ARTICLE IN PRESS
International Journal of Rock Mechanics & Mining Sciences 47 (2010) 81–93
Contents lists available at ScienceDirect
International Journal of
Rock Mechanics & Mining Sciences
journal homepage: www.elsevier.com/locate/ijrmms
Fissure formation and subsurface subsidence in a coalbed fire
Taku S. Ide a,, David Pollard b, Franklin M. Orr Jra
a
b
Department of Energy Resources and Engineering, Stanford University, Stanford, CA 94305, USA
Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305, USA
a r t i c l e in fo
abstract
Article history:
Received 1 January 2009
Received in revised form
26 April 2009
Accepted 11 May 2009
Available online 25 June 2009
Coalbed fires are uncontrolled subsurface fires that occur around the world. These fires are believed to
be significant contributors to annual CO2 emissions. Although many of these fires have been burning for
decades, researchers have only recently begun to investigate physical mechanisms that control fire
behavior. One aspect of fire behavior that is poorly characterized is the relationship between subsurface
combustion and surface fissures. At the surface above many fires, long, wide fissures are observed. At a
coalbed fire near Durango, Colorado, these fissures form systematic orthogonal patterns that align with
regional joints in the Upper Cretaceous Fruitland Formation. Understanding the mechanisms that form
these fissures is important, as the fissures are believed to play vital roles in sustaining the combustion in
the subsurface. In some of the coalbed fire simulation models available today, these fissures are treated
as fixed boundary conditions. We argue, using data collected, field observations and simulation result,
that there exists a relationship between the location and magnitude of subsidence caused by the fire
and the opening of fissures. The results presented suggest that fissures are believed to open when
subsurface subsidence gives rise to tensile stresses around pre-existing joints.
& 2009 Published by Elsevier Ltd.
Keywords:
Coalbed fire
Coal fire
Subsidence
Pre-existing joints
Fissures
Numerical modeling
CO2
1. Introduction
Uncontrolled subsurface fires in coalbeds account for significant releases of CO2 to the atmosphere. One of the world’s largest
active coalbed fires has been documented in Wuda, China [1],
where the estimated annual loss of coal is around 200,000 t,
equivalent to a yearly emission of 1.5 Mt of CO2 [2]. Coalbed fires
are burning in many locations in China, Indonesia, India, and the
United States [3]. They can be started naturally by forest fires that
burn near an outcrop, by lightning strikes, by human activities, or
by spontaneous exothermic reactions of pyrites [4]. Forest fires in
Indonesia in 1997 and 1998 ignited hundreds of coal fires at
outcrops [5]. A subsurface fire near Centralia, Pennsylvania, was
started in May of 1962 when the local government decided to
burn an unregulated trash dump in an abandoned strip mine to
reduce trash volume and control rodents. The fire ignited an
anthracite outcrop, eventually connected to and spread through
underground tunnels, and has been burning since. Fissures
created by the coal fire emit assorted hot gases, some of which
are toxic. A combination of subsidence and emissions from
fissures has caused the town of Centralia to be abandoned [4,6].
The particular fire examined in this study, called the North
Coalbed Fire, to distinguish it from other active fires in the region,
Corresponding author.
E-mail address: [email protected] (T.S. Ide).
1365-1609/$ - see front matter & 2009 Published by Elsevier Ltd.
doi:10.1016/j.ijrmms.2009.05.007
was discovered in 1998 on the Southern Ute Indian Reservation
when sets of fissures that are orthogonal to each other—similar to
those at other coal fires around the world—appeared at the
surface [7]. Anecdotal evidence provided by local Southern Ute
Tribe members [8] suggests that the fire may have been
smoldering for decades prior to the reported date of discovery.
The fire continues to burn today. The research effort described
here is an attempt to understand whether coal combustion
followed by subsurface subsidence can produce fissures with
systematic patterns at the surface. Subsidence can occur when a
burned coalseam loses its structural integrity and collapses under
the weight of the overburden. Understanding the formation of
fissures is important, as they appear to foreshadow the direction
of the combustion front propagation and may play a key role in
sustaining the underground fire.
First, we summarize the San Juan Basin geology, highlighting
key features in the NW section of the basin, where the coalbed fire
is located. Second, we characterize the geological features and the
surface anomalies in the vicinity of North Coalbed Fire. Surface
topography, images of fissures overlying the coalbed fire, and
measurements of fissure orientations are presented. We also
outline the process of mapping features over the North Coalbed
Fire and describe how they were combined with the subsurface
information obtained from the wells drilled in the area. In the
third section, the field data and previous geological surveys of the
area are used to suggest how subsidence can open pre-existing
joints in the area, leading to the formation of surface fissures over
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the combustion region. Finally, we model this phenomenon using
a simple boundary element numerical code, and explore relationships among key variables that contrast subsidence activities and
surface deformation. The results and the limitations of applicability of this simulation model are discussed.
