition!to!the!heat!flow!arrows!at!the!time!of!column!formation,!this!code!was!used.!!! !! 128! % Finds flowdata nearest to column formation temperature  % STEP 1 % SELECT 'EXPORT MESH' FROM 'MESH' MENU % % STEP 2 % SELECT 'EXPORT SOLUTION' FROM 'SOLVE' MENU   col=800; % column formation temperature  ut=pdeintrp(p,t,u); % turns node data u into triangle data ut for creating utx and uty vectors  flow=abs(col-ut); flow(1,:)=NaN; % sets emplacement temp space to NaN, otherwise find function gets confused  searchvector=zeros(size(flow,2),1); % sets the searchvector size  for i=1:size(flow,2)     searchvector(i,1)=find(min(flow(:,i))==flow,1,'first'); end % Finds the point in space and time at which flow temperature is closest to % column formation temperature and puts it into searchvector % If more than one point is returned, it only places first point into % searchvector  [ux,uy]=pdegrad(p,t,u(:,1)); % makes gradient of emplacement temperature (no gradient, only to find size % of ux and uy)  ux(2:size(u,2),:)=0; uy(2:size(u,2),:)=0; % creates gradient matrix, filling rows 2:end with zeros  for i=2:size(u,2)     [ux(i,:),uy(i,:)]=pdegrad(p,t,u(:,i)); end % fills in rest of gradients through time    utx=zeros(size(searchvector,1),1); uty=zeros(size(searchvector,1),1);   for i=1:size(searchvector,1) utx(i,1)=ux(searchvector(i)); uty(i,1)=uy(searchvector(i)); end  !! 129! flowdata=[utx,uty]; flowdata=flowdata';  % fills vectors utx and uty with heat flow direction at time of column % formation   % CONTOURING HEAT FLOW GRADIENT    % convert triangle data to node data   if size(flowdata,2)==size(t,2)     flowdata=pdeprtni(p,t,flowdata);   end    % Determine xy-grid from geometry:   xmin=min(p(1,t)); xmax=max(p(1,t));   ymin=min(p(2,t)); ymax=max(p(2,t));    % Set up gradient matrices, make sure that x and y directions match with   % the width and height of the flow - need (xmax-xmin)*na to create   % different delta lengths in x and y direction   na=(size(flowdata,1)/50);   x=linspace(xmin,xmax,(xmax-xmin)*na);   y=linspace(ymin,ymax,(ymax-ymin)*na);    uhat=tri2grid(p,t,flowdata(:,1),x,y);   vhat=tri2grid(p,t,flowdata(:,2),x,y);   fhat=intgrad2(uhat,vhat);  % Now set up like above but for arrows - use far large cell sizes, fewer % cells naquiver=5; xquiver=linspace(xmin,xmax,(xmax-xmin)*naquiver+1); yquiver=linspace(ymin,ymax,(ymax-ymin)*naquiver+1);    uhatquiver=tri2grid(p,t,flowdata(:,1),xquiver,yquiver);   vhatquiver=tri2grid(p,t,flowdata(:,2),xquiver,yquiver);   % % PLOTS! % pdeplot(p,e,t,'xydata',u(:,end-1)) hold on contour(x,y,fhat,8) colormap jet quiver(xquiver,yquiver,uhatquiver,vhatquiver) axis equal hold off !! 130! Appendix&C&–&Experiment&Photographs& ! This!appendix!contains!photographs!of!all!the!textural!experiments!conducted.!Because!most!samples!were!broken!in!half,!there!are!two!photographs!for!most!of!the!experiments,!each!photo!showing!one!half!of!the!sample.!!However,!some!samples!did!not!break!cleanly!down!the!middle,!so!there!may!be!more!than!two!photos!for!these!samples.!!In!some!cases,!the!sample!had!so!few!joints!in!it!that!the!weakest!surface!was!the!interface!between!the!synthetic!basalt!and!the!crucible.!!For!these!experiments,!the!entire!sample!can!be!seen!in!a!single!photo,!except!for!the!other!half!of!the!crucible,!which!only!has!a!thin!selvage!of!synthetic!basalt!on!it.!! !! 131! 	‹‰—”‡ǤͳǤš’‡”‹‡–ʹͲͳʹǦͲͷǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†˜‹ƒˆ‘”…‡†ƒ‹”…‘˜‡…–‹‘Ǥ Š‡•ƒ’Ž‡†‹†‘–„”‡ƒ…Ž‡ƒŽ›ƒ…”‘••‹–•‹††Ž‡ǡƒ†‹•–‡ƒ†„”‘‡‡ƒ”–Š‡…”—…‹„Ž‡™ƒŽŽˆ‘”—…Š ‘ˆ–Š‡•ƒ’Ž‡ǤŠ‡•ƒ’Ž‡‡š–‡†•–‘™ƒ”†•–Š‡˜‹‡™‡”ƒ’’”‘š‹ƒ–‡Ž›ͺ‹Ǥ 	‹‰—”‡ǤʹǤš’‡”‹‡–ʹͲͳʹǦͲ͵Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒˆ‘”…‡†ƒ‹”…‘˜‡…–‹‘Ǥ‘ …‘‘Ž‹‰Œ‘‹–•‹–‡”•‡…–‹‰–Š‡˜‹‡™‹‰•—”ˆƒ…‡ƒ”‡’”‡•‡–Ǥ A B A B 100 mm 100 mm 100 mm 100 mm !! 132! 	‹‰—”‡Ǥ͵Ǥš’‡”‹‡–ʹͲͳʹǦͲͶǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹ ™ƒ–‡”Ǥƒ’Ž‡„”‘‡‹–‘•‡˜‡”ƒŽ’‹‡…‡•ǡ–Š‡Žƒ”‰‡•–‘ˆ™Š‹…Šƒ”‡•Š‘™Ǥƒ†•Š‘™‹†‹˜‹†—ƒŽ …Š—•‘ˆ•ƒ’Ž‡–Šƒ–„”‘‡‘ˆˆƒˆ–‡”…‘‘Ž‹‰Ǥ 	‹‰—”‡ǤͶǤš’‡”‹‡–ʹͲͳʹǦͳ͸Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹ ™ƒ–‡”Ǥƒ’Ž‡„”‘‡‹–‘ƒ›’‹‡…‡•ǡ–Š‡Žƒ”‰‡•–‘ˆ™Š‹…Šƒ”‡•Š‘™Ǥ•Š‘™•–Š‡Žƒ”‰‡•–‹–ƒ…– •ƒ’Ž‡’‹‡…‡ǡ™Š‹Ž‡ƒ†•Š‘™–Š‡•ƒ‡ˆ”ƒ‰‡–ˆ”‘–™‘†‹ˆˆ‡”‡–ƒ‰Ž‡•Ǥ”‰ƒ‹œƒ–‹‘‘ˆ Œ‘‹–•‹–‘…”—†‡…‘Ž—•‹•˜‹•‹„Ž‡‹–Š‡•‡’Š‘–‘•ǡ‡•’‡…‹ƒŽŽ›‹–Š‡—’’‡”Ž‡ˆ–…‘”‡”‘ˆǤ–Š‡ „ƒ…‰”‘—†‘ˆƒ”‡‹ŽŽ‹‡–‡”ƒ”•‘ƒ”—Ž‡”ˆ‘”ƒ††‹–‹‘ƒŽ•…ƒŽ‡Ǥ 100 mm 40 mm 100 mm 40 mm 20 mm 40 mm A CB B C A !! 