sgr ms thesis - University of Maine

FRACTAL ANALYSIS AND THERMAL-ELASTIC MODELING OF A
SUBVOLCANIC MAGMATIC BRECCIA: THE SHATTER ZONE, MOUNT
DESERT ISLAND, MAINE
By
Samuel Geoffrey Roy
B.S. University of Maine, 2008
A THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
(in Earth Sciences)
The Graduate School
The University of Maine
May, 2011
Advisory Committee:
Scott E. Johnson, Professor of Earth Sciences, Advisor
Christopher C. Gerbi, Assistant Professor of Earth Sciences
Zhihe Jin, Assistant Professor of Mechanical Engineering
Peter O. Koons, Professor of Earth Sciences

THESIS/DISSERTATION/PROJECT
ACCEPTANCE STATEMENT
On behalf of the Graduate Committee for Samuel Geoffrey Roy, I
affirm that this manuscript is the final accepted thesis/dissertation/project.
Signatures of all committee members are on file with the Graduate School at
the University of Maine, 5755 Stodder Hall, Orono Maine 04469.
ii

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FRACTAL ANALYSIS AND THERMAL-ELASTIC MODELING OF A
SUBVOLCANIC MAGMATIC BRECCIA: THE SHATTER ZONE, MOUNT
DESERT ISLAND, MAINE
By Samuel Geoffrey Roy
Thesis Advisor: Dr. Scott E. Johnson
An Abstract of the Thesis Presented
in Partial Fulfillment of the Requirements for the
Degree of Master of Science
(in Earth Sciences)
May, 2011
The Shatter Zone of Mount Desert Island, Maine, is a 450-1000m thick
magmatic breccia that defines the perimeter of the Cadillac Mountain Intrusive
Complex. The 400 Ma complex consists of gabbro-diorite sheets overlain by
three different granites, the largest of which is an A-type granite emplaced at high
temperature (~900 o C) and at shallow crustal depth (

emplacement of mafic magma, resulting in elastic failure of the metasedimentary
and diorite wall rock and virtually instantaneous fragmentation and entrainment of
the clasts in hot granitic magma. The degree of brecciation is gradational, with
clast supported breccias at the outer margin of the zone grading inward to
granitic-matrix supported breccia, and finally into clast-free Cadillac Mountain
Granite. Field observations point to an explosive breccia mechanism, and clast
size distribution analysis yields fractal dimensions (D s > 3) that agree with those
known to result from explosion (D s > 2.5). Field and microstructural data and
observations suggest that the clast sizes and shapes of the metasedimentary
host rocks reflect post-brecciation modification by partial melting and thermal
fracture, while diorite dike fragments experienced little modification after the
original brecciation event. Clast circularity increases with proximity to the magma
reservoir, whereas clast boundary shape decreases; this implies thermal wear on
clast surfaces. Numerical modeling is employed to explore the possible thermalmechanical
effects on the size distribution of clasts. Instantaneous immersion is
assumed for metasedimentary clasts (650°C) in a hot granitic matrix (800°C -
900°C), and our thermal analysis is restricted to conductive heat transfer
corrected for latent heat. The amount of clast melt is primarily dependent on the
melt temperature of the clast, the matrix to clast volume ratio, and the initial
magma intrusion and clast temperatures. Results show that thermal fracture and
clast melt were viable secondary modification processes, and magma flow was
necessary for disaggregation of melted clasts to occur. Angular clasts are highly
susceptible to corner break-off owing to large tensile stresses associated with

thermal shock. Considering the effects of these processes on clast size
distribution, we conclude that the Shatter Zone formed from explosion, and latestage
magma emplacement effectively altered the size and shape for many of
the metasedimentary clasts.

© 2011 Samuel Geoffrey Roy
All Rights Reserved
iii

ACKNOWLEDGEMENTS
The completion of this thesis was made possible through the financial
support from the National Science Foundation (EAR-0810039, EAR-0911150,
and MRI-0820946), the Society of Economic Geologists, and University of Maine
Graduate Student Government. I thank my advisor, Scott E. Johnson, for the
opportunity to work on a unique project and to allow me the freedom to pursue
my own interests within the project. My research and my development as a
scientist benefited greatly from discussions with my advisory committee
members Peter Koons, Christopher Gerbi, and Zhihe Jin. The professional
attitude of my committee and the openness of discussions stemming from my
research gave me the direction I needed to keep on track. I would also like to
thank the Department of Earth Sciences, which has been an integral part of my
life both in my undergraduate and graduate career. I am thankful for the positive
support given by the faculty, staff, and my fellow graduate students. I want to
thank all of my friends for the wonderful memories and experiences in and out of
the classroom. Most importantly, I want to thank my fiancée Teagan for putting
up with my eccentricities. I couldn’t have made it this far without her love and
support!
iv

TABLE OF CONTENTS
ACKNOWLEDGEMENTS ..................................................................................... iv
LIST OF FIGURES ............................................................................................... ix
LIST OF TABLES ................................................................................................. xi
Chapter
1. INTRODUCTION ............................................................................................. 1
2. GEOLOGIC SETTING .................................................................................... 4
2.1. Regional Geology: The Coastal Maine Magmatic Province ...................... 4
2.2. Cadillac Mountain Intrusive Complex ........................................................ 4
2.3. Bar Harbor Formation ............................................................................... 7
2.4. Shatter Zone ............................................................................................. 8
3. PHYSICAL DESCRIPTION OF SUBVOLCANIC SYSTEMS ........................ 10
3.1. Magma Plumbing Systems ..................................................................... 11
3.1.1. Generation and Transport of Magma ............................................. 11
3.1.2. Emplacement and Growth of Magma Chambers ........................... 13
3.2. Subsurface Response to Volcanic Eruption ............................................ 15
3.2.1. The Mechanical Behavior of Wall Rock as a Control for
Eruption Behavior: from Magma Storage to Volcanic Eruption ..... 16
3.2.2. Volcanic Triggers and Chamber Rupture in a Rigid Reservoir ...... 19
3.2.3. Evidence for Wall Rock Readjustment in Modern Volcanoes ........ 23
v

3.3. Volcanic Energy ...................................................................................... 23
3.4. Emplacement and eruptive history of the Cadillac Mountain
Intrusive Complex ................................................................................... 25
4. THERMAL FRAMEWORK FOR CONTACT METAMORPHISM ................... 26
4.1. Characteristics of Contact Metamorphism .............................................. 26
4.1.1. Conductive, Convective, and Advective Heat Transfer................... 27
4.2. Contact Metamorphism in the Shatter Zone ........................................... 28
4.3. Methods for Contact Metamorphic Thermal Modeling ............................ 29
4.3.1. Model Setup ................................................................................... 34
4.3.2. Results and Discussion .................................................................. 39
4.4. Evidence for an Actively Mixing Chamber .............................................. 42
5. ROCK MECHANICS AND THE FRACTAL BEHAVIOR OF ROCK ............... 44
5.1. Brittle Failure of Rock ............................................................................. 45
5.1.1. Basic Principles of Griffith Fracture Theory .................................... 45
5.1.2. The Self-Similarity of Fracture Patterns .......................................... 48
5.2. Fractal Theory ......................................................................................... 49
5.3. Quantitative Methods of Breccia Classification ....................................... 51
5.3.1. Clast Size Distribution .................................................................... 51
5.3.2. The Fractal Dimension-Brecciation Mechanism Link for Clast
Size Distribution ............................................................................. 54
5.3.3. Clast Boundary Shape.................................................................... 57
5.3.4. The Fractal Dimension-Brecciation Mechanism Link for Clast
Boundary Shape ............................................................................. 61
vi

5.3.5. Clast Circularity Analysis ................................................................ 62
6. ANALYSIS AND RESULTS........................................................................... 64
6.1. Field Relations in the Shatter Zone ......................................................... 65
6.1.1. Gradational Characteristics ............................................................ 65
6.1.1.1. Type 1 .................................................................................... 65
6.1.1.2. Type 2 .................................................................................... 71
6.1.1.3. Type 3 .................................................................................... 71
6.2. Methods .................................................................................................. 74
6.3. Data ........................................................................................................ 78
6.3.1. Clast Size Distribution Data ............................................................ 78
6.3.2. Clast Boundary Shape Data ........................................................... 82
6.3.3. Clast Circularity Analysis Data ....................................................... 84
6.3.4. Summary of Data ........................................................................... 84
6.4. Discussion .............................................................................................. 86
6.4.1. Bifractal Distributions for Type 1 and 2 ........................................... 86
6.4.2. Differing rock types and clast modification evidence in Type 3 ...... 88
7. MECHANISMS FOR SECONDARY CLAST MODIFICATION: A
DISCUSSION ................................................................................................ 90
7.1. Potential Mechanisms for CSD and CBS Modification ............................ 91
7.1.1. Thermal Attrition ............................................................................ 91
7.2. Methods: Partial Melting of Clasts .......................................................... 92
7.2.1. Model Setup and Important Parameters ........................................ 92
7.2.2. Methods for Plotting Data .............................................................. 97
vii

7.2.3. Applications for Dimensionless Variables ...................................... 98
7.3. Clast Melt Results ................................................................................... 99
7.3.1. Discussion ................................................................................... 102
7.4. Thermal-Induced Fracture .................................................................... 108
7.4.1. Model Setup................................................................................. 109
7.4.2. Results and Discussion ............................................................... 112
7.5. Final Discussion .................................................................................... 115
REFERENCES ................................................................................................. 118
BIOGRAPHY OF THE AUTHOR ...................................................................... 137
viii

LIST OF FIGURES
Figure 2.1.
Figure 3.1.
Figure 3.2.
Figure 3.3.
Figure 3.4.
Figure 4.1.
Bedrock map of Mount Desert Island ............................................. 5
Formation of a laccolith ................................................................ 14
Generalized volcanic surface discharge rates .............................. 18
Two forms of subvolcanic breccias .............................................. 21
Common models for caldera collapse .......................................... 22
Mineralogy of the contact metamorphosed Bar Harbor
Formation ..................................................................................... 30
Figure 4.2.
Figure 4.3.
Figure 4.4.
Figure 4.5.
Figure 4.6.
An isograd map of the Shatter Zone ............................................ 32
Geometry of the intrusion model .................................................. 37
Time steps for the cooling chamber ............................................. 38
A temperature versus time plot from intrusion model results ....... 40
Maximum metamorphic temperature with orthogonal distance
from the contact ........................................................................... 41
Figure 5.1.
Figure 5.2.
Figure 5.3.
Figure 5.4.
Figure 5.5.
Figure 6.1.
An elliptical Griffith crack under compressive stress .................... 46
A cube displaying self-similar size distribution properties ............ 50
An example clast size distribution plot ......................................... 53
The Koch snowflake ..................................................................... 59
Euclidean distance mapping on a clast outline ............................ 60
The gradient of brecciation intensity through the Shatter
Zone ............................................................................................. 66
Figure 6.2.
Figure 6.3.
Type 1 Shatter Zone .................................................................... 67
Type 2 Shatter Zone .................................................................... 68
ix

Figure 6.4.
Figure 6.5.
Type 3 Shatter Zone .................................................................... 69
Centimeter-scale boudinage textures in Bar Harbor
Formation ..................................................................................... 70
Figure 6.6.
Figure 6.7.
Figure 6.8.
Brecciation textures in Type 2 Shatter Zone ................................ 72
Local flow textures in Type 3 Shatter Zone .................................. 73
Evidence for secondary clast size, shape, and boundary
modification ................................................................................. 75
Figure 6.9.
Figure 6.10.
Figure 6.11.
Figure 6.12.
Figure 6.13.
Figure 7.1.
Figure 7.2.
Figure 7.3.
Figure 7.4.
Figure 7.5.
An outcrop grid used for fractal analysis ...................................... 77
Clast size distribution data for Type 1 and 2 Shatter Zone ........... 80
Clast size distribution data for Type 3 Shatter Zone .................... 81
Clast boundary shape data ordered by Shatter Zone type .......... 83
Circularity data ordered by Shatter Zone type .............................. 85
Geometries used for thermal modeling ........................................ 93
Solidus migration trend for a spherical clast ............................... 100
A plot displaying clast melt over time ......................................... 101
Temperature changes over time for points in a clast ................. 103
The evolution of clast size distribution with progressive
thermal exposure ....................................................................... 107
Figure 7.6.
Figure 7.7.
Clast geometry used for thermal stress analysis ........................ 111
Time step results for thermal stress in metasedimentary and
diorite clasts ............................................................................... 113
x

LIST OF TABLES
Table 6.1.
Table 7.1.
Table 7.2.
Average CSD values ..................................................................... 79
Physical constants for thermal solutions ....................................... 95
Physical constants for thermal-mechanical solutions .................. 110
xi

Chapter 1
INTRODUCTION
Magma chambers are dynamic physical and chemical systems involving
multiple processes such as mixing, mingling, convection, recharge and
evacuation of magma. At deeper crustal levels, relatively high background
temperatures can lead to long-term physical and chemical evolution, obscuring
the spatial and temporal relations among individual magmatic events. In contrast,
the sequential evolution of magmatic systems high in the crust at the interface
between the plutonic and volcanic realms is commonly well preserved. These
subvolcanic systems (e.g. Johnson et al., 2002; Metcalf, 2004; Kemp et al., 2006;
Marianelli et al., 2006), much like eruptive sequences, can preserve a long and
varied history of instantaneous magmatic events. They typically contain a wide
variety of intrusive phases (e.g. cone sheets, ring faults and dikes, and massive
central intrusions) and are potentially a rich source of information about the
evolution of caldera/volcano root zones and the tops of upper-crustal magma
chambers. They also commonly preserve genetically related volcanic sequences
on their margins. The detailed intrusive relationships in these complexes and the
intimate timing relationships between the various intrusions and deformational
structures are preserved in part due to rapid quenching of some units, and in part
due to the sequential series of intrusions that produce a magmatic stratigraphy.
These complexes provide an unusual opportunity to evaluate the evolution of
1

subvolcanic magmatic systems, the links between plutonism and volcanism, and
upper-crustal magma plumbing systems in general.
In this thesis, I describe a subvolcanic igneous system known as the
Cadillac Mountain intrusive complex, emplaced at

likely explosive mechanism of breccia formation followed by modification of
metasedimentary clast shapes and sizes through partial melting and postbrecciation
thermal fracturing. Methods from this thesis provide a new approach
for the fractal analysis of breccias formed in a magmatic environment.
3

Chapter 2
GEOLOGIC SETTING
2.1. Regional Geology: The Coastal Maine Magmatic Province
The area of interest lies in the Coastal Maine Magmatic Province (Hogan
and Sinha, 1989), a group of over 100 plutons of granitic through gabbroic
composition located on the eastern coast of Maine with ages ranging from Late
Silurian to Early Carboniferous. Plutons in this complex display a bimodal
character (Chapman, 1962), with evidence for mafic and felsic magma mingling
(Chapman, 1962; Wiebe, 1993). Gravity studies imply that these plutons are less
than a few kilometers thick with shallow dipping floors and steep walls, underlain
by mafic sheets (Sweeney, 1976; Hodge et al., 1982). These intrusions follow a
NE-trend within fault-bounded continental crust that accreted onto the North
American craton prior to Acadian orogenesis (Hogan and Sinha 1989, Wiebe et
al. 2004). Hogan and Sinha (1989) suggested that the coastal Maine magmatic
province intruded the older crust during a post-collisional, extensional rifting
event related to the Acadian Orogeny (Coombs, 1994; Wiebe et al., 1997a).
2.2. Cadillac Mountain Intrusive Complex
The Cadillac Mountain intrusive complex of Mount Desert Island (Figure
2.1) is part of the Coastal Maine Magmatic Province (Hogan and Sinha, 1989).
The complex is roughly circular in map view covering an approximate area of
14km x 20km, and consists of the Cadillac Mountain Granite and the younger
4

-68.45° -68.30° -68.15°
44.40°
Type 1
Type 2
44.35°
Type 3
44.30°
44.25°
Type 1
Type 2
Type 3
4 km
N
500 m
Figure 2.1. Bedrock map of Mount Desert Island. A) The Cadillac Mountain Intrusive Complex. B) The Eastern coast of the island.
Blue dots represent Shatter Zone type localities.
5

