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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)  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 )"and!thermal! ∂t  ∂T )!experienced!by!the!lava!flows!during!their!formation.!!High!temperature! ∂x € experimentation!involving!basalt!rock!samples!is!then!used!to!determine!the!cooling! gradients!(  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.!  !  ii!  )  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) )  iii)  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)  )  iv)  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)  !  )  v)  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) )  )  vi)  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)  )  vii)  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) )  viii)  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) ) )  )  ix)  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.)  )  x)  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.)  )  1)  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.)  )  2)  )  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.)  )  3)  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.)  )  4)  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 column interface  lower colonnade  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.)  )  5)  )  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.)  0  1  m  ) 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.) )  6)  )  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 ,)where)T)is) ∂t  temperature)and)t)is)time))result)in)columns)with)larger)diameters,)while)higher)cooling) rates)(larger)  ∂T ))result)in)columns)with)smaller)diameters)(e.g.,)Hetényi)et)al.,)2012).)) € ∂t  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).)  )  7)  )  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 ,)columns)more)often)comprise)square)cross)sections)than)columns)on)the)interior)of) ∂t ∂T the)flow,)where)the)more)mature)column)systems)have)experienced)a)lower) ,)and)are) ∂t €  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.)  )  8)  )  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.)) )  9)  )  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  1  m  )  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.)  ) )  10)  ) 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.)  )  11)  )  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,)wedgec shaped)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) )  12)  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)“splittingc temperature”)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) )  13)  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).)  )  14)  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.)  )  15)  )  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)spacec centered)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) )  16)  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.) )  17)  )  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.)  )  18)  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.)  )  19)  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.)  )  20)  )  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) Railroad)Quarry) Brandywine)Falls) Pinecrest) Daisy)Lake)  Latitude) 50˚04.4’)N) 50˚01.6’)N) 50˚00.3’)N) 49˚59.2’)N)  Longitude) 123˚05.5’)W) 123˚07.2’)W) 123˚07.9’)W) 123˚08.7’)W)  UTM)Zone) Easting) Northing) 10) 493441) 5546788) 10) 491405) 5541603) 10) 490565) 5539195) 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.)))  )  21)  1  2  Dais y La  3  ke  Whistler  4  Vancouver Georgia Strait  0  1  2  3  4 km  0  10  20  km  ) 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).)  )  22)  Brandywine Falls  1 2  ine ndy w Bra  Highway 99  Railroad Quarry  ek Cre  3 4  99  5  6  C heaka mu sR  iv e  r  7  Hi gh wa y  Esker-like outcrop  50 m  50 m  Pinecrest  Daisy Lake  9 ay hw g i H  Daisy Lake West  9  Pinecrest West  Hi gh w ay 99  Pi ne cr es  tE as  t  Daisy Lake East  Daisy Lake Daisy Lake 50 m  50 m  )  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.)  )  23)  A  B  ) Figure)3.3.))Thin)sections)of)the)Cheakamus)Valley)basalt.))A)is)in)planecpolarized)light,)and)B)is)in)crossc polarized)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.)  )  24)  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) )  25)  (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.)  Chevron  Fan  Basin  )  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).)  )  26)  ) 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.)  )  27)  ) 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) )  28)  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.) )  )  29)  0  30  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.)  )  30)  ) 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.)  )  31)  A  0  1 m  B  C  ) 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.)  )  32)  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) )  33)  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.)  )  34)  1  A  0.90  B  0.80  Whistler Field Area Snake River Plain  Upper Colonnade / Total  0.70  Watchung Group  0.60  Yakima Group  C  % Entablature  0.50 Railroad Quarry Outcrop 1  0.40 0.30 0.20 0.10 0  75 % 0  0.10  0.20  50 0.30  0.40  25 %  % 0.50  0.60  0.70  Lower Colonnade / Total  0% 0.80  0.90  1  )  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.)  ) )  )  35)  1 2  3  bedrock ) 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))  )  36)  A  B 1  2  3  separate 0  2  m  )  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.)  )  37)  Upper Colonnade Column Widths  A 120  Mean: 143 cm Median: 135 cm  Number of Columns  100  80  60  40  20  0 <30  <60  <90 <120 <150 <180 <210 <240 <270 <300 <330 <360 <390 <420  Width (cm)  Lower Colonnade Column Widths  B  20 18  Mean: 223 cm Median: 213 cm  Number of Columns  16 14 12 10 8 6 4 2 0 <30  <60  <90  <120 <150 <180 <210 <240 <270 <300 <330 <360 <390 <420  Width (cm)  )  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.  )  38)  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.)  )  39)  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) )  40)  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⋅ C p ⋅  ∂u = c⋅ ∇ 2 u ) ∂t  or)expanded)and)rearranged)(in)two)dimensions))  €  ∂u c % ∂ 2u ∂ 2u ( = ⋅' + * ∂t ρC p & ∂x 2 ∂y 2 ) )  For)a)complete)list)of)variables)used)in)these)equations,)see)Table)4.1.)  )  €  41)  )  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! Thermal)conductivity) Heat)transfer)coefficient) Heat)capacity) Density) Boundary)temperature) Emplacement)temperature) Boundary)normal)vector) Temperature) Temperature)gradient) Volume) € Heat) Length) Height) Time)  )  Symbol! c"  Value! 2)W)mc1)˚Cc1))  h" C p" ρ" u ∞" u i"  1c6000)W)mc2)˚Cc1) 850)J)kgc1)˚Cc1) 2900)kg)mc3) 1c25)˚C) 1100)˚C) )) )) )) )) )) )) )) ))  n) u" ∇u" V" Q" L" z" t"  Source! Touloukian)et)al.)(1989)) Recktenwald)(2006),)Keszthelyi) and)Denlinger)(1996)) Bouhifd)et)al.)(2007)) wet/dry)measurements) )) ) )) )) )) )) )) )) )) ))  42)  ) )  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)groundc lava)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).)  )  43)  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 = C p ⋅ 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.) € n  ∑Q  boundary i  = Total heat through boundary )  i=1  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.)  )  44)  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) )  45)  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)  )  46)  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)  )  47)  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.) )  )  48)  0.6 700 0.4 600 0.2  Y (m)  500 0 400 -0.2 300 -0.4  200  -0.6  100 -1  -0.8  -0.6  -0.4  -0.2  0  0.2  0.4  0.6  0.8  1  X (m) 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.!  