133! 	‹‰—”‡ǤͷǤš’‡”‹‡–ʹͲͳʹǦͲ͸Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹ Ž‹“—‹†‹–”‘‰‡Ǥ‘…‘‘Ž‹‰Œ‘‹–•ƒ”‡’”‡•‡–™‹–Š‹–Š‡•ƒ’Ž‡Ǥ 	‹‰—”‡Ǥ͸Ǥš’‡”‹‡–ʹͲͳʹǦͲ͹Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹ Ž‹“—‹†‹–”‘‰‡Ǥ‘…‘‘Ž‹‰Œ‘‹–•ƒ”‡’”‡•‡–™‹–Š‹–Š‡•ƒ’Ž‡Ǥ BA A B 100 mm 100 mm 100 mm 100 mm !! 134! 	‹‰—”‡Ǥ͹Ǥš’‡”‹‡–ʹͲͳʹǦʹͳǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†ƒ–ͷǏ’‡”‹—–‡‹–Š‡Š‹‰Š –‡’‡”ƒ–—”‡ˆ—”ƒ…‡Ǥ‘…‘‘Ž‹‰Œ‘‹–•ƒ”‡’”‡•‡–‹–Š‡•ƒ’Ž‡ǡ–Š‘—‰Š•‘‡ˆ”ƒ…–—”‡•—”ˆƒ…‡•ƒ”‡ ˜‹•‹„Ž‡Ǥǡ–Š‡•ƒ’Ž‡‡š–‡†•–‘™ƒ”†•–Š‡˜‹‡™‡”ƒ’’”‘š‹ƒ–‡Ž›ͺǤ 	‹‰—”‡ǤͺǤš’‡”‹‡–ʹͲͳʹǦʹʹǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͲͲǏǡ…‘‘Ž‡†ƒ–ͷǏ’‡”‹—–‡‹–Š‡Š‹‰Š –‡’‡”ƒ–—”‡ˆ—”ƒ…‡Ǥ‘…‘‘Ž‹‰Œ‘‹–•ƒ”‡’”‡•‡–‹–Š‹••ƒ’Ž‡Ǥ 100 mm 100 mm 100 mm 100 mm A A B B !! 135! 	‹‰—”‡ǤͻǤš’‡”‹‡–ʹͲͳʹǦͳͷǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹water.  ‘‘Ž‹‰Œ‘‹–•ƒ”‡˜‹•‹„Ž‡‹„‘–Šƒ†ǡ’ƒ”–‹…—Žƒ”Ž›ƒ”‘—†–Š‡‡†‰‡•‘ˆ–Š‡•ƒ’Ž‡Ǥ 	‹‰—”‡ǤͳͲǤš’‡”‹‡–ʹͲͳʹǦͳ͹Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹ ™ƒ–‡”Ǥ‘‘Ž‹‰Œ‘‹–•˜‹•‹„Ž‡ǡ’ƒ”–‹…—Žƒ”Ž›‘–Š‡”‹‰Š–ŠƒŽˆ‘ˆ–Š‡•ƒ’Ž‡‹ǡƒ•™‡ŽŽƒ•‹–Š‡—’’‡” Ž‡ˆ–…‘”‡”‘ˆǤ 100 mm 100 mm 100 mm100 mm A A B B !! 136! 	‹‰—”‡ǤͳͳǤš’‡”‹‡–ʹͲͳʹǦͳ͵Ǥ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹water.  ‘‘Ž‹‰Œ‘‹–•ƒ”‡˜‹•‹„Ž‡‹„‘–Šƒ†ǡ’ƒ”–‹…—Žƒ”Ž›‡ƒ”–Š‡—’’‡”•—”ˆƒ…‡‘ˆ–Š‡•ƒ’Ž‡•ǡ ƒ†ƒŽ‘‰–Š‡Ž‡ˆ–‡†‰‡‘ˆ–Š‡•ƒ’Ž‡‹Ǥ 	‹‰—”‡ǤͳʹǤš’‡”‹‡–ʹͲͳʹǦͳͺǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ’ƒ”–‹ƒŽ•—„‡”•‹‘‹water.  ƒ’Ž‡„”‘‡‹–‘ƒ›’‹‡…‡•ǡ–Š‡Žƒ”‰‡•–‘ˆ™Š‹…Šƒ”‡•Š‘™Ǥ‘Ž—•˜‹•‹„Ž‡‘‡†‰‡•‘ˆ •ƒ’Ž‡•‹„‘–Šƒ†ǡ™‹–Š‡šŠ‹„‹–‹‰…‘Ž—ƒ”Œ‘‹–•ƒ•™‡ŽŽǤ 100 mm 100 mm 100 mm 100 mm 50 mm A A B B C !! 137! 	‹‰—”‡Ǥͳ͵Ǥš’‡”‹‡–ʹͲͳʹǦͳͳǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆͺͲͲǏǡ…‘‘Ž‡†˜‹ƒ…‘’Ž‡–‡•—„‡”•‹‘‹ ™ƒ–‡”Ǥ‘‘Ž‹‰Œ‘‹–•ƒ”‡˜‹•‹„Ž‡ǡ‡•’‡…‹ƒŽŽ›‹ǡ„‘–ŠƒŽ‘‰–Š‡‡†‰‡•ƒ†‹–Š‡…‡–‡”Ǥ 	‹‰—”‡ǤͳͶǤš’‡”‹‡–ʹͲͳʹǦͳʹǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͷͲǏǡ…‘‘Ž‡†˜‹ƒ…‘’Ž‡–‡•—„‡”•‹‘‹ ™ƒ–‡”Ǥ‘‘Ž‹‰Œ‘‹–•ƒ”‡˜‹•‹„Ž‡‹„‘–Šƒ†ǡ’ƒ”–‹…—Žƒ”Ž›‡ƒ”–Š‡—’’‡”•—”ˆƒ…‡‘ˆ–Š‡•ƒ’Ž‡•Ǥ 	‹‰—”‡ǤͳͷǤš’‡”‹‡–ʹͲͳʹǦͳͶǤ–ƒ”–‹‰–‡’‡”ƒ–—”‡‘ˆ͹ͲͲǏǡ…‘‘Ž‡†˜‹ƒ…‘’Ž‡–‡•—„‡”•‹‘‹water.  ‘‘Ž‹‰Œ‘‹–•ƒ”‡˜‹•‹„Ž‡‹„‘–Šƒ†ǡ’ƒ”–‹…—Žƒ”Ž›‡ƒ”–Š‡—’’‡”•—”ˆƒ…‡‘ˆ–Š‡•ƒ’Ž‡•Ǥ A A A B B B 100 mm 100 mm 100 mm100 mm 100 mm 100 mm !

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