Somesville granite suite to the west, both of which are inferred to be underlain by
composite gabbro-diorite sheets (Hodge et al., 1982; Wiebe, 1994). The entire
complex dips slightly to the east, exposing the intrusive layers and their relative
contact relationships. The Cranberry Island volcanic series, located in the south,
features a bimodal geochemistry that correlates well with the intrusive complex,
leading some authors to consider it as genetically related to the Cadillac
Mountain intrusive complex (e.g. Seaman et al., 1995, 1999; Wiebe et al.,
1997a). The complex was emplaced into the Ellsworth Schist, Bar Harbor
Formation, and the Cranberry Island volcanic series. The Southwest Harbor
Granite is a poorly studied, older unit cross-cut by the main intrusion.
Several factors indicate shallow crustal emplacement of the intrusive
complex, including evidence for plutonic intrusion within its own eruptive
products, miarolitic textures in the upper section of the Cadillac Mountain
Granite, and relatively low pressure metamorphic mineral assemblages in
surrounding wall rock (Metzger, 1959; Chapman, 1962; Berry and Osberg, 1989;
Seaman et al., 1995; Wiebe et al., 1997a; Seaman et al., 1999). Cadillac
Mountain Granite compositions in the Quartz-Orthoclase-Albite-H 2 O system plot
between 0.5-1kbar, and presence of edenitic hornblende indicates low pressure
crystallization. Emplacement likely occurred at approximately 2-5km depth
(Wiebe et al., 1997a; Nichols and Wiebe, 1998). Gravity data from Hodge et al.
(1982) indicate a saucer-shaped floor geometry for the Cadillac Mountain Granite
with a thickness of approximately 2.5km, underlain by gabbro-diorite sheets of a
potentially similar thickness. Wiebe et al. (1997a) have suggested that the
6

Cadillac Mountain Granite and gabbro-diorite partially mixed and formed an A-
type granite, which is a dry, Fe-enriched granite typically related to anorogenic
extensional tectonic processes. Thus, the A-type characteristics of the Cadillac
Mountain Granite may relate more to upper crustal mixing processes rather than
the original source composition.
2.3. Bar Harbor Formation
This study focuses on the contact between Cadillac Mountain Granite and
Bar Harbor Formation on Mount Desert Island. The Bar Harbor Formation is a
metasedimentary rock found in Frenchman’s Bay and in isolated segments along
the eastern shore of Mount Desert Island. The majority of Bar Harbor Formation
has undergone regional diagenesis followed by contact metamorphism along the
perimeter of the Cadillac Mountain Granite. The unit is approximately 610m thick
and stratified with dominant rock types including pelitic clays, sandstones,
conglomerates, and volcanic tuff. The Bar Harbor Formation varies in modal
abundance between these rock types, but generally consists of plagioclase (1-
25%), quartz (2-28%), microcline (3-14%), actinolite (0-13%), lithic fragments of
volcanics and quartzite (9-50%), and fine granular matrix (23-52%). The matrix
consists of plagioclase (10%), quartz (50%), microcline (30%), biotite (5-10%),
chlorite (0-3%), and pyrite (0-3%) (mineral abundances determined by point
counting, Metzger, 1959). Biotite is interstitial to the other grains and displays
kinking and crushing along foliae that indicate post-crystallization deformation.
7

Biotite is metamorphic in origin, and some grains show replacement by chlorite.
Pyrite and magnetite are also common and are assumed to be authogenic.
Metzger (1959) determined three different sediment sources that
produced the observed stratified rock types within the Bar Harbor Formation. The
vast majority of sediments came from Ellsworth Schist and amphibolite units that
lie just below the Bar Harbor Formation. Detrital quartzite and microcline could
only have come from the Ellsworth Schist as it is the only facies in which both
exist in abundance. Where present, microcline is often heavily altered to sericite.
Volcanic tuff layers were produced by the volcanic activity along the convergent
boundary. The volcanic lithic shards are heavily altered and rounded, implying
that they are more mature sediments from a distant source. Biotite and chlorite
are an authigenic result of weak metamorphism. Beds are often well sorted and
display micrograding, and it is believed that these sediments were deposited in a
subaqueous fan (Metzger, 1979). There are no detrital biotite or muscovite
grains, possibly suggesting very rapid, turbulent deposition (Metzger, 1959;
Metzger and Bickford, 1972).
2.4. Shatter Zone
The perimeter of the Cadillac Mountain Granite is defined by the Shatter
Zone, an aureole of fragmented country rock that varies in apparent thickness
from 450-1000 m (Chapman, 1962; Gilman et al., 1988). The rock fragments in
the eastern Shatter Zone consist of: (1) Bar Harbor Formation; (2) Devonian
diorite dikes; and (3) large, relatively rare felsic volcanic xenoliths near the
8

gradational contact with the CMG. Clast sizes range from millimeter to meter
scale (Gilman et al., 1988). The matrix of the shatter zone appears as both a fine
grained biotite leucogranite and as late stage pegmatitic quartz veins, both of
which differ compositionally from the dry, A-type Cadillac Mountain Granite.
Average matrix grain size gradually increases toward the Cadillac Mountain
Granite (Coombs, 1994; Wiebe et al., 1997a). The Shatter Zone is related to this
intrusive complex, and the primary focus of this thesis is to determine the
conditions of wall rock fragmentation, and how the deformation event was related
to volcanic activity.
9

Chapter 3
PHYSICAL DESCRIPTION OF SUBVOLCANIC SYSTEMS
A rarely described and intricately formed feature of volcanism, subvolcanic
systems can yield a great deal of information about the link between deeper
magma plumbing systems and upper crustal volcanic regions. Exposures of
these systems are uncommon because they occur at a depth between magma
reservoir and volcanic edifice, providing only a small window into the processes
that occur between the two. Subvolcanic systems can hold a wealth of
information on the evolution of calderas, volcanic root zones, and the upper
sections of reservoirs because they can contain intrusive phases such as cone
sheets, ring faults and dikes, and massive central intrusions produced during
active volcanism. The evolution of the subvolcanic magmatic system is recorded
by these features due in part to the rapid quenching of some units and the
inherent sequential series of intrusive behavior (Lipman, 1984; Johnson, 1999).
Below I review the mechanisms behind magma generation, segregation,
transport, emplacement, and volcanic eruption. Deformation features recorded in
the subvolcanic system are also reviewed, and I discuss how volcanic energy is
translated into deformation features, and how they relate to modern examples
and the Shatter Zone.
10

3.1. Magma Plumbing Systems
3.1.1. Generation and Transport of Magma
The development of magma plumbing systems and the geometry of
igneous intrusions remains a major focus for many researchers who attempt to
determine their correlation to tectonism and the evolution of the lithosphere (e.g.
Clague, 1987; Bons et al., 2003a, 2003b; Hayashi and Morita, 2003; Jellinek and
DePaolo, 2003; Bartley et al., 2006; Marianelli et al., 2006; Bohrson, 2007;
Lipman, 2007; Cruden, 2008; Dietyl and Koyi, 2008). Igneous complexes form by
the processes of magma generation, segregation, ascent, and emplacement. In
order to relate the magma plumbing systems to volcanism, the generation and
transport of magma through the lithosphere must first be explained. I focus this
discussion on a continental-oceanic convergent tectonic margin.
In a continental-oceanic convergent margin, subduction of the oceanic
plate initiates mantle flow. Heat advection from flow in the mantle wedge can
lead to melt in the asthenosphere, the subducting oceanic plate, and in the
overlying lithosphere. Dehydration reactions in the subducting oceanic slab
release water into the mantle wedge, reducing the solidus temperature of
peridotite and allowing for partial melt in the asthenosphere (e.g. Manea et al.,
2005; Johnson and Jin, 2009). Lithospheric melt occurs from crustal thinning
produced by thermal advection from mantle wedge flow. Further heating of the
lithosphere reduces its viscosity, and extensional deformation occurs between
the stationary continental interior and the retreating hinge of the subducting slab
(e.g. Billen and Gurnis, 2001, Billen, 2008). The sharper thermal gradient in the
11

thinned lithosphere allows for partial melt. The partially melted lithosphere
becomes weakened and allows segregation and transport of the melt fraction
(e.g., Petford et al., 2000; Jackson et al., 2003; Bergantz and Barboza, 2005;
Aizawa et al., 2006). Asthenospheric melt occurs directly below the volcanic front
of the convergent margin, while lithospheric melting occurs below back-arc
extensional basins. Melts from both sources can undergo significant crystal
fractionation, producing chemically evolved magmas (e.g. Johnson and Jin,
2009).
The density anomaly produced by lithospheric melting provides a
buoyancy potential for the generated magma, which then rises upward into the
lithosphere. The dominant mechanism of magma transport is debatable.
Traditionally, diapirism was used to explain the mass transport of large igneous
bodies. This explanation is flawed for upper crustal emplacement because the
driving force of buoyancy cannot surpass the strength of brittle upper crustal
rock. Also, the large amounts of thermal energy spent on weakening the wall
rock to allow ascension reduces the potential magma transport distance before
solidification (Clemens and Mawer, 1992; Petford et al., 2000; Aizawa et al.,
2006). Diapirism may be plausible in the lower lithosphere where wall rock can
deform under viscous strain to accommodate ascent of large magmatic bodies
(Weinberg and Podladchikov, 1994), but magma transport by dike propagation is
thought to be the dominant mechanism for transport through much of the mid to
upper lithosphere (e.g., Gudmundsson et al., 1999; Accocella et al., 2006;
Johnson and Jin, 2009).
12

3.1.2. Emplacement and Growth of Magma Chambers
A buoyant, mobile dike will propagate upwards, normal to the pressure
and density gradients that exist in the host rock. Propagation is assisted by
magma reservoir overpressure if the dike remains connected to the reservoir
(Rubin, 1995a; McLeod and Tait, 1999; Apuani and Corazzato, 2009; Johnson
and Jin, 2009). Propagation will continue as long as overpressure in the dike can
overcome the fracture toughness of the wall rock (Rubin, 1995b, Dahm, 2000).
Dike propagation halts when 1) the dike tip freezes, 2) overpressure in the dike
body reduces to a subcritical level, 3) the dike intersects a pre-existing sill or
chamber, 4) the dike tip arrests on contact with a stiffer boundary, 5) the dike
reaches a level of neutral buoyancy, or 6) tectonic stress unloading reduces dike
overpressure (Chen et al., in press). An unhindered dike will propagate vertically
beyond the level of neutral buoyancy until it rapidly reduces speed, arrests, and
begins to grow laterally (Aizawa et al., 2006; Chen et al., in press).
Reservoir formation at shallow (

A
B
C
Figure 3.1. Formation of a laccolith. A) Dike arrest near the level of neutral
buoyancy leads to lateral expansion of intruding magma. B) As the sill expands,
volumetric expansion is accommodated by lateral expansion and vertical uplift.
C) A tabular pluton forms. A minor amount of volume expansion is
accommodated by floor subsidence. Overpressure within the chamber leads to
vertical dike formation, which may intersect the surface.
14

pluton margins (Johnson et al., 2001, 2003, 2004; Gerbi et al., 2004; Aizawa et
al., 2006). However, wall rock shortening can only account for 25-40% of a
magma chamber’s volume, so other processes must provide additional volume
for chamber expansion (Paterson and Fowler, 1993; Johnson et al., 1999).
There has been much discussion on the topic of volume accomodation by
stoping (e.g. Clarke et al., 1998; Glazner & Bartley, 2006; Clark & Erdman, 2008;
Glazner & Bartley, 2008; Paterson et al., 2008; Yoshinobu & Barnes, 2008),
assimilation (melt and mixture) of crust (e.g. Beard & Ragland, 2005; Clarke,
2007), visco-elastic deformation of host rock (e.g. Cruden & McCaffrey, 2001;
Jellinek and DePaolo, 2003; Cruden, 2005; Dietyl & Koyi, 2008; Paterson &
Farris, 2008) and dike propagation and sill accretion (e.g. Baer, 1987; Pinel &
Jaupart, 2004; Bartley et al., 2006; Michel et al., 2008). All of these processes
allow progressive growth of a shallow intrusive complex.
The continued uplift from progressive shallow intrusion magma
emplacement is often observed as a precursor for eventual magma reservoir
overpressure and rupture, wall rock failure, and caldera collapse. The
subvolcanic system is the zone between the ruptured magma reservoir and the
collapsed volcanic edifice, and it is here that the intrusive history of the volcanic
event is stored (Johnson et al., 2002).
3.2. Subsurface Response to Volcanic Eruption
Many geologists have studied the linkage between magma chambers and
volcanism through subvolcanic wall rock deformation (Lipman, 1984; Lipman,
15

1997; Branney and Kokelaar, 1998; Johnson et al., 1999; Aizawa et al., 2006;
Acocella, 2007; Kawakami et al., 2007; Saito et al., 2007) and still others with the
aid of lithological, geochemical, and geochronological associations (Metcalf,
2004; Marianelli et al., 2006; Bachmann et al., 2007; Bohrson, 2007). Although
the surface manifestations of volcanism are easily witnessed during volcanic
eruptions, study of the physical processes that occur below the surface at the
level of the erupting magma reservoir is more difficult (Bachmann et al., 2007;
Gottsman & Battaglia, 2008). The study of magma reservoir walls is important
because they record devolatilization, cooling, magma recharge, or other
processes integral to volcanic stability through deformation patterns that can be
observed at the surface for eroded volcanic systems, such as the Shatter Zone,
or through geophysical methods such as seismology for active systems.
3.2.1. The Mechanical Behavior of Wall Rock as a Control for
Eruption Behavior: from Magma Storage to Volcanic Eruption
Volcanic eruptions result from the rupture of a magmatic feeder reservoir.
An overpressure above the lithostatic value is necessary to start an eruption, and
this overpressure is controlled by the mechanical behavior of the reservoir walls.
The conditions of magma flow are dependent on the viscosity of the migrating
magma (Scandone, 1996). Chamber growth and pressurization is partially
compensated through viscoelastic deformation of wall rock because of the
amount of heat introduced by the intrusion and the duration (10 5 -10 6 years)
required for a volcanic feeder reservoir to develop (Jellinek and DePaolo, 2003).
16

The potential for volcanic eruption is dependent on the critical rate of reservoir
pressurization by magma replenishment. If the rate of reservoir pressurization is
lower than the critical level defined by the visco-elastic strength of the wall rock,
volume expansion is accommodated by viscous deformation and magma is
stored in the reservoir. Magma storage is controlled by a viscous regime. If the
rate of pressure increase exceeds the critical level, the reservoir walls are
compromised by elastic failure, a conduit forms (Barnett and Lorig, 2007), and
volcanic eruption commences. Volcanic eruption is controlled by an elastic
regime (Jellinek and DePaolo, 2003, Scandura et al., 2007, 2008).
Much like viscous regime magma reservoir growth, elastic regime volcanic
eruption is controlled by the mechanical behavior of the reservoir walls. There
are two possible end-member responses depedent on the rigidity of wall rock: the
“elastic reservoir”, where elastic energy stored in a non-rigid wall rock is
immediately released by the formation of a conduit to the surface, and the “rigid
reservoir model”, where the elastic strength of rigid wall rock is surpassed by
pressure changes in the reservoir, leading to brecciation (Wadge, 1981;
Scandone, 1996). Elastic, non-rigid behavior of wall rock can be seen in some
basaltic eruptions where there is a rapid and effusive initial peak in magma
discharge that slowly reduces over time (Figure 3.2). Rigid reservoir behavior is
reflected in felsic eruptions, where magma cannot be “squeezed out” elastically,
but as a conduit forms to the surface, pressure release in the chamber causes
volatiles to volumetrically expand, leading to explosive eruption. Peak magma
discharge occurs later on, when a conduit is well developed and the abundant
17