49!  !  !  0.5 0.4  700  0.3 600 0.2 500  Y (m)  0.1  400  0 -0.1  300  -0.2 200 -0.3 100  -0.4 -0.5  -1.2  -1  -0.8  -0.6  -0.4  -0.2  0  0.2  X (m) 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.  50!  !  !  A  0.5 0.4  700  0.3 600 0.2 500  Y (m)  0.1  400  0 -0.1  300  -0.2 200 -0.3 100  -0.4 -0.5  -1  -0.5  0  0.5  X (m)  B  0.5 0.4  700  0.3 600 0.2 500  Y (m)  0.1 0  400  -0.1  300  -0.2 200  -0.3  100  -0.4 -0.5  -1  -0.5  0  0.5  X (m)  !  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.!  !  51!  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& & 1! 2! 3! 4! 5! 6! 7! 8! 9!  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)& 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 5! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 20! 1! 5! 1! 5! 1! 5! 1! 5! 1!  1! 2! 3! 4! 5! 6! 7! 8! 9!  time& step&(s)& 600! 2000! 600! 2000! 1000! 1000! 1000! 500! 600!  Trial&  total& y&size& total&area& time&(s)& x&size&(m)& (m)& (m2)& 720000! 4! 4! 16! 3600000! 8! 8! 64! 1080000! 4! 4! 16! 3600000! 8! 8! 64! 1800000! 16! 4! 64! 1440000! 16! 4! 64! 3600000! 16! 4! 64! 1800000! 6! 6! 36! 2160000! 6! 6! 36!  Q1DQend& Q&through& (J)& boundaries&(J)& 2.44E+10! 2.45E+10! 1.10E+11! 1.11E+11! 2.39E+10! 2.41E+10! 9.89E+10! 1.00E+11! 9.10E+10! 9.10E+10! 9.79E+10! 9.76E+10! 1.38E+11! 1.37E+11! 5.84E+10! 5.90E+10! 5.47E+10! 5.54E+10!  ! !  !  52!  Identical Boundary Condition Heat Change 1012  1011  1010 1010  1011  1012 i  ! 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.!!EdgeQ dependent!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.!! !  53!  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!edgeQ dependent!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.!!  !  54!  !  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.! !  !  55!  0.6 700 0.4 600  Y (m)  0.2 500 0 400 -0.2 300 -0.4 200 -0.6 -1  -0.8  -0.6  -0.4  -0.2  0  0.2  0.4  0.6  0.8  1  X (m) 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.!  56!  !  !  0.5 700  0.4 0.3  600  0.2 500  Y (m)  0.1 400  0 -0.1  300 -0.2 200  -0.3 -0.4 -0.5  100  -1.2  -1  -0.8  -0.6  -0.4  -0.2  0  0.2  X (m) 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.!  57!  !  !  A  0.5 0.4  700  0.3 600  Y (m)  0.2 0.1  500  0  400  -0.1 300 -0.2 200  -0.3 -0.4 -0.5  100  -1  -0.5  0  0.5  X (m)  B  0.5 0.4  700  0.3 600  Y (m)  0.2 0.1  500  0  400  -0.1  300  -0.2 200  -0.3 -0.4 -0.5  100  -1  -0.5  0  0.5  X (m)  !  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.!  !  58!  ! 1 700 0.8 0.6  600  0.4 500  Y (m)  0.2 400  0 -0.2  300  -0.4 200 -0.6 100  -0.8 -1 -1.5  -1  -0.5  0  0.5  1  1.5  X (m) 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.  59!  !  !  ! 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)& & h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& h&factor& T∞&(˚C)& 10! 70! 1! 500! 1! 3! 1! 11! 70! 1! 500! 1! 3! 1! 12! 70! 1! 500! 1! 3! 1! 13! 70! 25! 500! 1! 3! 25! 14! 7! 25! 40! 1! 1! 25! 15! 7! 25! 40! 1! 1! 25! 16! 7! 25! 40! 1! 1! 25! 17! 70! 25! 500! 1! 3! 25! 18! 70! 25! 500! 1! 3! 25! 19! 7! 25! 40! 1! 1! 25! time& total& total&area& Trial& Q1@Qend&(J)& step&(s)& time&(s)& x&size&(m)& y&size&(m)& (m2)& 10! 600! 1800000! 6! 6! 36! 5.75E+10! 11! 12! 13! 14! 15! 16! 17! 18! 19!  600! 1800000! 600! 600! 1000! 600! 2000! 2000! 1000! 1000!  900000! 900000! 1080000! 720000! 7920000! 7200000! 3600000! 3600000!  16!  4!  64!  9.88E+10!  4! 4! 4! 10! 40! 40! 8! 8!  4! 4! 4! 2! 10! 10! 8! 8!  16! 16! 16! 20! 400! 400! 64! 64!  2.62E+10! 2.60E+10! 2.51E+10! 2.60E+10! 5.01E+11! 5.53E+11! 1.07E+11! 9.89E+10!  Boundary&4&(Left)& h&factor& T@∞&(˚C)& 500! 1! 500! 1! 500! 1! 500! 1! 7! 1! 7! 1! 7! 1! 500! 1! 500! 1! 7! 1! Q&through& boundaries&(J)& 5.76E+10! 