Effusive-Type Eruption
max
10 0 - 10 3
m 3 /sec
Magma Discharge Rate
time (days-months)
Explosive-Type Eruption
max
10 3 - 10 6
m 3 /sec
Magma Discharge Rate
time (hours-days)
Figure 3.2. Generalized volcanic surface discharge rates. Two possible
endmembers are displayed. Elastic reservoir walls depressurize with effusivestyle
surface discharge that tapers off as time progresses. Magma is “squeezed”
out of the chamber by elastic energy stored in the reservoir walls. Rigid
reservoirs experience peak explosive-style eruption after a conduit forms. Rapid
pressure fluctuations in the reservoir cause elastic failure of the wall rock. The
reservoir walls cannot elastically compensate for pressure fluctuations produced
by the volumetric expansion and discharge of volatiles.
18

volatiles within the chamber are free to exsolve and volumetrically expand.
Viscous, felsic magmas produce explosive eruptions because, with a limited
ability to accommodate expanding gases, exsolved volatiles must force their way
through. (Scandone, 1996; Scandone and Giacomelli, 2001; Scandone et al.,
2007). The explosive nature of a rigid reservoir eventually leads to severe wall
rock fragmentation and caldera collapse (Fisher, 1960; Acocella, 2007).
3.2.2. Volcanic Triggers and Chamber Rupture in a Rigid Reservoir
Overpressure may be triggered by sudden exsolution of a volatile phase,
intrusion/replenishment of new magma or volatiles into the chamber, or
weakening of the wall rock by tectonism or the development of fluid-filled cracks
along the reservoir walls (Scandone, 1996, Macias et al., 2003; Davis et al.,
2007; Dziak et al., 2007). The trigger effectively unloads the retaining lithostatic
pressure on the reservoir, causing rapid and violent expansion of volatiles
(Mader et al., 1994; Gardner, 1999; Scandone & Giacomelli, 2001; Gonnermann
& Manga, 2007; Grosfils, 2007; Gernon et al., 2008). The differential stresses
produced by volumetric expansion are directed at the wall rock, which must
readjust itself either elastically or through brittle failure. I now explore the
readjustment of wall rock by fragmentation, as this model appears most
applicable for the development of a Shatter Zone.
The differential stresses produced by pressure fluctuations in the chamber
are enough to explosively fracture the wall rock (Legros and Kelfoun, 2000,
Macias et al., 2003). Driven by volume expansion in the reservoir, volatile-rich
19

magma quickly intrudes the developed fractures (Scandone, 1996; Oliver et al.,
2006). These perimeters of fragmented rock can be large, such as in the Shatter
Zone (Figure 3.3). For shallow intrusions, interaction between relatively hot
magmatic volatiles and cool ground water can lead to continuous
phreatomagmatic explosions inside the wall rock (Wohletz, 1986; Lorenz and
Kurszlaukis, 2007).
Additionally, caldera collapse is caused by the progressive fracture
weakening of the reservoir roof in the region of local uplift (Lipman, 1984;
Branney and Kokelaar, 1994). Fractures act as channels for volatile rich magma
to escape to the surface, and as the chamber continues to lose volume, the
weakened roof material begins to subside into the collapsing chamber. There are
many models that attempt to explain these observed subsidence patterns (Figure
3.4, Lipman, 1997; Cole et al., 2005; Acocella, 2007). Shear breccias form by
abrasion in large ring faults that develop along the perimeter of the subsiding
caldera (Lipman, 1984; Johnson et al., 1999). Where these ring faults form is
dependent on the subsidence pattern of caldera collapse. For example, pistonstyle
collapse would produce a concentric ring of abrasive breccia material, while
a piecemeal-style collapse produces many shear breccias throughout the entire
subvolcanic complex. Although formed in the same system, explosive and
caldera collapse breccias are fundamentally different. This will be further
explained in chapter 5.
20

A
B
Figure 3.3. Two forms of subvolcanic breccias. A) A subvolcanic explosion in a
magma reservoir. Pressure fluctuations cause brittle failure in wall rock, with the
greatest intensity of brecciation adjacent to the reservoir interface. B) Shear
along the ring faults of a collapsing caldera produces a breccia with a preferred
fabric parallel to the sense of shear. Clasts from the ring fault are transported
downward into the sides of the magma reservoir.
21

Piston
Downsag
Piecemeal
Funnel
Trap-Door
Figure 3.4. Common models for caldera collapse. Piston collapse: caldera
subsidence occurs by a single, coherent, piston-shaped body of roof rock.
Piecemeal: the roof rock subsides by incrementally stoped blocks that fall into the
chamber. Trap-door: an asymmetric pluton, or wall rock with heterogeneous
strength distribution breaks and causes subsidence on one side of the caldera.
Downsag: a pluton that is too small or deep to reach the surface may
depressurize passively, causing roof rock subsidence. Funnel: a small or deep
pluton creates a skinny surface conduit, forming a small caldera. The first three
models produce ring faults during caldera collapse, which result in rings of
brecciated wall rock around the collapsed caldera (modified from Lipman, 1997).
22

3.2.3. Evidence for Wall Rock Readjustment in Modern Volcanoes
In active volcanic regions, seismic activity at subvolcanic depths
represents reservoir wall readjustment from rock fragmentation and settling
(Scandone, 1996). During the May 1980 eruption of Mount St. Helens, seismic
activity generally increased to a maximum that coincided with peak pyroclastic
flow at the surface (Shemeta and Weaver, 1986; Barker and Malone, 1991). The
depth of seismic activity was noted to begin at shallow levels, then to increase in
abundance at both shallow and deeper levels. The seismic activity is interpreted
to represent the fracture and readjustment of wall rock caused by the
mobilization of magma during the formation and widening of a conduit, then the
fracture of wall rock bordering the reservoir during maximum magma discharge.
Seismic activity subsided proportionately to reduced surface discharge until a
final decrease in activity, approximately a day after the start of the eruption
(Shemeta and Weaver, 1986; Carey, 1991; Caruso et al., 2006). Geologists
observed similar behavior for the Mount Pinatubo eruption in 1991 (Rutherford
and Devine, 1991).
3.3. Volcanic Energy
The size of the volcanic eruption depends on the amount of energy
contained in the volcanic system. The release of volcanic energy can take
several modes, including the kinetic energy of surface ejecta, the potential
energy of the rising magma column and dissolved gases, seismic energy passing
through rock, water (tsunamis), or air (shockwaves), kinetic energy of rock
23

fragmentation, and thermal energy held in the reservoir. For subvolcanic study,
only three relative partitions of energy need to be considered: thermal energy,
the kinetic energy converted into wall rock fracture and fragmentation, and the
remainder of the energy budget partitioned into surface mechanisms (Hedervari
1963, Shimozuru 1968, Heffington 1982).
The thermal energy contained within the volcanic system is at least an
order of magnitude greater than all of the other energy forms, and it can even be
three or four orders of magnitude greater depending on the magma composition
(Heffington, 1982). The study of thermal energy in volcanism can reveal
information about the overall energy of the system. As mentioned previously,
contact metamorphism is a product of the thermal presence of the magma
reservoir, but this can also lead to partial melt, viscous deformation, and thermal
fracture of wall rock as well. The Shatter Zone shows evidence for all of this, and
it will be discussed in detail in Chapter 4 (contact metamorphism) and Chapter 7
(outcrop-scale thermal-mechanical modeling).
Subvolcanic kinetic energy causes wall rock fragmentation through
reservoir explosion, caldera subsidence and wall rock abrasion along a ring fault,
or as a more passive result of chamber expansion by stoping (Lipman, 1997;
Scandone and Giacomelli, 2001). The Shatter Zone is intensely fractured, and to
better understand its development I examine brecciation mechanism that may
have produced such a damage aureole in Chapter 5.
24

3.4. Emplacement and eruptive history of the Cadillac Mountain Intrusive
Complex
The Cadillac Mountain Granite formed by crustal thinning in an
extensional terrane (Wiebe et al., 1997a). The intrusive complex provides a
record of episodic basaltic magma injection before, during, and after
emplacement and crystallization of the granitic pluton. Injection sequences are
recorded in the gabbro-diorite-granite sheets at the base of the complex. Wiebe
(1994) hypothesized that the formation of the Cadillac Mountain Granite pluton
enhanced the potential to attract and trap basaltic dikes at the base of the
chamber. Continuous replenishment of the reservoir extended the life of the
pluton, and the steady addition of thermal energy drove convection (Chapman,
1962). Based on the prevalence of enclaves throughout the Cadillac Mountain
Granite, there was some amount of granitic and basaltic mixing during
convection (Wiebe et al., 1997b). The continued addition of thermal energy and
volumetric expansion by basaltic replenishment were also the likeliest triggers for
reservoir overpressurization and subsequent volcanic eruption (e.g. Wiebe, 1994;
Seaman et al., 1999; Annen and Sparks, 2002).
25

Chapter 4
THERMAL FRAMEWORK FOR CONTACT METAMORPHISM
To fully understand the development of the Shatter Zone, it is first
necessary to determine the characteristics of contact metamorphism within the
unit. In this chapter, I discuss how thermal energy drives metamorphism along
the contact between the Cadillac Mountain Granite and Bar Harbor Formation,
and how modeling and isograd data can potentially tell us about the condition of
the wall rock before the formation of the Shatter Zone. Important constraints are
discussed in order to develop a useful model for intrusive thermal behavior. I use
a conductive heat transfer-based, instantaneous single intrusion model. Although
the model is a simplified version of the intrusion complex, it provides endmember
results for the true thickness of the metamorphic zones, the dominant
heat transfer mode, and the effect of extended chamber activity and wall rock
brecciation on contact metamorphism. I find that the model is a good first order
approximation for contact metamorphism in the Shatter Zone, but convective
heat transfer, extended pluton activity, and wall rock brecciation are all important
factors that have been ignored here.
4.1. Characteristics of Contact Metamorphism
Contact metamorphism involves a balance of heat transfer (Bergantz,
1991; Labotka, 1991): as the wall rock heats up from contact, the intrusion must
cool down by a proportional amount. Contact metamorphism is limited to a
26

elatively thin aureole surrounding an igneous intrusion. There are significant
changes in metamorphic grade through the aureole, and in many cases it is
possible to track the entire prograde metamorphic gradient within a single rock
unit (Kerrick, 1991). The highest grade metamorphic facies is found adjacent to
the intrusive contact and peak metamorphic temperature decreases outward.
The effect pressure has on contact metamorphism is dependent on the depth of
the intruding heat source (Furlong et al., 1991). At shallow depths, temperature is
the driving force of metamorphism and the contact aureole is typically well
contrasted to the host material, which may be unmetamorphosed. For deep
pluton aureoles, it is more difficult to distinguish the aureole from the already
regionally metamorphosed rocks (Kerrick, 1991). The size of the aureole
correlates positively to the size of the intrusion, therefore it directly relates to the
heat source reserve (Kerrick, 1991).
4.1.1. Conductive, Convective, and Advective Heat Transfer
Heat transfer from pluton to wall rock can be dominantly driven by
conduction and by convection and/or advection. The rate of conductive heat
transfer is a function of the thermal diffusivity of the wall rock, while convective
and advective heating rate is a function of the velocity of a flowing body, such as
groundwater or magmatic flow (Turcotte and Schubert, 1982). Convection is a
buoyancy driven process caused by the heating of a mobile fluid, and implies a
circulating flow path of fluids driven by a heat source. Advection applies to an
open system where fluids are permanently driven off by the heat source. In
27

contrast, conduction is heat transfer through a non-flowing material (Stuwe,
2002). It is important to determine which mode of heat transfer is dominant
because their fundamental differences produce different aureole characteristics
and different timing for peak metamorphism.
Wall rock permeability and the availability of fluids are the two major
factors that determine the degree to which conduction or convection may
dominate in a system. The aureoles of intrusions emplaced at shallow crustal
levels are generally dominated by convection, due to the availability of
substantial fluid volumes and the higher permeability of upper crustal rock
(Johnson et al., 2011). There has been significant work done, especially from
studies in porphyry ore deposits, to determine the probability of hydrothermal
flow as a dominant mechanism for wall rock metamorphism (Cathles, 1977;
Norton and Knight, 1977; Norton and Taylor; 1979; Parmentier and Schedl, 1981;
Johnson and Norton, 1985; Hanson and Barton, 1989; Cook et al., 1997). At
greater depths (below ~8-10km), the role of fluid convection becomes
overshadowed by conduction due to reduced fluid availability and permeability
(Walther, 1990). At these depths, conduction can be a rate controlling factor if
there are no developed fractures that allow direct transfer of magmatic volatiles
into the wall rock (Furlong et al., 1991).
4.2. Contact Metamorphism in the Shatter Zone
Bar Harbor Formation clasts within the Shatter Zone exhibit metamorphic
textures which indicate an increase in thermal influence relative to the intrusive
28

contact (Figure 4.1). The metamorphic intensity increases from the biotite-chlorite
assemblage found in the undeformed Bar Harbor Formation to the cordieritegarnet
assemblage that dominates most of the Shatter Zone, finally increasing
grade to orthopyroxene-cordierite hornfels facies proximal to the Cadillac
Mountain Granite contact. Isograds (Figure 4.2) were determined by a set of 11
samples taken along a traverse of the Shatter Zone. The samples from this
traverse represent all known facies within the contact metamorphic aureole. Most
mineral identification was done optically and some with electron microprobe.
4.3. Methods for Contact Metamorphic Thermal Modeling
Many attempts have been made to calculate the cooling history of igneous
intrusions. The problem is described as a volume of magma with known shape
and initial temperature that intrudes the wall rocks with known temperature, and
the subsequent variation in thermal gradient caused by the contact is to be
calculated (Jaeger, 1961, 1964; Hart, 1964; Parmentier and Schedl, 1981; Attoh
and van der Meulen, 1984; Hanson and Barton, 1989; Bowers, 1990; Annen and
Sparks, 2006; Johnson et al., 2011).
Conduction models can serve as a baseline observation to better
constrain some first order variables, including the dominant mode of heat
transfer. For example, if the thermal gradient produced by the model does not
match the isograds identified in the field, it could be that convection and/or
advection played a large part in heat distribution. If isograd and model data
match well, heat transfer was more likely dominated by conductive heat transfer
29

A
B
Grt
C
Grt
D
Crd
Crd
E
1 mm
F
Crd
Crd
Crd
Bt
1 mm
Figure 4.1. Mineralogy of the contact metamorphosed Bar Harbor Formation. A)
Biotite in a metapelite layer 1000m in map distance from the reservoir contact. B)
and C) are garnets found in a sample 950m from the contact. D) and E) are
examples of abundant cordierite within 950m of the contact, often with
groundmass inclusions displaying growth stages. F) Cordierite porphyroblasts
found 450m from the contact, with biotite rims.
30

G
H
Opx
Opx
I
J
Opx
K
1 mm
L
Granite
Matrix
Diorite
Clast
Opx
1 mm 1 mm
Figure 4.1. Continued. G) Pyroxene begins to appear 450m from the intrusive
contact, and becomes more prevalent H) within meters of the contact, shown in
plane light and I) crossed polars. J) The groundmass of the Bar Harbor
Formation near the contact displays abundant ilmenite grains. The rim of a diorite
clast K) in plane light and L) with crossed polars.
31

!
!
!
!
Biotite Zone
Garnet Zone
!
!
!
Cordierite Zone
!
Pyroxene Zone
500 m
N
Figure 4.2. An isograd map of the Shatter Zone. Isograd data comes from 11 samples collected in a transect of the
northeastern Shatter Zone. Most of the metamorphic aureole is contained within the Shatter Zone.
32

(Furlong et al., 1991; Johnson et al., 2011). These discrepancies can give
information about the balance between convection and conduction, and may lead
to a conclusion on the dominant mode of heat transfer. One may also consider
the dynamic heat input from incremental pluton emplacement, chamber
convection, and recharge events (e.g. Hanson and Barton, 1989; Bergantz,
1991; Pignotta et al., 2010), which would all effectively elevate the maximum
temperature achieved in the wall rock and drastically change the spatial range of
metamorphism (e.g. Turcotte and Schubert, 1982; Furlong et al., 1991; Stuwe,
2002). Regardless, it is most beneficial to use conduction modeling for initial
observations because 1) dependent variables for conduction are easily
constrained, 2) using conduction modeling will give an end-member constraint on
the rate of heating and possible isograd trends, and 3) it provides a simple yet
realistic thermal behavior for a contact metamorphic zone (Bergantz, 1991).
For precise modeling, where a solution is required near the contact
between magma reservoir and wall rock, it is beneficial to correct for latent heat
of fusion for the crystallizing magma body (e.g. Jaeger, 1961). A crystallizing
granite can produce 400kJ Kg -1 °K -1 before the solidus is reached (e.g. Burnham
and Nekvasil, 1986; Furlong et al., 1991). Additionally, endothermic metamorphic
reactions, such as dehydration in pelites, can absorb 60 to 110kJ mol -1
of
released H 2 O or CO 2 , depending on the particular reaction (e.g. Furlong et al.,
1991). Applications of these components are discussed below and in Chapter 7.
33