9.81E+10! 2.62E+10! 2.59E+10! 2.52E+10! 2.54E+10! 4.83E+11! 5.33E+11! 1.08E+11! 9.99E+10!  !  !  60!  ! Edge-Dependent Boundary Condition Heat Change 1012  1011  1010 1010  1011  1012 i  ! 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.!  !  61!  ! !  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!  !  62!  ! 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.!  !  63!  ! !  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! !  64!  ! 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.  !  65!  !  2.5  9000  2  8000  1.5 7000 1 6000  Y (m)  0.5 5000  0  -0.5  4000  -1 3000 -1.5 2000 -2 1000 -2.5 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  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.! 12000  2.5  2 10000 1.5  1 8000  Y (m)  0.5  0 6000 -0.5  -1  4000  -1.5  2000  -2  -2.5 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  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.!  !  66!  !  2  12000  1  10000  Y (m)  8000  0  6000  4000  -1 2000  -2  -5  -4  X (m)  -3  -2 !  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.!  !  !  67!  !  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).!!! !  !  68!  !  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! !  69!  ! 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! !  70!  ! 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.!  !  71!  ! 100  Crystal Percentage  80  60  40  20  0 1100  1000  900  800  750  700  ! 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.!  !  72!  ! 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! Oven!(5˚C!per!minute)!  800!  750!  700!  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!  !  73!  ! 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.! ! ! !  !  74!  ! 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!  !  !  75!  !  legend  0  melt  10  mm  thermocouples  cooling material  A  forced air convection  cooling surface  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.!  !  76!  !  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! !  77!  ! 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.  !  78!  !  0  5  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.!  !  79!  !  0  5  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.!  !  80!  !  A  0  5  mm  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.!  !  81!  !  A  0  5  mm  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.!  !  82!  ! 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.!  !  83!  ! !  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!  ! ! ! ! ! ! ! ! ! ! ! ! ! !  84!  ! 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.! Cooling! Maximum!Averaged!˚C!s>1! Maximum!Averaged!J!s>1! (Heat!Flow)! Experiment! Thermocouple! Mechanism! (∂T/∂t(Cooling!Rate)! oven! 1! >0.08! >0.83! 2012>21! oven! 2! >0.08! >0.81! oven! 1! >0.61! >6.11! 2012>22! oven! 2! >0.08! >0.80! air! 1! >2.6! >26.54! 2012>23! air! 2! >2.4! >24.70! 2012>24! 2! air! >6.2! >62.52! partial!sub.! 1! >14.5! >145.51! 2012>19! partial!sub.! 2! >12.9! >129.84! partial!sub.! 1! >15.3! >154.78! 2012>20! partial!sub.! 2! >20.5! >207.05! full!sub.! 1! >18.0! >181.21! 2012>25! full!sub.! 2! >24.3! >245.25! full!sub.! 1! >17.3! >172.64! 2012>26! full!sub.! 2! >32.8! >327.83!  !  !  85!  !  A  Experiment 2012-21 800  1  700  Temperature (C)  600  2  500  2  400  1  300  Max -1  200  Therm. 2: -0.08  100 0  0  1000  2000  3000  -1  4000  5000  6000  7000  Time (seconds)  B  Experiment 2012-22 800 700  2  Temperature (C)  600  1  500  2  400  1  300  Max -1  200  Therm. 2: -0.08  100 0  0  1000  2000  3000  -1  4000  5000  6000  7000  Time (seconds)  !  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.!  !  86!  !  A  Experiment 2012-23 800  Max  700 600  temperature (C)  1  -1  Therm. 2: -2.4  1  500  2  -1  2  400 300 200 100 0  0  50  100  150  200  250  300  350  400  450  500  time (seconds)  B  Experiment 2012-24 800 700  Max Therm. 