4.3.1. Model Setup
The model is used to produce a maximum temperature gradient with
distance into the metamorphosed zone, and to compare these results with
observed isograd data. This comparison will allow us to constrain the thermal
evolution of the Cadillac Mountain intrusive complex and surrounding wall rock.
The thermal evolution of the wall rock surrounding the intrusion was solved
numerically by use of COMSOL Multiphysics (www.comsol.com), a finite element
program equipped with a conductive heat transfer module. Behavior of the
thermal conductive system is dependent on the thermal conductivity, specific
heat, and density of the intrusion and wall rock as well as latent heat of fusion for
the crystallizing intrusion, endothermic metamorphic reactions in the wall rock
that consume heat energy, the initial intrusion temperature, and the initial wall
rock temperature during emplacement (Jaeger, 1961; Johnson et al., 2011).
It must be noted that the Cadillac Mountain intrusive complex was
emplaced around 2-5km depth, so the wall-rock thermal evolution was probably
affected by convective flow of water (e.g Walther, 1990; Johnson et al., 2011).
Also, the duration of intrusion activity plays an important role in determining
maximum temperature for contact metamorphism. Multiple dike-fed
emplacements are common for shallow intrusives, and the gabbro-diorite sheets
that form the base of the Cadillac Mountain intrusive complex are evidence for
this type of activity (Jellinek and DePaolo 2003, Glazner et al. 2004, Cruden
2005, Bartley et al. 2006, Lipman 2007, Walker et al. 2007, Michel et al. 2008,
Miller 2008). Plutons reinvigorate with the continued introduction of magma,
34

causing contact aureoles to become wider and achieve higher peak metamorphic
temperatures over far longer timescales compared to those with a single intrusive
sequence (Hanson and Barton, 1989). The model is limited by assuming a single
instantaneous intrusion in a conduction dominated system, but the results will
provide a foundation for future studies with more realistic constraints (e.g., Attoh
and van der Muellen, 1984).
For the conduction dominated model, I assume that the Bar Harbor
Formation was metamorphosed before wall-rock brecciation and there was a
single, instantaneous intrusion event that was allowed to thermally equilibrate
with the wall rock. Latent heat correction was included during magma
solidification within the range of 700-800°C, producing 400kJ kg -1 °K -1 of extra
heat energy (see Chapter 7 for a more detailed explanation on how latent heat of
crystallization is calculated). I disregard the expenditure of heat energy by
endothermic metamorphic reactions, which can account for 60-110 kJ per mole
of H 2 O or CO 2 released from a dehydrating pelite (Furlong et al., 1991). Intrusion
geometry plays a major role in the resulting spatial distribution of the thermal
gradient. The rate of conduction is entirely dependent on the material’s thermal
diffusivity and the thermal gradient, but an object with high surface area to
volume ratio is more exposed to the diffusive contact, allowing much faster heat
transfer (Jaeger, 1961). It is important that the model geometry closely
approximates that of the real intrusive system. Therefore, I produce a 3
dimensional model by digitally tracing the Cadillac Mountain Granite in map view,
simplifying the geometry for use in COMSOL, and extruding it 2km into z space
35

to make a “hockey puck” style geometry (figure 4.3). The gabbro-diorite unit is
added to the base and is given the same shape and thickness of 1km. Model
boundaries must be placed at a substantial distance from the region of interest
so as to not interfere with the heat transfer model. Therefore, the outer model
boundaries lie 100 km away from the pluton center and are thermally insulated.
The interface between the intrusion and the country rock is open and allows for
free conductive heat transfer. A tetragonal mesh is used, with a fine boundary
mesh located at the intrusive contact for increased resolution of the thermal
evolution adjacent to the heat source.
Initial wall rock temperature is 150°C at an emplacement depth of 5km
based on a typical upper crustal geotherm of 30°C/km. I am concerned with the
lateral evolution of the thermal gradient, so there is no need to calculate the local
geothermal gradient for this model. The intrusion temperature was approximately
900°C, higher than average for a granitic magma (Wiebe, 1997). The gabbro
diorite sheet is given an initial temperature of 1200°C. The thermal diffusivity ( )
of Bar Harbor Formation is set at 1.30E-6 m 2 /s calculated from
(4.1)
Where is thermal conductivity, is density, and is specific heat. Thermal
diffusivities for Cadillac Mountain Granite and gabbro are given values of1.34E-6
m 2 /s and 1.01E-6 m 2 /s, respectively. A series of 300 time steps are taken from
time = 0s to time = 1E14s, producing solutions for the evolving thermal gradient
nearly up to a point of thermal equilibrium (Figure 4.4).
36

A
B
C
D
Figure 4.3. Geometry of the intrusion model. A) A view of the entire model, with
wall rock boundaries located 100km away from the reservoir’s center. B) A
closeup of the Cadillac Mountain Granite reservoir geometry in map view and C)
displaying the “hockey puck” style extrusion into 3 dimensions, with the basal
gabbro-diorite unit in green. D) The mesh used to solve the conductive heat
transfer equation, with the greatest node frequency near the contact between the
reservoir and the wall rock to obtain the most accurate results in the zone of
interest.
37

t = 0s
t = 1E11
t = 1E12s
t = 1E13s
t = 1E15s
Figure 4.4. Time steps for the cooling chamber. Time steps show temperature
distributions in x-y and x-z space.
38

4.3.2. Results and Discussion
Results (figure 4.5) show temperature versus time curves for 100m
interval points from the chamber-wall rock contact, points located at the observed
isograds, and a point 400m into the intrusion. The peak metamorphic
temperature, 635°C, occurred at the intrusive contact at t = 1.9E11s (~6000
years). Peak temperature 500m from contact was 510°C at t = 3.2E12s (~1E5
years), and 1000m from the contact, peak temperature was 458°C at t = 6.2E12
(~2E5 years).
The single intrusion model provides a similar gradient trend within the
metamorphosed zone, but the model did not attain the temperatures required to
form the observed peak metamorphic facies (figure 4.6a). For this model, Garnet
and cordierite are stable at temperatures as low as 460°C, which is possible for
low pressure metamorphism (Blatt et al., 2006). This simplified conductive model
cannot fully explain the metamorphic pattern seen for pyroxene, however.
Metamorphic orthopyroxene requires a temperature of at least 650°C at 1.5 kbar
pressure or ~5 km depth (Spear et al., 1999; Blatt et al., 2006).
If the pluton contact is not actually vertical, the surface exposures of the
metamorphic zones may be oblique from their true thicknesses (figure 4.6b). This
could explain the wider than expected thickness of the pyroxene zone and it may
provide a constraint on the geometry of the magma reservoir and the Shatter
Zone. If the metamorphic aueole dips outward or inward with respect to the
chamber by 45 degrees, the “true” thickness of the pyroxene zone is
39

850
750
650
550
450
400m Into Chamber
Temperature (°C)
350
Chamber Contact: Pyroxene Zone
Cordierite-Garnet Zone: 450m
250
Garnet Zone: 950m
Bio te Zone: 1000m
150
100m Intervals from Contact
0 50000 100000 150000 200000 250000 300000
me (years) a er intrusion
Figure 4.5. A temperature versus time plot from intrusion model results. Colored curves are for points on the isograd
borders. Grey curves are points located on 100m intervals from the reservoir contact.
40

A
650
Orthogonal Distance from Chamber Contact (m)
0 100 200 300 400 500 600 700 800 900 1000
630
610
Peak Temperature (°C)
590
570
550
530
510
B
490
470
450
5710 25710 45710 65710 85710 105710 125710 145710 165710 185710
Time (years) a er intrusion
650
630
610
Orthogonal Distance from Chamber Contact (m)
0 100 200 300 400 500 600 700 800 900 1000
observed Tmax vs. distance trend
45 degree contact dip correc on
Peak Temperature (°C)
590
570
550
530
510
490
470
450
5710 25710 45710 65710 85710 105710 125710 145710 165710 185710
Time (years) a er intrusion
Figure 4.6. Maximum metamorphic temperature with orthogonal distance from
the contact. A) Isograd positions are located from colored points. Cordierite,
garnet, and biotite could form at the observed maximum temperatures, but the
conductive model cannot explain the formation of metamorphic pyroxene. B) A
comparison between the apparent thickness of metamorphic zones (solid line)
and the thickness of zones if the intrusive contact is dipping at 45 degrees
(dashed lines). If the observed contact is oblique, the metamorphic aureole would
be skinnier.
41

approximately 140m thinner. The Shatter Zone thickness is 300m thinner.
Unfortunately, there is not enough data on the depth geometry of the Shatter
Zone, and there is no proof for a tilted section on the eastern side of the Cadillac
Mountain intrusive complex.
4.4. Evidence for an Actively Mixing Chamber
The maximum temperature achieved by this model does not explain the
existence of a pyroxene zone. The assumptions used for this model are therefore
unrealistic for the Cadillac Mountain intrusive complex, proving that magma
reservoir convection and replenishment were active components of heat transfer.
Additionally, wall-rock groundwater convection from 2-5km depth likely played a
part in contact metamorphism. The Cadillac Mountain intrusive complex was part
of a volcanically active region, which experienced several eruptive sequences
(Chapman, 1962; Berry and Osberg, 1989; Seaman et al., 1995; Seaman et al.,
1999). Widespread presence of enclaves (Wiebe et al., 1997b), evidence of
magma mixing (Chapman, 1962), and the presence of interlayered gabbro and
diorite sheets at the chamber base prove that the Cadillac Mountain Granite was
host to magma replenishment and actively mixing before eruption. Bimodal
chamber systems can often undergo several sequences of reactivation from
mafic dike “entrapment” (e.g. Wiebe, 1994, Wiebe et al., 2004), and chamber
replenishment can lead to overpressurization and potential eruption (e.g. Folch
and Marti, 1998). The thermal input after wall rock brecciation, discussed in
Chapter 7, would have been substantial. The Cadillac Mountain Granite likely
42

followed this open system behavior, therefore contact metamorphism in the
Shatter Zone was additionally affected by 1) convection of magma within the
chamber, 2) magma replenishment, which provides an additional thermal input,
and 3) the thermal input from magma intrusion after wall rock brecciation. These
factors contribute greatly to the resulting metamorphic aureole within the Shatter
Zone, and they reflect the crucial link between magma plumbing systems and
volcanic systems.
Development of the Shatter Zone is directly dependent on the thermal and
mechanical properties of the subvolcanic system to which it is linked. Having
discussed how the thermal potential energy of the intrusive complex affects the
surrounding wall rock, it is now necessary to discuss the mechanical energy
involved in wall rock fragmentation.
43

Chapter 5
ROCK MECHANICS AND THE FRACTAL BEHAVIOR OF ROCK
As contact metamorphism reflects a part of the thermal component of
volcanic energy, wall rock brecciation is the manifestation of the kinematic
component of subsurface volcanic energy. In order to begin the physical
description of the Shatter Zone, I now describe the component of volcanic energy
partitioned into wall rock fragmentation. I use the Griffith fracture theory to
explain the basic physical mechanisms involved in rock fragmentation. It is
possible to link characteristic fragmentation patterns such as clast size
distribution and clast boundary shape to the rock’s original brecciation
mechanism. These characteristic patterns are dependent on the self-similarity of
rocks and how the fragmentation patterns will tend to repeat themselves
regardless of scale. Methods have been put forward to quantitatively describe
these self-similar patterns to better determine the link between fragmentation
characteristics and brecciation mechanism. Clast size distribution (CSD) and
clast boundary shape (CBS) are two fractal methods used in this thesis to
quantitatively determine the origin of the Shatter Zone. Clast circularity analysis
(CCA), though not a fractal property, is also used to determine the amount of
clast wear with distance from the magma reservoir.
44

5.1. Brittle Failure of Rock
5.1.1. Basic Principles of Griffith Fracture Theory
Failure occurs when a rock is no longer able to support a stress increase
without fracture; for brittle failure this implies the loss of cohesion along fractured
planes within the rock. Differential stresses are necessary to provide brittle failure
and shape change in a rock, and the value of differential stress achieved at
failure is a measure of the rock’s strength (Goodman, 1980; Grady and Kipp,
1987; Hoek and Brown, 1997; Twiss and Moores, 2007). Fracture development
can be described by the work of A. A. Griffith (1920), whose theory successfully
explained the inequality between material strength as calculated by the strength
of atomic bonds in the material, and the actual observed strength of the
respective material. Griffith’s theory states that all solids contain many
microscopic cracks of random orientation, which greatly reduce the potential
strength of the material. These cracks are meant to represent the imperfections
in crystal lattice planes or grain boundaries, and are typically modeled as
elliptical and penny shaped in three dimensions, with an extremely small radius
of curvature at the crack tip (Figure 5.1a).
Failure of the material at the fracture tip is determined by a critical tensile
stress
defined as
(5.1)
where is Young’s modulus, is the specific surface energy required to break
the atomic bonds of the material (surface tension), and
is the fracture half
45

A
β
δ
σ 1
σ 3
σ t
c
a
σ 1
σ 3
β
Direction of crack
propagation
δ
B
σ t
Figure 5.1. An elliptical Griffith crack under compressive stress. Given a crack
orientation normal to β, tensile stress will concentrate at a point along δ. A
greater ratio of crack half length (a) to width (c) produces a reater local
concentration of tensile stress. B) When the crack fails under compression,
tensile cracks propagate parallel to δ and shear is accommodated along the
fracture walls (modified from Twiss and Moores, 2007).
46

length (Griffith, 1920). The shape of the crack plays an important role in stress
concentration: an elliptical crack with a high length to width ratio will provide a
greater concentration of stress at the fracture tips, promoting propagation. Given
the same host material, an order of magnitude increase in fracture length
decreases the required critical tensile stress by a factor of approximately 3.2.
This implies that once large fractures develop, they require less tensile stress to
continue propagation and they have a greater ability for growth than smaller
nearby cracks (Goodman, 1980; Twiss and Moores, 2007). Pore pressure
in
fluid-filled cracks will directly reduce ( ). The fracture will propagate
normal to the stress gradient, parallel to σ 1 . Propagation ends when the fracture
tip reaches an interface that it cannot penetrate, such as the wall of another
crack, or when the applied stress decreases to the point at which local stress
concentrations are subcritical.
The orientation of the applied stresses with respect to the Griffith crack will
determine the behavior of local stress concentrations. The local stress gradient is
dominated by a concentration of maximum tensile stress at an angle δ between
the axial length of the crack and the maximum principal stress direction σ 1 near
the crack tip. The orientation of the most critically stressed Griffith crack under
compression is at an angle between 0-45° from σ 1 , depending on the values of
σ 1 and minimum principal stress σ 3 , and this is generally the range in which most
shear fractures form (Figure 5.1b). If a Griffith crack’s axial length is parallel to
σ 1 , δ is located at the fracture tip and longitudinal cracking will occur with no
shear component (Mode I). For a crack with axial length not parallel to σ 1 ,
47

friction along the closed crack surfaces caused by the compressive normal
stresses produce a local stress distribution slightly different from those cracks
that experience purely tensile fracture. Tensile cracks begin to form along the
direction of δ to allow accommodation of shear along the main body of the
fracture plane (Mode II and III). The orientation of the newly developed tensile
crack tends to migrate parallel to the σ 1 direction. Because of this, shear
fracturing in a compressed rock is actually dependent on the development and
growth of small tensile fractures (Grady and Kipp, 1987; Twiss and Moores,
2007).
5.1.2. The Self-Similarity of Fracture Patterns
Although Griffith fracture theory describes initiation of cracks at the
microscopic level, fracture behavior can be described this way at any scale.
Brecciated rocks display the scale independent, or self-similar, characteristics of
fracture propagation by the patterns produced along fracture surfaces and size
distribution of clasts. Physical brecciation is the result of fracture propagation
carried over many scales. Breccias form from the nucleation, propagation, and
intersection of these fracture paths (Laznicka, 1988). It is the self-similar pattern
of these fracture surfaces and frequency of intersections that define a breccia.
The form of the repeated pattern is dependent on the mechanism of
fragmentation, and study of these patterns can provide information on the
characteristics of the resulting breccia. The numerous different mechanisms that
produce breccias provide noticeable differences in their physical characteristics;
48

therefore it is possible to relate a breccia to its mechanism of formation by
analyzing these self-similar characteristics.
5.2. Fractal Theory
When an object shows self-similar properties, it is described as fractal.
Fractal theory sprouted from the desire to quantitatively describe geometries
observed in nature. Unlike Euclidean geometry, fractals refer to complex shapes
defined by a fractional, or fractal, dimension (D) (Mandelbrot, 1967, 1983; Urtson,
2005). Founded by Benoit Mandelbrot in 1967, fractal theory has since been
applied to many scientific problems. The self-similarity of fractals implies that
patterns tend to repeat themselves at all scales, and for a true fractal, the
number of scales of natural patterns is infinite. For the initial purposes of this
thesis, it is best to consider the fractal dimension in terms of a repeated pattern
of size distribution. Consider the repeated pattern in Figure 5.2 (Sammis et al.,
1987). Sections of a cube are repeatedly split into smaller and smaller
components, producing a distribution of various sizes. This pattern is quantified
by
(5.2)
Assuming that the pattern of size distribution produced by breaking the cube is
fractal, the fractal dimension is a function of the number of cubes with side
length . For the broken cube, the pattern of size distribution is fractal, and =
2.58. This value is unique to this size distribution and any change from this
pattern would produce a different
. Interest lies in the self-similar characteristics
49

h
h/2
h/4
Figure 5.2. A cube displaying self-similar size distribution properties. The cube is
segmented over several scales, with each broken cube equal to half the height
and an eighth the volume of the next biggest cube. Using equation 5.2, the fractal
dimension for this object is 2.58 (modified from Sammis et al., 1987).
50

of size distributions and surface patterns of Shatter Zone clasts, so fractal theory
will now be applied to these breccia characteristics.
5.3. Quantitative Methods of Breccia Classification
5.3.1. Clast Size Distribution
Particle size distribution is a commonly applied method for determining
brecciation mechanisms from observed clast characteristics (e.g. Harris, 1966;
Harris, 1968; Hartmann, 1969; Schoutens, 1979; Sammis et al., 1986; Turcotte,
1986; Sammis & Biegel, 1987; Englman et al., 1988; Marone and Scholz, 1989;
Blenkinsop, 1991; Shimamoto and Nagahama, 1992; Nagahama and Yoshii,
1993; McCaffrey & Johnston, 1996; Jebrak, 1997; Tsutsumi, 1999; Perfect, 1997;
Zhang, 1999; Higgins, 2000; Blott & Pye, 2001; Wilson et al., 2001; Elek and
Jaramaz, 2002; Saotome et al., 2002; Clark & James, 2003; Spieler et al., 2003;
Barnett, 2004; Zi-Long et al., 2006; Farris & Paterson, 2007; Bjork et al., 2009).
The term “clast size distribution” (CSD) is preferred because of its relevance to
breccias. Brittle materials have the general tendency to fracture in a self-similar
pattern in which clast frequency increases exponentially with a decrease in clast
size, and it has been proven possible to relate the size distribution of clasts to the
mechanism of brecciation (Turcotte, 1986; Jebrak, 1997; Perfect, 1997). The
relationship between clast size and cumulate frequency is defined by the power
law equation (similar to equation 5.2)
(5.3)
51

where N (≥r) is the count of clasts with a radius greater than or equal to r, k is a
unit-dependent constant, and D s is the fractal dimension for clast distribution, and
it is considered to be a measure of fracture resistance relative to the mechanism
or process of fragmentation. D s is proportional to the magnitude and rate of
stress loading, the inherent strength properties of the rock, and the possibility of
repeated fracturing events, and therefore can be used to determine the
mechanisms involved in rock fragmentation (Figure 5.3). It is also sensitive to
any secondary mechanisms that may alter the original distribution. The negative
slope signifies the advance of clast population with decreased size.
When producing results for CSD, the clasts in breccias are not perfect
spheres, therefore one must correlate the volume of the clast with an equivalent
value for radius (equal area diameter of Brittain, 2001; Bjork et al., 2009)
calculated by defining a circle with an area identical to that of the clast of interest
(5.4)
The radius value is directly proportional to the area of the clast and is therefore
both suitable for CSD analysis and allows for coherent comparison of data to
other studies, as using an equivalent radius/diameter value is the most popular
method to display CSD data from 2 dimensional sources (Barnett, 2004; Farris
and Paterson, 2007; Bjork et al., 2009).
Sample bias from the inability to see the finest clast populations can
produce a non-fractal trend for finer-scale populations; therefore it is necessary
52

53
Figure 5.3. An example clast size distribution plot. Ds is solved by plotting the cumulate number N of clasts below a radius
r over several radius intervals. A steeper slope implies a more intense brecciation mechanism as observed from hydraulic,
shear, and explosion breccias.

to place a minimum size limit when measuring clasts (Blenkinsop, 1991; Clark
and James, 2003; Barnett, 2004).
CSD data are commonly presented with respect to 3-dimensional space. If
an object is fractal in 2-dimensions, it is also fractal in 3-dimensions, and
(5.5)
This conversion is validated by the fact that D s refers to the line, surface, or
space that dissects the object. An increase in Euclidean dimension requires the
same increase in D s (e.g. Sammis et al., 1987). This conversion is justified for a
breccia made of a homogeneous, isotropic material, but error can be introduced
if this assumption is used on anisotropic materials (e.g. Barnett, 2004; Farris and
Paterson, 2007). To reduce this potential error, outcrops with 3 dimensional
exposures can be used. Clast distribution can also be expressed as a function of
clast frequency versus mass (e.g. Hartmann, 1969; Blenkinsop, 1991), or percent
sample by weight versus diameter (see Schoutens, 1979), both of which are
directly related to a 3-dimensional distribution. These results also pertain to
power law distributions and therefore their slopes are proportional and can be
converted to D s (Blenkinsop, 1991; Perfect, 1997).
5.3.2. The Fractal Dimension-Brecciation Mechanism Link for Clast
Size Distribution (CSD)
Understanding the brecciation mechanism will provide important
information on the mechanical response to subsurface volcanic eruption. As CSD
results are a function of the self-similar manner by which fractures proliferate
54

through a medium, the fractal dimension D s is influenced by the intensity of
fracturing. There are several potential mechanisms that could have formed the
Shatter Zone, and three possible end-members will be discussed: 1) pre-eruptive
magma emplacement caused hydraulic fracture of wall rock, 2) caldera
subsidence produced an abrasive collapse breccia along ring faults, or 3) the
rapid volume expansion of volatiles during eruption lead to explosive fracture of
chamber walls. These three mechanisms are fundamentally different and will
therefore produce different breccias with unique D s values.
In rock mechanics studies there are two end-member mechanisms for
minimum and maximum D s : hydraulic fracture and explosion (Jebrak, 1997; Clark
and James, 2003; Barnett, 2004). Abrasive breccias tend to produce size
distributions defined by a relatively intermediate D s (Jebrak, 1997; Sammis et al.,
2007). Hydraulic breccias are well defined by Griffith fracture theory because
they form from fluid assisted (for this paper, magma and groundwater could be
considered) incremental fracture propagation driven by tensile stress loading at
the fracture tip (Goodman, 1980; Clark and James, 2003; Genet et al., 2008).
Fracture propagation is driven by the condition of pore fluid pressure (
) in the
cracks (Dutrow and Norton, 1995; Clark et al., 2006; Genet et al., 2008).
Hydraulic fractures typically form due to an increase in
by volume increase
driven by fluid flow and thermal expansion. This is generally an incremental
process, with a rate determined by the amount of fluid and interconnected
cracks, the thermal gradient, and the rate of fluid flow (Clark and James, 2003).
Cracking usually occurs by an oscillating pattern of incremental
buildup to the
55

moment of sudden fracture tip failure and sudden reduction of
(Dutrow and
Norton, 1995). As hydraulic brecciation is a low stress intensity mechanism, the
rate of propagation is generally slow and fractures will tend to develop along
inherent planes of weakness in the rock. Hydraulic breccias tend to have a
shallow slope for size distribution due to an inability to produce new fractures
(D s =1-2; Jebrak, 1997; Clark and James, 2003; Barnett, 2004; Clark et al., 2006;
Farris and Paterson, 2007).
Abrasive breccias form during shear failure in a rock (Goodman, 1980;
Jebrak, 1997). Shear along ruptured surfaces can lead to abrasive fragmentation
along fracture walls. Like hydraulic breccias, abrasive breccias can also form
incrementally, but simple shear kinematics produce more complex fragmentation
patterns (Sammis et al., 1987; Blenkinsop, 1991). Continued grinding, plucking,
and reduction of clast size results in the development of fault gouge. Rotation
and flow of elongate clasts cause a preferred alignment with respect to flow
(Jebrak, 1997). The characteristics of abrasive breccias are more difficult to
constrain due to the complexities that arise in shear kinematics. D s values can
range widely based on strain rate, the amount of stress normal to the fracture
plane, and the number and duration of abrasion events (Sammis et al., 1986;
Sammis, 1987; Blenkinsop, 1991). For a collapse breccia, a single fragmentation
event linked to caldera subsidence is assumed. This breccia would produce D s
values on the order of 2-2.7 (Sammis, 1987; Blenkinsop, 1991). Fabric produced
by sense of shear and transport of clasts would also be visible, and clasts would
show evidence of imbrications and preferred orientation.
56

Explosion breccias are formed by an instantaneous localized volume
expansion and resulting shockwave of released elastic energy (Schoutens, 1979;
Ivanov et al., 2005; Goto et al., 2001; Lorenz and Kurszlaukis, 2006; Nikolaevskiy
et al., 2006; Sanchidrian, 2007). Brecciation intensity decreases with distance
from the point source of explosion. These breccias tend to have a high gradient
of increasing particle frequency with decreasing particle radius (D s ≥2.5;
Schoutens, 1979; Barnett, 2004; Bjork et al., 2009). This is the result of a chaotic
proliferation of fractures at a finer scale. As opposed to hydraulic brecciation,
explosive fragmentation is driven predominantly by the power of the explosion
and the bulk strength of the rock (Grady and Kipp, 1987; Jebrak, 1997). Higher
D s values correlate with high power mechanisms because there is skewed
preference for small fracture proliferations during high energy fracture events
(Turcotte, 1986; Jebrak, 1997).
Bedrock anisotropy is an additional variable that can lead to relatively nonuniform
and unexpected fracture patterns when compared to fractures in
homogeneous rock. The fracture patterns in the rock are dominated by inherent
weaknesses, preferring the widening of existent fractures as opposed to the
proliferation of new fractures (Takashi, 2008). D s would be partially influenced by
structural anisotropy.
5.3.3. Clast Boundary Shape
Boundary shape is another natural expression of self-similar patterns. A
fragment’s boundaries appear to be fractal in that the process by which they are
57

produced results in a self-similar geometry. Several authors have successfully
quantified this phenomenon for coastline statistics (Mandelbrot, 1967, 1983;
Klinkenberg, 1992, 1994; Allen et al., 1994; Andrle, 1996; Jiang and Plotnick,
1998; Xiaohua et al., 2004; Tanner et al., 2006) and for boundary analysis of rock
fragments and fracture paths (Jebrak, 1997; Berube and Jebrak, 1999; Bonnet et
al., 2001; Dellino and Liotino, 2002; Lorilleux et al., 2002; Jebrak and Lalonde,
2005). For example, consider the repeated pattern in Figure 5.4. Much like
Figure 5.2, boundary shapes are defined by a set of repeated patterns and can
be quantified by equation 5.2. The fractal dimension D r increases with greater
pattern complexity (Mandelbrot, 1983). The pattern is defined by the surface’s
tendency to follow a repeated configuration, in the case of this paper defined by
fragmentation and modification processes discussed in the next chapters.
Fragment surfaces display fractal-like characteristics but results are limited by
the ability to measure small-scale surface patterns (Lorilleux et al., 2002).
There are four major methods to quantify D r : step method, box counting,
dilation, and Euclidean distance mapping (Danielsson, 1980). Berube and Jebrak
(1999) published a comprehensive analysis of several boundary analysis
methods and concluded that Euclidean distance mapping is the most accurate
method to obtain D r for a non-Euclidean geometry. Euclidean distance mapping
is a method suited for computer algorithms applied to a black and white
silhouette of the clast (Figure 5.5). The algorithm produces a grayscale image
where each pixel is designated a brightness value proportional to its proximity to
the nearest pixel that makes up the outline of the given clast. The result is an
58

L/9
L
Figure 5.4. The Koch snowflake. The boundary shape pattern is self-similar at
any scale. Four length sections are continually repeated, each section spanning
1/3 the length of the next biggest feature. The fractal dimension of this repeated
pattern is ~1.26.
L/3
59

13
ln(area) (pixels)
12
11
10
9
ln(a) = 0.9322ln(w) + 6.9532
2
D r =1.0678
8
7
0 2 4 6
ln(width) (pixels)
Figure 5.5. Euclidean distance mapping on a clast outline. Given a minimum
grayscale, a ribbon of a given area and width is formed from the above clast
outline. This data is plotted and the slope is proportional to the fractal dimension
for CBS using equation (5.6).
60

outline of the clast, with a dark backbone directly over the border that brightens
up with distance from the outline. The brightness of the pixel is directly
proportional to the distance to the clast border, and an outline of known width is
made by setting a threshold to that value of brightness. D r can be calculated by
plotting the log of ribbon area A versus the grayscale number W and is obtained
by
(5.6)
with S as the slope subtracted from the Euclidean dimension of 2 to yield D r . The
Euclidean dimension 2 signifies that the clast exists on a two-dimensional
surface (Berube and Jebrak 1999, Lorilleux et al. 2002).
5.3.4. The Fractal Dimension-Brecciation Mechanism Link for Clast
Boundary Shape (CBS)
The most complex boundary shapes come from chemical breccias (D r
≥1.25), while the simplest are found in hydraulic or magmatic breccias (D r ≤ 1.1)
(Jebrak, 1997; Barnett, 2004). Explosive and abrasive breccias initially produce
angular clasts that may show relative complexity, but D r would still be relatively
low (≤ 1.25). CBS would tend to be low in a physically brecciated material
because fractures tend to align themselves with the direction of the maximum
principal stress. Because the direction of fracture would tend not to change, the
surface pattern of the fracture is defined by the paths of relatively straight cracks
(Berube and Jebrak, 1999). Modification processes that involve clast rounding
and corner break-off would also effectively reduce D r . It is unlikely that chemical
61

eaction processes were involved in the formation of the Shatter Zone, so a D r
value greater than 1.25 would not be expected (Jebrak, 1997; Lorrileaux et al.,
2002).
5.3.5. Clast Circularity Analysis
Although it is not a fractal property, circularity is directly influenced by the
degree of abrasion, dilation, and transport that occurs in the development of a
breccia, and it could prove important in comparing modified and unmodified
clasts (e.g. Dellino and Volpe, 1996, Clark, 1990). The greater the wear on the
clast, the more circular it will become owing to loss of high surface-area corners.
Circularity is a measure of the compactness of a shape, unlike boundary analysis
which is meant to quantify the complexity of surface patterns. Because a circle is
the most compact two-dimensional geometry, a shape’s compactness is
compared to the circle as the ratio
(5.7)
To calculate circularity of a clast, its area and perimeter must be determined.
Consider the area of a circle:
(5.8)
To define the area of a circle as a function of a given perimeter (the perimeter of
the noncircular clast), r must be replaced with p:
(5.9)
62

(5.10)
Substituting this into equation (3) for circularity (C):
(5.11)
This successfully produces a ratio between the area of a clast and the area of an
imaginary circle with perimeter equal to that of the clast. The ratio can range from
0 to 1, with very elongate shapes trending to 0 and very compact shapes
trending to 1.
63

Chapter 6
ANALYSIS AND RESULTS
The Shatter Zone represents the brittle response to magma reservoir
pressure fluctuations during evacuation. Reservoir overpressure occurs when the
rate of pressure loading cannot be accommodated by visco-elastic deformation
of wall rock. The differential stresses produced by overpressurization and
subsequent evacuations are substantial enough to overcome the elastic limit and
fracture wall rock, after which a volatile rich component of magma quickly
intrudes the fractures. Luckily, these intrusive features chill relatively quickly,
providing evidence for volcanic activity. The impetus of this thesis is to better
understand the mechanics of rigid rock in a subvolcanic setting. The Shatter
Zone formed from a subvolcanic reaction to volcanic eruption and I explore the
possible brecciation mechanisms that may have been active in the development
of the Shatter Zone. Field observations within the Shatter Zone describe the
gradational breccia characteristics. I discuss the methods used to collect CSD,
CBS, and CCA data, then provide the results of the analysis and move on to
confirm explosive brecciation as the likeliest developmental mechanism for the
Shatter Zone.
64

6.1. Field Relations in the Shatter Zone
6.1.1. Gradational Characteristics
The Shatter Zone is characterized by a transitional development of the
breccia (Figure 6.1) in which the degree of rock fragmentation is distributed as a
gradient. This gradient is interpreted to represent various time stages of breccia
development. The Shatter Zone can be divided into four breccia types based on
observational differences, three of which pertain to this study. The transition
ranges from highly brecciated and intruded rock to weakly brecciated beddingparallel
fractures, finally grading into unfractured bedrock.
6.1.1.1. Type 1. Type 1 Shatter Zone is interpreted to represent the initial
stage of breccia development (Figure 6.2). The Type 1 locality is Sols Cliffs,
positioned in northeast Mount Desert Island (44.37363, -68.18903). The
transition from solid, coherent Bar Harbor Formation to Type 1 Shatter Zone is
gradual. Granite veinlets (typically

Type 1
Type 2
500 m
N
Type 1
Type 2
Type 3
Type 3
Figure 6.1. The gradient of brecciation intensity through the Shatter Zone. The
gradient is represented by three types, with the greatest intensity of brecciation
adjacent to the Cadillac Mountain Granite. Red scale bars are 9cm for Type 1
and 10cm for Types 2 and 3.
66

A
B
Figure 6.2. Type 1 Shatter Zone. A) One outcrop image and B) its outline used
for CSD analysis. Scale bar is 9cm. Partial, uncounted clasts are dark grey.
67

A
B
Figure 6.3. Type 2 Shatter Zone. A) One outcrop image and B) its outline used
for CSD analysis. Scale bar is 10cm. Partial, uncounted clasts are dark grey.
68

A
B
Figure 6.4. Type 3 Shatter Zone. A) One outcrop image and B) its outline used
for CSD analysis. Scale bar is 10cm. Partial, uncounted clasts are dark grey, Bar
Harbor Formation clasts are light grey, and diorite dike clasts are black.
69

A
B
Figure 6.5. Centimeter-scale boudinage textures in Bar Harbor Formation. A)
Overburden cuases rigid calc-silicate layers to be pulled apart by pure shear and
weaker pelitic layers flow around them. B) A closeup image of a boudinage neck
filled with quartz.
70