2: -20.5  2  temperature (C)  600  1  -1  2  500 400 300 200 100 0  0  50  100  150  200  250  time (seconds)  300  350  400  450  500  !  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.!  !  87!  !  A  Experiment 2012-19 800  Max  700 600  temperature (C)  -1  2  Therm. 2: -12.9  1  500  2 1  -1  400 300 200 100 0  0  20  40  60  80  100  120  140  time (seconds)  B  Experiment 2012-20 800  2  700  -1  600  temperature (C)  Max  1  Therm. 2: -20.5  1 2  -1  500 400 300 200 100 0  0  20  40  60  80  100  120  140  time (seconds)  !  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.!  !  88!  !  A  Experiment 2012-25 800 700  Max  1  temperature (C)  600  Therm. 2: -24.3  2  500  1 -1  2  -1  400 300 200 100 0  0  20  40  60  80  100  120  140  time (seconds)  B  Experiment 2012-26 800  1  700  Max  1 -1  temperature (C)  600  2  Therm. 2: -32.8  2  -1  500 400 300 200 100 0  0  20  40  60  80  100  120  140  time (seconds)  !  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! !  89!  ! 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.! ! Maximum Temperature Difference 250  Oven cooled Air/convection cooled  200  Water cooled (sides and bottom) Water cooled (fully submerged) 150  100  50  0 2012-21  2012-22  2012-23  2012-19  Experiment  2012-20  2012-25  2012-26  !  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.!  !  90!  !  35  Negative Degrees C per second  30  Thermocouple 1 Thermocouple 2  25  20  15  10  5  0  2012-21  2012-22  oven cooled  2012-23  air cooled  2012-19  2012-20  partially submerged  2012-25  2012-26  fully submerged  !  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! !  91!  ! 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! !  92!  ! 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.! !  -1  )  25  20  Unjointed Jointed  15  Joint Forming Forming  10  Non-Joint Forming 5  0 0  5  10  15  20  25  30 -1  35  )  !  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.! !  93!  ! !  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! !  94!  ! 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! !  95!  ! 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.!  !  96!  !  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.! !  97!  ! !  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! !  98!  ! 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  0  1 m  !  Figure!6.2.!!Daisy!Lake!West!outcrop!showing!upper!and!lower!colonnade,!along!with!column! interface!zone!(bounded!by!dashed!lines).!  !  99!  !  0  1  m  ! 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! !  100!  ! 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! !  101!  ! 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,! !  102!  ! 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! !  103!  ! 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.”! ! ! ! !  104!  ! 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.! !  105!  ! 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.! !  106!  ! !  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.! ! 3 700  30%  70%  2  600  1  500  0  400  300  -1  200 -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  !  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.!  !  !  107!  !  A  B  3 700 2 600  Y (m)  1  500  0  400  300  -1  200 -2 100 -3 -5  -4  -3  -2  -1  0  X (m)  1  2  3  4  5  !  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.!  !  108!  !  ! 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.!  !  !  109!  Y (m)  h factor value = 6000  !  3  600  2  500  1  400  0  300  -1  200  -2  100  -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  3  600  2  500  1  Y (m)  h factor value = 1000  X (m)  400  0  300  -1  200  -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  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.!  !  110!  !  