6.1.1.2. Type 2. The observed breccia pockets seen in Type 1 may be a
precursor to those of Type 2 (Figure 6.3), which shows a greater frequency of
higher intensity breccia pockets and is deemed to represent the intermediate
stage in the developmental brecciation time scale. The Type 2 locality is along
Seely Road, located south of the Type 1 location (44.36303, -68.18332).
Brecciation in Type 2 outcrops appear to be more chaotic with minimal
preservation of the original bedding structures (Figure 6.6). Again, all matrix
material is fine grained and there is no evidence for late stage fracture. Diorite
dikes are more frequent, and some are brecciated.
6.1.1.3. Type 3. Type 3 Shatter Zone is the most evolved stage of
brecciation, in which isolated clasts are abundant, generally sub-equant, and
completely suspended in granite matrix (Figure 6.4). The Type 3 locality is on
Great Head, in the southeastern section of the island (44.32872, -68.17986). The
observed clasts in the Type 3 breccias are dominantly diorite, which contrasts
with Types 1 and 2. Many clasts appear well rounded with concentrations of
biotite along their rims. The matrix is generally fine grained with pegmatitic
material present in late stage cracks. Evidence for late stage cracking in diorite is
not uncommon. Many of the Bar Harbor clasts appear to have recrystallized, and
the most abundant Bar Harbor Formation clasts appear to be from the more
resilient layers. There are no flow textures in the matrix except for occasional
local features that apparently formed from minor clast rotation and settling
(Figure 6.7).
71

A
B
Figure 6.6. Brecciation textures in Type 2 Shatter Zone. A) A typical brecciation
pattern in Type 2 Bar Harbor Formation clasts. B) Late-stage fracture of a diorite
dike near the Type 2 locality leaves freshly fractured, angular clasts in a
pegmatitic matrix.
72

A
B
Figure 6.7. Local flow textures in Type 3 Shatter Zone. A) flow patterns
surrounding a diorite clast. B) Complex flow patterns surrounding relict Bar
Harbor Formation clasts.
73

The final breccia classified in this study, Type 4, is found within the
Cadillac Mountain Granite and consists of large, meter scale xenoliths of Bar
Harbor Formation, diorite, and felsic volcanics. The matrix is nearly as coarse
grained as the Cadillac Mountain Granite, and there are schlieren textures
surrounding some of the xenoliths. No more will be said of the Type 4 xenoliths.
There is significant change in clast morphology of Bar Harbor Formation
clasts between Type 2 and Type 3. This implies an additional modification
process that altered the original size and shape of Type 3 Bar Harbor clasts.
Additionally, outcrop observations suggest that Type 3 diorite clasts exhibit
additional size and shape modification by late stage fracturing (Figure 6.8). I use
clast size distribution (CSD), clast boundary shape (CBS), and clast circularity
analysis (CCA) methods to identify the primary developmental mechanisms and
to determine possible secondary progressions that could lead to clast
modification. The results lead to a discussion involving the use of thermalmechanical
modeling to explain the modification of clast size and shape, and in
doing so explain the transition from explosive to magmatic breccia.
6.2. Methods
Data from 12,732 clasts have been used to identify the brecciation
mechanism and quantify the physical modifications to clast size and shape. Clast
data were calculated from image mosaics collected from outcrops representative
of Types 1, 2, and 3 of the Shatter Zone (blue dots on Figure 2.1, Figure 6.1).
Grids were overlain on flat outcrops with individual boxes of 30x25cm. High
74

A
B
C
Figure 6.8. Evidence for secondary clast size, shape, and boundary modification.
A) Metapelite clast surface disaggregation and internal melting textures in Bar
Harbor Formation, B) late-stage fracture in a layered clast, and C) fracture of a
diorite dike clast imply post-brecciation modification.
75

esolution images of each box were stitched to create the image mosaics (Figure
6.9). Clasts were manually outlined from each mosaic in a drafting program to
differentiate between clast and matrix, producing a black (clast) and white
(matrix) image. Manual outlining was required because the grayscale separation
between clasts and matrix was commonly too small to accurately distinguish
them using image analysis software (e.g. Sudhakar et al. 2005). The outlines
were analyzed with NIH ImageJ for clast count, area, circularity, and boundary
shape. CSD, CBS, and CCA data were calculated from these output data. The
number of clasts used for CBS was limited compared to CSD because each
randomly chosen outline had to be analyzed individually.
For CSD of the Shatter Zone breccias, the equivalent radius was used to
plot data on a logarithmic size cumulate frequency plot, with a clast radius
interval of 10 0.02 cm. Only clasts greater than 1mm radius were plotted because
of difficulty in distinguishing between smaller clasts and the granite matrix.
Cumulate frequency was standardized to the total area covered for each outcrop
location to allow better comparison between locations with greater or smaller
outcrop representation. D s values were calculated from equation (5.3).
CBS data were produced by 42 ribbon width and area measurements for
428 clast outlines. Measurements were taken in NIH ImageJ. The log of ribbon
width was plotted with respect to the log of ribbon area, and D r was calculated
from the slope using equation (5.6).
76

Figure 6.9. An outcrop grid used for fractal analysis. The 30x25cm grid is lain
over the well exposed outcrop and a picture is taken for each rectangle. Images
are then later stitched together in a drafting program to perform manual clast
boundary tracing.
77

Clast circularity data were produced in NIH ImageJ using equation (5.11).
Clast frequency plots were produced using a 0.05 circularity interval for 0.1-1cm,
1-10cm, and >10cm clast radius intervals.
6.3. Data
6.3.1. Clast Size Distribution (CSD) Data
A total sample size of 14 imaged outcrops yielding 12,732 clasts with size
ranges spanning 3 orders of magnitude (0.1-40cm) was used for CSD analysis.
Types 1-3 of the Shatter Zone are represented and results are shown in Figures
6.10 and 6.11. Data are shown in Table 6.1. Type 1 Shatter Zone shows a
bifractal distribution, or two observed power law distributions divided by a slope
breakpoint, with an average D s value of 3.027 above clast radius of 1.25cm and
1.5 for clasts below. The R 2 values for these two distributions are 0.9868 above
the breakpoint and 0.9778 below. The curve for Type 1 represents 1,519 clasts
from four outcrop grids with a size range of 0.1-23.4cm. Type 1 has 16.1%
average matrix component by area.
Type 2 has an average D s value of 3.166 above clast radius of 1.52 cm
and D s = 1.875 below. The bifractal R 2 values for the Type 2 distribution are
0.9932 above and 0.9865 below the breakpoint. The total sample size for Type 2
is 5538 outlined clasts from four outcrop with a size range of 0.1-13.02cm. Type
2 has 34.4% average matrix component by area.
Clast size populations in Type 3 Shatter Zone are divided by rock type due
to the marked increase in diorite dike clast abundance. These results show the
78

Type 1 Type 2
Type 3
Bar
Harbor
Type 3
Mafic
dike
fine D 1.5 1.875 1.66 2.625
coarse D 3.027 3.166 4.06 2.625
ΔD s 1.527 1.291 2.4 -
breakpoint 1.25 cm 1.52cm 1.6cm -
% matrix 16.10% 34.40% 74.96% 74.96%
# clasts 1519 5538 284 5480
# outcrops 4 4 7 7
Table 6.1. Average CSD values
79

A
1000
Clast Size Distribu on: Type 1
Cumulate Frequency N/m 2
100
10
1
Type 1
D sc
= 3.02
R² = 0.9778
D sf
= 1.51
R² = 0.9868
Count:1519
B
Cumulate Frequency N/m 2
0.1
1000
100
10
1
0.1
0.1 1 10
clast radius r (cm)
Clast Size Distribu on: Type 1
Type 2
D sc
= 3.2
R² = 0.9865
D sf
= 1.9
R² = 0.9932
Count:5538
0.1 1 10
clast radius r (cm)
Figure 6.10. Clast size distribution data for Type 1 and 2 Shatter Zone. A)
Trendlines for Type 1 are split between coarse (D sc ) and fine (D sf ) distributions.
B) Coarse and fine distributions are also presented for Type 2. For comparison to
three dimensional studies from 2 dimensional data, D = slope +1.
80

A
1000
CSD Type 3 compared to Type 2
Type 2 Bar
Harbor clasts
D = 3.2
count: 5538
R² = 0.9865
Type 3 diorite
clasts
D = 2.63
count: 5391
R² = 0.9891
100
Type 3 Bar Non-fractal
Harbor clasts
count: 284
R² = 0.9915
Cumulate frequency/m^2
10
1
cumulate frequency/m^2
1000
100
10
1
B
D sf
= 1.66
R 2 = 0.9867
Diabase clasts (count=5391)
Bar Harbor clasts (count=284)
D sf
= 4.06
R 2 = 0.9492
D = 2.63
R² = 0.9891
0.1
0.1
0.1 1 10
radius (cm)
0.1 1 10
Clast radius r (cm)
Figure 6.11. Clast size distribution data for Type 3 Shatter Zone. A) Type 3 data
are split by rock type: Bar Harbor Formation (red) and diorite (blue) size
distributions are compared to Type 2 distributions. Type 3 Bar Harbor formation
best fits an exponential (i.e., nonfractal) trend. B) An alternative bifractal
interpretation for Type 3 Bar Harbor Formation size distribution trend.
81

diorite dike with D s = 2.62 and R 2 = 0.9865 for the clast size range of 0.41-
11.82cm. The Bar Harbor CSD can be best defined in two ways: a bi-fractal
distribution with a breakpoint at 1.6cm and D s equal to 1.66 above and 4.06
below, or a non-fractal, exponential curve. The bifractal R 2 values are 0.9867
above and .9492 below the 1.6cm breakpoint. The R 2 value for the exponential
curve distribution is 0.9915. There are a total of 5675 outlined clasts from seven
outcrops, less than 20% of which are Bar Harbor Formation clasts. Diorite size
ranges are 0.1-11.8cm and Bar Harbor Formation size ranges are 0.1-4.24cm.
Type 3 has 75% average matrix component by area.
6.3.2. Clast Boundary Shape (CBS) Data
A total of 433 clasts from Type 1, 2, and 3 Shatter Zone, with an additional
outcrop (named 2.5) located between types 2 and 3 (44.35714, -68.18371), were
used for CBS (Figure 6.12). The CBS dataset comes from Hawkins and Johnson
(2004). Values of D r vary only slightly with most values approaching 1 (1.04-
1.12). Type 1 Shatter Zone has the highest average D r value of 1.125 but with a
relatively high standard deviation of 0.062 from 123 clasts. Type 2 has an
average D r of 1.052 with a standard deviation of 0.037 from 79 clasts, and Type
2.5 has an average D r of 1.047 with a standard deviation of 0.035 from 66 clasts.
Type 3 has an average D r of 1.040 with a standard deviation of 0.019 from 56
clasts.
82

Dr
1.2
1.18
1.16
1.14
1.12
1.1
1.08
1.06
1.04
1.02
1
Average D r
Clast samples size by type:
Type 1: 123
Type 2: 79
Type 2.5: 66
Type 3: 165
Type 1 Type 2 Type 2.5 Type 3
Figure 6.12. Clast boundary shape data ordered by Shatter Zone type. Error bars
denote one standard deviation from the average value shown by the colored bar
(From Hawkins and Johnson, 2004).
83

6.3.3. Clast Circularity Analysis (CCA) Data
Circularity data were collected for 8,724 outlined clasts over three orders
of magnitude for Shatter Zone Types 1-3 (Figure 6.13). Many of the same clasts
used for CSD were used for CCA. Type 1 clasts have the lowest average
circularity value of 0.48, and the circularity averages for the 0.1-1cm, 1-10cm,
and >10cm intervals are 0.54, 0.36, and 0.19, with population sizes of 925, 431,
and 5, respectively. Type 2 clasts have an average circularity of 0.58, and the
circularity averages for the 0.1-1cm, 1-10cm, and >10cm intervals are 0.61, 0.47,
and 0.27, with population sizes of 2,155, 595, and 9, respectively. Type 3 clasts
have the highest degree of circularity with an average of 0.76, and the circularity
averages for the 0.1-1cm, 1-10cm, and >10cm intervals are 0.77, 0.67, and 0.63,
with population sizes of 3,945, 644, and 14, respectively.
6.3.4. Summary of Data
All three types of Shatter Zone yield a value of D s above 2.5 for
distributions of radius greater than 1cm. Below this clast size, D s varies greatly
but is always lower than the D s of the coarser size range. The “breakpoint” in the
bifractal slope occurs over a small and consistent size range in Types 1 and 2.
Data from Types 1 and 2 come dominantly from Bar Harbor Formation clasts,
whereas data from Type 3 is split between diorite dike and Bar Harbor Formation
clasts. Magmatic fabric dominates in Type 3, with no clast preferred orientation.
Granitic matrix becomes more abundant with proximity to the Cadillac Mountain
Granite interface. Circularity increases with proximity to the intrusive contact and
84

% of clasts
40
35
30
25
20
15
10
Type 1
0.1-1cm radius clasts
1-10cm radius clasts
10+ radius clasts Total mean
1-
10cm
radius,
431
0.1-
1cm
radius,
925
10+cm
radius,
6
5
% of clasts
0
40
35
30
25
20
15
10
5
0
35
30
0 0.2 0.4 0.6 0.8 1
Circularity
Type 2
0 0.2 0.4 0.6 0.8 1
Circularity
40
Type 3
1-10cm
radius,
644
10+cm
radius,
14
1-
10cm
radius,
595
0.1-
1cm
radius,
2155
10+cm
radius,
9
Circularity
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Clast Circularity Analysis
0.1-1cm 1-10cm 10+cm
Type 1 Type 2 Type 3
% of clasts
25
20
15
0.1-1cm
radius,
3945
10
5
0
0 0.2 0.4 0.6 0.8 1
Circularity
Figure 6.13. Circularity data ordered by Shatter Zone type. Percent of clasts with
respect to circularity with slast radius bin sizes of 0.1-1, 1-10, and 10+cm
represented by red, green, and blue, respectively. Mean circularity values are
given by the bar graph to the right, and the pie charts display clast bin size
populations. The circularity interval is 0.05.
85

with decreasing clast size in all Types. CBS decreases with proximity to the
intrusive contact (Hawkins and Johnson 2004).
6.4. Discussion
6.4.1. Bifractal Distributions for Type 1 and 2
The change in slope for Types 1 and 2 represent some scale dependent
factor that limits the self-similar nature of rock fragmentation to a finite size
range. In this case, there are two clast size distributions with the slope change at
clast radius of approximately 1.5cm. Although the data are variable, bifractal
distributions with breakpoints at 1.25cm for Type 1 and 1.52cm for Type 2 best
represent these size distribution data trends.
Two possible factors affecting a rock’s fractal properties include scale
dependent rock heterogeneity (e.g. Clarke et al., 1998) and individual
mechanisms that are limited to a finite size range (Barnett, 2004, Farris and
Paterson, 2007). Interests lie in the mechanism or condition that produces a
relatively large D s for the coarse scale and a small D s for the fine scale. This
would imply greater fragmentation intensity forming the coarse clasts. One
possibility worth consideration involves the secondary modification of small clasts
entrained along previously formed fracture paths during intrusion. Soon after
fractures formed, volatile rich magma travelled up the fracture network. With the
introduction of a water-rich heat source, small clasts entrained in these fracture
networks would be highly susceptible to thermal disaggregation. This is a
mechanism dependent on clast melt and magmatic flow that produces bifractal
86

and non-fractal distributions (Jebrak, 1997; Clark and James, 2003). The matrix
only makes up 16% of volume in Type 1; therefore there would have been
enough heat to disaggregate small clasts, but not large ones, assuming that the
local matrix percentage by volume is greater than 16% in the magma channels
that hosted the smaller clasts (hypothetically, clasts with radius greater than
1.25cm saw little effect of disaggregation). This agrees with the high intensity,
large D s value for larger clast sizes (D s >3) and a low intensity, small D s value for
finer clast sizes (D s =1.5) because they are defined by differing mechanisms. The
D s values for the fine clast range of Type 1 are within the hydraulic brecciation
range. It is possible that clasts were host to fluid and thermal assisted fracture,
which would produce a D s below 2. The original fine clasts could have
disaggregated during magma intrusion, then new small clasts formed by thermal
fracture could produce a D s value similar to what are seen for the fine Type 1
distributions.
For Type 2, D s increases to 3.17 for the coarse clast size range and 1.875
for the fine range, with a breakpoint at 1.52cm. The matrix of Type 2 composes
34% of total volume, therefore there is greater potential for disaggregation of
small clasts. The D s value for the fine clast ranges of Type 2 is greater than Type
1, which may imply a greater intensity of fluid and thermal assisted fracture at the
fine scale.
Whereas D s values for the fine distributions of Types 1 and 2 imply a low
energy manner of formation, D s for coarse size distributions are above 3 for
Types 1 and 2, implying a high intensity mechanism. The two most viable
87

possibilities as postulated previously are collapse abrasion and chamber
explosion. Shear is the fundamental mechanism that produces an abrasive
breccia. The clasts of Type 1 and 2 fractured in place and they show no shear or
transport fabric. Additionally, the structures observed in the Shatter Zone imply a
450-1000m thick breccia gradient with intensity nearest to the intrusive contact. A
gradient such as this would be formed by a rapid, localized point of power
release, such as from the rapid volume expansion of volatiles in the magma
reservoir. The calculated D s values are within the explosion range, indicating that
chamber explosion was the likely cause of brecciation.
6.4.2. Differing rock types and clast modification evidence in Type 3
If the transitional character of the Shatter Zone is a record for the phases
of brecciation, Type 3 would be the final stage and closest position to the point
source for peak brecciation intensity. Diorite dike clasts have a D s that relates
well to an explosive breccia (Schoutens, 1979; Turcotte, 1986), but Type 3 may
be unrelated to Types 1 and 2, and could possibly represent a collapse breccia
based solely on the fractal dimension. Collapse breccias typically have lower D s
values (abrasive breccias typically fall between 2-2.7, e.g. Sammis et al. 1987;
Blenkinsop, 1991), and the diorite clasts do have a lower size distribution, but
this is likely caused by a fundamental difference in rock type. The homogeneous,
coarse grained diorite could not be expected to produce a D s equal to the Bar
Harbor metasedimentary rock, which has lower strength due to its composition.
Much like Types 1 and 2, there is also no evidence for clast fabric, imbrication, or
88

sense of shear. Type 3 Shatter Zone must be related to Types 1 and 2, which
have been confirmed as explosive.
The transition from fractal to non-fractal CSD slope for Type 3 Bar Harbor
clasts requires a significant change in mechanism, implying that some major
secondary modification process was at work to alter the size and shape of clasts.
This modification mechanism is unable to provide a self-similar size distribution,
which ties in to the marked drop in Bar Harbor clast abundance. CBS and CCA
data imply increased clast wear with proximity to the Cadillac Mountain Granite,
which also supports the hypothesis of secondary modification having a
noticeable effect on the alteration of Type 3 Bar Harbor clasts. In all cases, D r
decreases and circularity increases with closer proximity to the Cadillac Mountain
Granite interface. Much like CSD, one cannot interpret CBS as a complete
product of the brecciation event; it is more a manifestation of secondary
modification. If the clasts of Type 3 were originally as angular as Types 1 and 2,
CCA data show that there is substantial clast rounding after the major explosive
event. Possible modification mechanisms include thermal disaggregation, fluid
assisted fracture, and thermal induced fracture. These potential mechanisms are
fully discussed in the next chapter.
89

Chapter 7
MECHANISMS FOR SECONDARY CLAST MODIFICATION: A DISCUSSION
The thermal influence from the intruded granitic matrix of the Shatter Zone
had a significant influence on clast size distribution (CSD) data trends,
specifically for Bar Harbor Formation Type 3 clasts. The marked decrease in
small clast populations and boundary shape values as well as the increase in
clast circularity implies a non-fractal mechanism was active in the modification of
clast size, shape, and abundance. Potential mechanisms are explored for post
brecciation modification and I determine that disaggregation through partial melt
of clasts is the dominant mechanism at play. Transient two-dimensional models
are produced in order to quantitatively characterize the migration of solidus
temperatures through a conductively heated clast, and to determine the evolution
of CSD as clasts begin to partially melt. I show that disaggregation of clasts can
lead to a bi-fractal and eventually non-fractal CSD. Magma flow, a constraint
ignored in the thermal-mechanical model, is required to physically disaggregate
the melted clasts. Thermal fracture is another possible secondary mechanism
and is treated in a transient two-dimensional thermal stress model. Results show
that late-stage thermal fracture occurred in diorite clasts, but less is known about
the thermal stress characteristics of the structurally anisotropic Bar Harbor
Formation.
90

7.1. Potential Mechanisms for CSD and CBS modification
A secondary mechanism is required to produce the observed results for
CSD, CBS, and CCA. Potential mechanisms include 1) thermal disaggregation,
or the disintegration of clasts, by partial melt and assimilation into the
surrounding magma and 2) thermal fracture of clasts during magma intrusion.
These two options are considered because they are are relatively easily treated
numerically, and because field observations suggest that they played important
roles in the modification process. Although abrasion would play a part during the
active stages of wall rock readjustment, it cannot explain the nonfractal
distribution of sizes for Type 3 Bar Harbor Formation clasts. Clasts that are host
to late stage fracture show no evidence for kinetic impact or abrasion between
other clasts, therefore the only input that could produce fracture at this stage is
heat transfer from the enveloping matrix.
7.1.1. Thermal Attrition
Thermal disaggregation requires supersolidus temperatures to be reached
and presence of magma flow to physically disaggregate the clast (e.g. Braun and
Kriegsman, 2001). Thermal fracture is dependent on a heated material’s thermal
expansivity and requires the elastic response to sharp thermal gradients in rock. I
assume these two components to be agents of thermal attrition that had a
marked effect on Bar Harbor clasts and less of an effect on diorite clasts.
Thermal attrition is defined as any process or mechanism that directly enhances
the potential for removal or assimilation of clast material into the intruding
91

magma. To prove the viability of thermal attrition, thermal-mechanical equations
are solved using the finite element method (COMSOL Multiphysics). Partial melt
can play a large part in the volumetric removal of clasts and has been linked to
alteration of clast size distribution trends and reduced D s values (Farris and
Paterson, 2007). I assume that clast volume is disaggregated once the solidus
temperature is achieved, altering clast sizes with respect to time from the start of
intrusion (Marko et al., 2005; Clarke, 2007). Because of this, clast size
distribution evolves with the progression of heat conduction. However, this
assumption requires flow of the matrix magma in order to disperse the products
of partial melting, in addition to diffusional processes that would facilitate mixing.
Field observations do suggest local flow around clasts, but I did not quantitatively
evaluate the problem.
7.2. Methods: Partial Melting of Clasts
7.2.1. Model Setup and Important Parameters
In order to address thermal-mechanical coupling, I use two geometries
(figure 7.1): one is an ideal spherical clast and the other is an outcrop image from
Type 3 Shatter Zone. These two geometries are used to compare ideal
conditions with the complex clast geometries observed in the field. The twodimensional
models are closed systems that examine the instantaneous
immersion of Bar Harbor Formation metasedimentary clasts with D s of 2.5 in a
hot magma matrix. The model’s outer boundaries are periodic. Nodes are
defined by a triangular mesh. All clast-matrix boundaries have a fine boundary
92

A
B
Figure 7.1. Geometries used for thermal modeling. A) Type 3 Shatter Zone
outcrop geometry and mesh; box is 1x0.8m. B) A spherical clast geometry used
for optimization.
93

mesh to better evaluate large thermal gradients at these boundaries. All models
portray the transient behavior of thermal diffusion, and time steps were used to
collect thermal data for clast sizes that cover 3 orders of magnitude. Although
there was obviously some magmatic flow to fully disaggregate clasts, field
evidence does not suggest large-scale flow. Therefore, these models are limited
to conductive heat transfer. The ideal isolated spherical clast model was used to
define an ideal trend for phase boundary migration without geometric
interference. The outcrop-scale model was used to plot cooling patterns for the
observed geometry. Models are defined by the parameters in Table 7.1.
Geometry is the dominant factor that determines the pattern of conductive
heat transfer (Jaeger, 1961). Conductive heat transfer across a boundary is
fastest when surface area to volume ratios and thermal gradients are large
(Jaeger, 1961; Bowers et al., 1990; Furlong et al., 1991; Stuwe, 2002). I assume
a kinetically static interface between the clast and its granitic matrix; therefore the
rate of heat transfer is entirely dependent on the thermal diffusivities of the
granitic magma and the metasedimentary clast.
Initial temperatures for clast and magma must be determined to solve the
conductive heating equation. The relatively sparse occurrence of pyroxene
implies that the rocks were heated to the lower-temperature end of
orthopyroxene hornfels facies, so initial clast temperature is set to T clast = 650°C
(e.g. Spear et al., 1999; Milford et al., 2001; Blatt et al., 2006, Kriegsman and
Alvarez-Valero, 2010). Magmatic temperatures are modeled at T magma = 900°C
(Wiebe et al., 1997a). The outcrop-scale model contains 75% matrix by volume,
94

C p solid 850J/kg °K
C p magma 950J/Kg °K
L, Latent heat 4E5J/Kg °K
T intrusion
T clasts
900°C (1173°K)
650°C (923°K)
ΔT 250°C
T granite solidus
T feldspar crystallization
T clast solidus
800°C (1073°K)
825°C (1098°K)
720°C (993°K)
Thermal conductivity 3W/m °K
Density 2650 Kg/m 3
, diffusivity coefficient 1.33E-6 m 2 /s
Model area 0.8m 2
% matrix by area 75%
Table 7.1. Physical constants for thermal solutions.
95

consistent with Type 3 breccias. The solidus for the Bar Harbor Formation is
720°C, calculated using an optimization algorithm in PerpleX (Connolly, 2009)
and the thermodynamic database provided by Holland and Powell (1998).
Chemical data required for the thermodynamic calculations came from mineral
abundance data from Metzger (1959), and results were compared to melt data
from similar metasedimentary and metapelite rocks from the Ballachulish aureole
(Pattison and Harte, 1988) and from metapelite P-T-t paths (Spear et al., 1999).
I assume a single emplacement event in the Shatter Zone as there is no clear
field evidence for multiple injections.
Latent heat of granitic magma crystallization must be considered owing to
the large percentage of granite matrix in Type 3 Shatter Zone (Nekvasil, 1988;
Bowers et al., 1990; Furlong et al., 1991; Petcovic and Dufek, 2005; Huber et el.,
2009; Lyubetskaya and Ague, 2009; Dufek and Bachmann, 2010, Bea, 2010).
Latent heat correction is obtained by considering the heat of fusion in the
calculation of the specific heat (C p ) of a material. For granite, C p liquid is 100 J kg -1
K -1 greater than C p solid , and latent heat (L) is 4x10 5 J kg -1 (Bea, 2010). The
correction for latent heat would occur within a temperature range, dT, with the
lower limit defined by the solidus. Within dT, the latent-heat corrected C p takes
the form (e.g. Bea, 2010)
(7.1)
For this equation, latent heat is released within the range of dT = 100°C above
T granite solidus = 700°C, when most crystallization occurs. Latent heat causes a
heightened rate of clast heating when the matrix temperature is within dT and is
96

necessary to account for precise changes in temperature. The model cannot
address the non-linear effect of magma crystallization rates, so latent heat is
evenly dispersed during the entire duration dT. I assume that the Bar Harbor
Formation was previously metamorphosed to avoid including endothermic
metamorphic reactions that counterbalance latent heat (Kerrick, 1991). In
addition, the short time frames associated with granite crystallization would
probably limit the progress of potential metamorphic reactions.
7.2.2. Methods for Plotting Data
Temperature contouring is a useful method for evaluating the degree and
time frame of partial melting in clasts. I took a transient thermal solution and
plotted the continuously migrating solidus of the Bar Harbor Formation clasts in
order to determine the rate of clast partial melt (the Stefan problem, Turcotte and
Schubert, 1982). Two solidus migration plots are produced. The spherical twodimensional
clast model was used to find the general trend of solidus migration
into a clast with time. COMSOL results were used to collect transient thermal and
spatial data along a transect through the clast center. The second plot used data
from outcrop geometry to plot percent partial melt volume with respect to time.
The plot was produced from model images of clast area above the solidus
temperature for 30 chosen time steps. Clast area remaining below the solidus
temperature was calculated in NIH ImageJ, and percent partial melt by area
( ) was
calculated for each time step.
97

A temperature versus time plot was made from the ideal clast model
temperature data for points located in the center, edge, and a distance 1.06
times the clast radius into the magma. This plot is used to determine the pattern
of heat transfer in the clast for supersolidus temperatures, and to determine the
cooling history of surrounding magma similar to that of Okaya et al. (in press).
The same data from percent partial melt over time plot was used to
produce hypothetical clast size distribution (CSD) curves. CSD methods for these
plots are similar to those used for results in Chapter 6. Equivalent radius values
are calculated from the area below the solidus temperature for every clast
(collected using NIH ImageJ) and data are plotted with a radius interval of 10 0.3 .
7.2.3. Applications for Dimensionless Variables
Okaya et al. (in press) evaluated heat transfer using dimensionless
variables. This is a useful way to compare heat diffusion patterns by removing
the solution’s dependence on clast size, thermal gradient, and thermal diffusivity.
The following dimensionless variables are used to define this heat transfer study
(Okaya et al., in press):
(7.2)
(7.3)
(7.4)
where , , and are dimensionless time, temperature, and clast radius,
respectively. is the diffusivity coefficient of the heated material. is a
98

characteristic length and it refers to the clast’s radius in this study. Because is
normalized time with respect to the diffusivity and clast radius ratio, migration of a
phase change through any size clast would show similar results. This allows
easy comparison in a breccia with clast sizes spanning more than three orders of
magnitude.
7.3. Clast Melt Results
Figure 7.2 displays phase boundary migration for the three-dimensional
ideal model. The additional curve is formulated from Turcotte and Schubert
(1982), and defines phase migration in a semi-infinite slab from an infinite heat
source. The time it takes for the ideal clast to completely reach its solidus is =
0.2 (about 15 seconds for a 1 cm radius clast, 150,000 seconds or almost 2 days
for a 1m radius clast). Results (Figure 7.3) from the outcrop model show trends
for 800°C (ΔT = 150°C) and 900°C (ΔT = 250°C) intruding magma. For the ΔT =
250°C model, clasts with radii below 1cm completely reach solidus within 4
seconds, and all clasts with radii below 5cm reach solidus before 300 seconds.
The partially melted area at 300 seconds is equal to 35% of the initial bulk clast
area. Approximately 50% of clast area achieves solidus by 900 seconds, and all
clast area achieves solidus by 5800 seconds. For the ΔT = 150°C model, solidus
temperatures are achieved later and all clast area achieves solidus by 9000
seconds. Both models achieve equilibrium temperature within approximately 2
days.
99

Dimensionless time
0
0.05
0.1
0.15
R
0 0.2 0.4 0.6 0.8 1
2D clast
Stefan curve (Turco e and
Schubert, 1982)
0.2
Figure 7.2. Solidus migration trend for a spherical clast. The blue curve is the
Stefan analytical solution for a half-infinite block exposed to an infinite heat
source. Red dots mark the position of the 720°C isotherm as it migrates through
the clast over time.
100

t = 0 t = 10 t = 100 t = 1500
% Clast partial melt by area
100
90
80
70
60
50
40
30
20
10
0
ΔT=150°C
ΔT=250°C
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time (seconds)
Figure 7.3. A plot displaying clast melt over time. The total area of clast material
below the 720°C isograd decreases quickly as small clasts melt, then progresses
more slowly when few large clasts remain.
101

Figure 7.4 displays model results from the transient temperature path for
points within the spherical clast model with ΔT = 150°C and ΔT = 250°C runs.
The ΔT = 250°C results show that, for a magmatic breccia with 75% matrix,
homogenization temperature is reached by = 1.6. For this model, clast centers
achieve supersolidus temperatures by = 0.2 for T i = 900°C and = 0.3 for T i =
800°C. Equilibrium temperature is 840°C (θ = 0.76) and 770°C (θ = 0.48)
respectively. Results from the 34% magma by volume model show a constant
intrusion temperature of 900°C for T c = 650°C with
= 0.24 and 450°C, which
does not reach the solidus temperature at the clast center. Results from the 16%
magma by volume model show a constant intrusion temperature of 900°C for T c
= 650°C and 400°C, both of which do not reach the solidus temperature at the
clast center.
7.3.1. Discussion
Based on thermal modeling results and the calculated solidus temperature
of 720°C, All Bar Harbor Formation clasts with the average bulk chemistry
(Metzger, 1959) achieved supersolidus temperatures with 75% magma matrix by
volume, allowing partial melt to occur. Small, noncircular clasts melt first, and
because there is such a large population of small clasts, there is a rapid increase
in percent partial melt seen in Figure 7.3. The melt percent by area slope
decreases when only larger clasts remain. An order of magnitude change in clast
radius will cause two orders of magnitude change in the amount of time for the
clast to achieve supersolidus temperatures (Okaya et al., in press). Although the
102