3  600  500  1  Y (m)  h factor value = 70  2  400  0  300  -1 200 -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  3 600  500 1 400  Y (m)  h factor value = 25  2  0 300 -1 200 -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  !  X (m) 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.!  !  !  111!  !  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! !  112!  ! 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.! !  113!  ! !  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.! !  114!  !  0  10 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.! !  115!  ! !  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.!  !  116!  !  References& Allain,!C.!and!Limat,!L.,!1995.!Regular!Patterns!of!Cracks!Formed!by!Directional! Drying!of!a!Collodial!Suspension.!Physical!Review!Letters,!74(15):!2981> 2984.! Armstrong,!J.E.,!Crandell,!D.R.,!Easterbrook,!D.J.!and!Noble,!J.B.,!1965.!Late! Pleistocene!Stratigraphy!and!Chronology!in!Southwestern!British!Columbia! and!Northwestern!Washington.!Geological!Society!of!America!Bulletin,!76(3):! 321>330.! Arndt,!J.!and!Häberle,!F.,!1973.!Thermal!expansion!and!glass!transition!temperatures! of!synthetic!glasses!of!plagioclase>like!compositions.!Contributions!to! 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Geophys.,!35(2):!191>218.! Webb,!S.L.,!Knoche,!R.!and!Dingwell,!D.B.,!1992.!Determination!of!silicate!liquid! thermal!expansivity!using!dilatometry!and!calorimetry.!European!Journal!of! Mineralogy(1):!95>104.! Wright,!H.M.N.,!Lesti,!C.,!Cas,!R.A.F.,!Porreca,!M.,!Viramonte,!J.G.,!Folkes,!C.B.!and! Giordano,!G.,!2011.!Columnar!jointing!in!vapor>phase>altered,!non>welded! Cerro!Galán!Ignimbrite,!Paycuqui,!Argentina.!Bulletin!of!Volcanology,!73(10):! 1567>1582.! ! !  !  121!  !  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.! ! ! 3  600  2  500  Y (m)  1  400  0  300  -1  200  -2 100 -3 -5  -4  -3  -2  -1  0  X (m)  1  2  3  4  5  !  Figure!A.1.!!Model!has!h!factor!value!of!6000.!  !  122!  !  3  600  2  500  Y (m)  1  400  0  300  -1  200  -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  Figure!A.2.!!Model!has!h!factor!value!of!1000.! 3  600  2  500  Y (m)  1  400  0  300  -1 200 -2 100 -3 -5  -4  -3  -2  -1  0  X (m)  1  2  3  4  5  !  Figure!A.3.!!Model!has!h!factor!value!of!100.!  !  123!  !  3  600  2  500  Y (m)  1  400  0  300  -1  200  -2 100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  Figure!A.4.!!Model!has!h!factor!value!of!70.! 3 600 2 500 1  Y (m)  400 0 300 -1 200 -2 100 -3 -5  -4  -3  -2  -1  0  X (m)  1  2  3  4  5  !  Figure!A.5.!!Model!has!h!factor!value!of!25.!  !  124!  Y (m)  !  3  700  2  600  1  500  400  0  300  -1  200  -2  100 -3 -5  -4  -3  -2  -1  0  1  2  3  4  5  X (m)  !  Figure!A.6.!!Model!has!h!factor!value!of!10.! 3  950 900  2  850  Y (m)  1  800 750  0  700 -1  650 600  -2  550 -3 -5  -4  -3  -2  -1  0  X (m)  1  2  3  4  5  500  !  Figure!A.7.!!Model!has!h!factor!value!of!1.!  !  125!  !  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,...  !  126!  ! '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.! ! !  !  127!  ! % 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  !  128!  ! 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  !  129!  !  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.! !  !  130!  ! A  0  B  10 mm  A  0  !  0  10 mm  B  10 mm  0  10 mm  131!  ! C  B  A  0  10 mm  A  0  4  mm  0  2  mm  B C  0  !  10 mm  0  4  mm  0  4  mm  132!  ! B  A  0  10 mm  !  10 mm  B  A  0  0  10 mm  0  10 mm  133!  ! B  A  0  10 mm  A  10 mm  B  0  !  0  10 mm  0  10 mm  134!  ! B  A  0  10  0  mm  10 mm  water.  B  A  0  !  10 mm  0  10 mm  135!  ! B  A  0  10  mm 10  0  mm  water.  A  0  C  B  10  0 mm  5  mm 0  10  mm  water.  !  136!  ! B  A  0  0  10 mm  B  A  0  10 mm  0  10 mm  10 mm  B A  0  water.  !  10 mm  0  10 mm  !  137!  

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