A
900
Temperature versus time curves
Spherical clast in 75% matrix
850
R*1.1
T i = 900°C, τ = 0.1995
Temperature ( C)
800
750
R
R*0
Solidus
T i = 800°C, τ = 0.3
700
B
Temperature (°C)
650
900
850
800
750
700
650
600
550
500
0 0.5 1 1.5 2
tK/r2
R*1.1
R
R*0
Temperature versus time curves
Spherical clast in 34% matrix
Solidus
Tc = 650°C, τ = 0.24
Tc = 450°C
C
450
900
850
0 0.2 0.4 0.6 0.8 1
tK/r 2
Temperature versus time curves
Spherical clast in 16% matrix
800
Temperature (°C)
750
700
650
600
550
R
R*1.1
T i = 650°C
T i = 400°C
Solidus
500
450
R*0
400
0 0.1 0.2 0.3 0.4 0.5
tK/r 2
Figure 7.4. Temperature changes over time for points in a clast. R*0, R, and
R*1.1 represent points in the center, edge, and 1/10th the clast radius into the
magma, respectively. A) Magma is initially 75% of total volume, T i = 900°C and
800°C, T c = 650°C. B) Magma is initially 34% of total volume, T c = 650°C and
450°C, T i = 900°C. C) Magma is initially 16% of total volume, T c = 650°C and
400°C, T i = 900°C. Dimensionless time values for when the clast center reaches
720°C are given where applicable.
103

thermal model ignores advection of heat due to flow of the matrix magma relative
to the clasts, there had to be an advective component at least during magma
intrusion. Flow of magma around the partially melting clasts would have
facilitated dissagregation, though “ghosting” of some clast margins suggests that
diffusion, or local mixing of the two magmas, may have occurred without marked
flow of the matrix magma. Flow is the physical component for complete
disaggregation to occur. Without it, clast melting and local mixing would still
occur, but flow is more effective at mixing the melted material into the magma,
essentially removing that clast. Small clasts reach melt temperatures within
seconds after emplacement, when there is a greater potential for magmatic flow.
This could lead to small clast disaggregation well before the cores of large clasts
reach solidus. There is no constraint on magma flow because there is no
evidence for its existence except at the local scale. Regardless of this, Bar
Harbor Formation clasts with the average bulk chemistry eventually achieve
supersolidus temperatures and given any magmatic flow, they have the potential
to disaggregate.
The degree of melt in Bar Harbor Formation clasts is dependent on the
melt temperature, the matrix to clast volume ratio, and the initial temperatures of
clast and intruding magma. As mentioned in sections (2.3) and (6.1), The Bar
Harbor Formation is heterogeneous with layers consisting of pelites, sandstone,
volcanic tuff, detrital quartzite, calc-silicates, and volcanic tuff. It should not be
expected that all Bar Harbor Formation clasts within the Shatter Zone should
have the same solidus temperature, and it is possible that some units did not
104

achieve supersolidus temperatures. For example, volcanic tuff, quartzite, or calcsilicate
layers would not melt with the pelitic layers, leaving a preference to
preserve the clasts produced from the higher melting temperature layers. This
means that not all clasts would follow the same trend of melting, and could
explain why not all Bar Harbor Formation clasts completely melted in Type 3
Shatter Zone.
For the 900°C intrusion model, the clasts and matrix reach equilibrium at a
temperature well above Cadillac Mountain Granite feldspar crystallization
temperatures (Wiebe et al., 1997a), but the 800°C intrusion model is well below
the 825°C feldspar crystallization of the Cadillac mountain Granite (Wiebe et al.,
1997). Although the temperature remains above the Bar Harbor Formation
solidus for a relatively long time, feldspar crystallization would significantly
increase viscosity (e.g. Baker, 1996; Bea, 2010). If magma partially solidifies
around a clast, there is a reduced chance for disaggregation (e.g. Beard and
Ragland, 2005). For the 900°C intrusion model, the equilibrium temperature is
too high for a viscosity increase, but for the 800°C intrusion model, magma
crystallization may have been able to protect clasts from disaggregation with an
envelope of more viscous material.
The initial temperature and volume fraction of wall rock and magma
determine the equilibrium temperature. As seen in Figure 7.4, a lower magma
matrix percent by volume would cause less clast melting. Several initial intrusion
and clast temperatures are used to replicate potential magma temperatures and
wall rock temperatures with distance from the reservoir. Type 1 and 2 Shatter
105

Zone experienced a relatively weaker thermal pulse and therefore would have
experienced less melt as compared to Type 3. It is likely that Type 3 Shatter
Zone initially had a lower matrix volume percent, but continued melt and
disaggregation of clasts allowed greater accommodation of granitic magma. Type
3 Shatter Zone may originally have looked similar to Type 2 because of this, and
clast melt may have followed the conditions used for Figure 7.4.B. For a Type 2
geometry, small clasts entrained in the magma channels surrounding larger
clasts would also experience a greater than average exposure to magma. Melt of
small clasts in these channels would be preferred, while the surrounding larger
clasts could not melt under the conditions.
The characteristics of CSD evolution with partial clast melt are visible in
figure 7.5. D s decreases over time with the loss of small clasts and generally no
change in large clast populations. Starting with a fractal distribution at time zero,
as small clasts quickly disaggregate, a bifractal trend appears to develop.
Eventually, the slope changes completely to a trend that can be better defined by
an exponential size distribution. This model can explain the progression of D s
from Type 2 to Type 3 in Bar Harbor Formation clasts. Type 3 Bar Harbor
Formation size distributions have the most evolved slope and the greatest
thermal exposure. I cannot assume that the Bar Harbor Formation clasts
completely followed this migrating CSD trend because of the compositional
differences between layers. CSD for Bar Harbor Formation clasts therefore
reflect the trend of partial melt in most of the clasts and the remnant clasts that
did not attain melting temperatures.
106

A
1.E+04
1.E+03
N
1.E+02
1.E+01
Modification of Clast Size Distribution produced by
modeled transient melt progression
Unexposed
1 second
5 seconds
20 seconds
50 seconds
100 seconds
200 seconds
500 seconds
1000 seconds
1.E+00
B
cumulate frequency
100
10
0.01 0.1
r (cm)
1 10
Evolution of clast size distribution caused by
modeled transient melt progression
t = 4
Bifractal:
D = 2, 1.5
t = 100
Non-Fractal
t = 0
D = 2.5
t0
t4
100
1
1 10 100
radius (pixels)
Figure 7.5. The evolution of clast size distribution with progressive thermal
exposure. A) A fabricated CSD with D s = 3, T c = 650°C and subjected to T i =
900°C, 34% magma: small clast populations quickly melt, evolving from a fractal
to non-fractal distribution of clast sizes. B) CSD results from chosen time steps
from the outcrop model used in Figure 7.3; T i = 900°C, T c = 650°C.
107

7.4. Thermal-Induced Fracture
Field observations, specifically the late stage fractures in diorite clasts,
show that late stage fracturing occurred with the introduction of magma into the
Shatter Zone. Clasts when exposed to magma undergo rapid heating and a
transient, non-uniform temperature distribution develops within them. Most
materials tend to volumetrically expand when heated (e.g. Clarke, 1998). No
critical stresses would be induced if the material under uniform heating is free to
expand. Non-uniform volume expansion in a constricted solid, however, leads to
stress buildup and potential fracture propagation. In a clast of irregular shape
subjected to surface heating, temperatures in the interior and in the root regions
of the corners are lower than those at the surfaces. Tensile stresses thus
develop in these regions of non-uniform expansion as the materials there are
stretched by the hotter surface materials, causing potential corner break-off.
Thermal fracture could be significant for CSD because 1) it directly
produces new clasts from the breakdown of old ones in a pattern different from
explosion-derived populations, and 2) it increases surface area of clasts that
could enhance the speed of temperature homogenization. A one-dimensional
equation is used to approximate the required temperature gradient necessary to
cause tensile fracture (Manson, 1953)
(7.5)
where is Young’s Modulus, is Poisson’s ratio, is the coefficient of linear
thermal expansion,
is the temperature difference experienced by the body,
and
is the thermally induced tensile stress. An average rock can fracture
108

under 20 MPa of tensile stress (critical tensile stress,
), which is achieved when
is greater than approximately 30°K using the material properties listed in
Table 7.2. The temperature difference between magma and clast is 250°K, which
implies that the temperature gradient in the interior part of the clast will exceed
30°K required to fracture.
7.4.1. Model Setup
A single clast model is used in a manner identical to the previously
mentioned models, but with a focus on thermal stresses. Finite elements are
used to solve the thermal stress equations. Figure 7.6 shows the clast in a
magma matrix and the finite element mesh used in the simulation. Models are
run for 650°C metasedimentary and diorite clasts in 900°C, low viscosity (~10 6
Pa s, CIPW Norm calculation based on bulk rock chemistry data from Wiebe et
al., 1997a) magma. Strength anisotropy is not considered in the models. The
matrix is an elastic material with assigned properties that allow it to behave
similarly to a magma. Thermal expansion of the matrix is set to zero, and
theYoung’s modulus is set to three orders of magnitude lower than a typical rock.
This is done in order to accommodate thermal expansion in the clast with limited
resistance, in an attempt to simulate a magma that would be able to flow away
from the site of clast expansion. The model is run with confining pressure typical
to 5km depth (~0.13GPa).
109

Metapelite/hornfels Diorite dike
E 70E9 Pa (2) 80E9 Pa (2)
9E-6 K -1 (1) 7E-6 °K -1 (1)
0.25 (1) 0.25 (1)
ΔT 250°K 250°K
-15E6 Pa (2) -20E6 Pa (2)
(1) Clark, 1966; (2) Lama and Vutukuri, 1978
Table 7.2. Physical constants for thermal-mechanical
solutions.
110

Figure 7.6. Clast geometry used for thermal stress analysis. Box is 1.25x1.25m.
111

7.4.2. Results and Discussion
COMSOL follows engineering convention, meaning that tensile stress is
positive and compressive stress is negative. The first principal stress relates to
maximum tensile stress, while the second principal stress relates to minimum
tensile stress for a two-dimensional model. Figure 7.7 shows transient
development of the first principal stress distribution in the clast (also see
Animation 2, 3). Local tensile stress buildup begins in the roots of sharp corners
and moves inward as the clast heats up. Two patterns of fracture are evident
from the experiment. The first phase of thermal fracture shows preference for
edge break off. Arrows denote the direction of the second principal stress, or the
direction of minimum tensile stress that a tensile fracture would prefer to follow.
For this clast there is a preferred cuspate-shaped fracture pattern that would
produce more corners. Eventually the number of corners would be reduced by
successive fragmentation and circularity would increase. Next, as the clast
continues to warm, tensile stress in the center of the clast reaches a critical
value, allowing larger fractures to nucleate from the center and break the clast in
half. The clast is slightly elongate, and
increases inward and parallel to
elongation. The first principal stress directions run perpendicular to elongation,
preferring to fracture along the short axis. At this time of thermal exposure,
originally elongate clasts would be preferentially broken up into more equant
fragments, and each new fracture surface provides a fresh face to repeat the
process. The potential for thermal fracture declines as the clast heats up and the
thermal gradient is reduced.
112

t: 500
t: 5000
A
B
t:500
t:5000
C
Figure 7.7. Time step results for thermal stress in metasedimentary and diorite
clasts. A) Bar Harbor Formation clast exposed to magma at 500 seconds and B)
5000 seconds. C) diorite clast exposed to magma at 500 seconds and D) 5000
seconds. The surface plot displays the first principle stress field, with tensile
stress plotted as red and compressive stress plotted as blue. Arrows designate
the second principle stress direction, or the assumed direction of fracture
propagation. Maximum tensile stress is the result of nonuniform expansion, first
in the roots of corners, then later on in the core of the clast as it is continually
heated. Stresses gradually reduce as the clast temperature equilibrates with the
magma.
D
113

This thermal fracture model explains the late stage fracture for diorite
clasts, but it does not take into account the anisotropic nature of the Bar Harbor
Formation. Rock heterogeneity creates a far more complex thermal stress
problem because crack formation is not solely dependent on the thermal
gradient. Clarke et al. (1998) discuss the three different possibilities for fracture
development in anisotropic xenoliths. The first is determined by the thermal
gradient and this is used in the above model (thermal gradient cracking). The
second mechanism for crack formation in a layered material becomes operative
when one layer has a differing thermal expansion coefficient than its counterpart
(thermal expansion mismatch cracking). Third, a material may have an
anisotropic fabric that leads to preferred crack propagation in one direction
(thermal anisotropy cracking). Bar Harbor Formation rocks can exhibit all three of
these fracture types due to their compositional layering, and they may be more
susceptible to thermal fracture than suggested by this model. The thermal
gradient cracking model therefore provides a low end-member possibility for the
proliferation of thermal cracks in Bar Harbor clasts.
If thermal fracture was prevalent, each clast would fracture according to a
new size distribution: for thermal fracture, D s = 2.156 (Glazner and Bartley,
2006). The new value of D s is the combination of the explosive fracture event and
the secondary thermal fracture event, and repeated fracture events always
increase D s by a fractional amount (Jebrak, 1997). Also, field evidence suggests
that not all diorite clasts experienced thermal fracture, therefore late-stage
thermal fracture did not have a significant effect on diorite dike CSD results.
114

7.5. Final Discussion
Results from clast size distribution imply that the Shatter Zone originally
formed from a subvolcanic explosion. The volcanic eruption was likely triggered
by replenishment of mafic magma at the chamber base, which reinvigorated the
overlying granite (Wiebe, 1994). The explosion was triggered by rapid volume
expansion of volatiles within the chamber. Overpressure of the chamber led to
immediate wall rock failure, providing channel ways for incoming magma. Size
distributions for clasts above ~1.5cm radius in Types 1 and 2 record the
explosive origin of the chamber walls, whereas distributions for clasts below 1.5
cm radius imply a secondary mechanism related to disaggregation and hydraulicthermal
fracture during magma introduction. Diorite clast size distributions in
Type 3 digress from D s values seen for Types 1 and 2, but they are still also
thought to have an explosive origin. The decrease in D s between Types 1 and 2
and Type 3 is likely related to a change in dominant wall rock type as a function
of rock strength differences rather than a difference in brecciation mechanism.
Type 3 Bar Harbor clasts show a non-fractal size distribution trend,
implying a secondary modification process that effectively reduced clast size and
abundance. Data from clast boundary shape and clast circularity analysis also
argue that clast modification has occurred from type 1 to type 3, showing relative
decrease in clast surface complexity and increase in clast compactness with
proximity to the Cadillac Mountain Granite. I suggest that clast modification was
dominantly caused by thermal attrition: the thermal fracture, melt, and
115

disaggregation of Bar Harbor clasts driven by the intruding 900°C magma. I
explored the possibility of thermal attrition by thermal-mechanical modeling of
clast geometries instantaneously immersed in an intruding magma. Thermal
fracture and partial melt are likely to occur during magma intrusion, but my
conclusions are limited by the thermal conduction model because disaggregation
requires some component of viscous flow of the matrix magma to mechanically
disintegrate a clast. Results from the phase boundary migration model show that
all Bar Harbor clasts of appropriate composition had potential to melt. Assuming
that the volcanic eruption underwent days of activity, this would be enough time
to melt and disaggregate a large component of the smallest Bar Harbor clast size
populations. This agrees with the trend that is seen in clast size distribution for
Type 3 Bar Harbor Formation clasts.
Thermal fracture was driven by the immediate intrusion of magma after
explosive wall rock fragmentation. Late-stage fractures in diorite clasts are likely
caused by the large thermal gradients caused by the granitic intrusion into the
Shatter Zone. Rapid thermal expansion in clasts provided great enough tensile
stresses to cause fracture propagation of corners. Although the thermal fracture
effect on clast size distribution is not as well understood, D s will increase slightly
with repeated fracturing events, assuming that there is no removal of any clast
populations through melting. The contribution from thermal fracture is small and
had little effect on diorite clast D s . Diorite clasts did not reach their solidus
temperatures, therefore D s represents the initial fracturing event plus thermal
fracture, presumably creating a fractionally higher D s . Thermal fracture in a
116

structurally anisotropic material is more difficult to constrain because local
stresses are produced by thermal gradient, differing thermal expansion
coefficients of layered materials, and the presence of materials that have
anisotropic expansion and conduction characteristics. These characteristics are
beyond the scope of the current thermal stress models, which are therefore most
applicable to the homogeneous diorite clasts.
117

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BIOGRAPHY OF THE AUTHOR
Samuel Geoffrey Roy was born in Waterville, Maine on September 9, 1985. He
was raised in Oakland, Maine and graduated from Messalonskee High School in 2004.
He attended the University of Maine and graduated in 2008 with a Bachelor’s degree in
Earth Sciences. After an internship at the Stillwater Mining Company in Nye, Montana,
and a semester of graduate courses at Southern Illinois University, Carbondale, Samuel
returned to the University of Maine in 2009 and entered the Earth Sciences graduate
program. Samuel is a candidate for the Master of Science degree in Earth Sciences
from the University of Maine in May, 2011.
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