2. San Juan Basin geology
The San Juan Basin is an asymmetric, coal bearing basin that
covers approximately 16,800–19,400 km2, stretching approximately 145 km west–east and 160 km north–south [9,10]. It is
located near the Four Corners, and spans across northwest New
Mexico and southwest Colorado as shown in Fig. 1. The basin is
well characterized due to the abundance of both coal and coalbed
methane resources in the Upper Cretaceous Fruitland Formation
(Fig. 2). One study has estimated that a coalbed methane reserve
of nearly 1.4 1012 m3 (50 1012 ft3) adsorbed onto 219 109 Mt
of coal that underlies the San Juan Basin [9]. The flat Central Basin
is bounded by several key geologic features, which are described
in detail in previous geologic surveys of the area [9,10,11]. The
western and northwestern regions of the basin are circumscribed
by the Defiance and the Hogback monoclines, respectively, and
the Nacimiento uplift borders the basin on the east side [11]. As
shown in Fig. 1, the North Coalbed Fire is located along the
Hogback Monocline in the northwestern portion of the basin. The
Hogback monocline is believed to have formed either due to
the shortening of the Cretaceous strata that induced a right-lateral
strike-slip motion along the western and eastern margins during
the Laramide orogeny [11], or through reactivation of western
dipping thrust faults underlying the Hogback monocline that
Fig. 2. Stratigraphic columns representative of the San Juan Basin (left) and the top
25 m of the lithology over the North Coalbed Fire (right). Over the coalbed fire,
formations above the blue dotted line have been removed due to weathering.
Stratigraphic column on left adapted from Molenaar, 1977. (Figure not drawn to
scale.) [For interpretation of the references to color in this figure legend, the reader
is referred to the webversion of this article.]
Fig. 1. San Juan Basin and its characteristic geologic features. The North Coalbed
Fire location is highlighted in the box in the northwestern corner of the basin along
the Hogback Monocline. The green area denotes outcrops of Pictured Cliffs
sandstone. Figure reproduced from [11]. [For interpretation of the references to
color in this figure legend, the reader is referred to the webversion of this article.]
resulted in the uplift [12]. In the former view, the shortening can
be attributed to the Zuni uplift thrusting northward and north
northeastward into the San Juan Basin from the south, and the San
Juan uplift indenting southward into the basin [11]. Today, only
the forelimb of the Hogback Monocline is exposed and some of
the formation members of the Upper Cretaceous are exposed
on the western side of the basin. Along the northern perimeter of
the Basin, including areas affected by the North Coalbed Fire, thick
coalseams crop out along the Hogback monocline [13].
Formations that make up the Upper Cretaceous rocks in the
San Juan Basin are described by Molenaar [14]. The Fruitland
Formation, which includes the coalbed fire, and adjacent geologic
units are depicted in the stratigraphic column in Fig. 2. The left
column is representative of the entire San Juan Basin. The right
column shows the top 25 m of rock found directly over the North
Coalbed Fire. Above the coalbed fire, formations above the dotted
line—the Kirtland Shale and most of the Fruitland Formation—have been removed by weathering and erosion. The Kirtland Shale
and the Fruitland Formation lie atop of the Pictured Cliffs (PC)
Sandstone, which was deposited as regressive marine sands [15]
parallel to the shoreline stretching northwest–southeast [10]. The
Fruitland Formation is a mixture of mudstones, siltstones,
carbonaceous shales and coals deposited landward and parallel
to this shoreline [10]. Coalseams in the Fruitland Formation are
often referred to as Lower Coal, Middle Coal and Upper Coal, and
the thickest, most continuous coalbeds are found in the Lower
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Coal Zone in the northeastern region of the San Juan Basin [16].
The Lower Coal is burning at the North Coalbed Fire.
At the North Coalbed Fire, 14 boreholes were drilled in 2007
over an area of 600 200 m. The high density of boreholes
allowed reliable subsurface correlations to be made at the site.
Both the PC and the Fruitland Formation rise in a step-like fashion
from the southwest to the northeast with respect to the
isochronously deposited Huerfanito Bed in the Lewis shale,
representing a migrating regression–transgression cycle over 1.2
million years [16,17]. The deposition pattern suggests that the
subsurface correlation along the shoreline in the northwest–
southeast direction is warranted, as this is the trend of the long
axis of most coal deposits [18]. The echelon geometry of coal
deposits can make subsurface correlations difficult in the
transverse direction [18], but it has been shown that Fruitland
Formation coalbed correlation was possible when well-logs
spaced less than 4 km apart were obtained [17,18].
The San Juan Basin contains several sets of natural fractures
that have been extensively mapped and documented. Previous
studies have offered various explanations for fracture formations,
which are summarized in [11]. Ruf suggests that the fractures
formed due to post-Laramide extension [19], while Taylor and
Huffman describe a Proterozoic crystalline basement with
reactivated faults that may have influenced the orientations of
the fractures in overlying strata [20]. Lorenz and Cooper suggest
that the orientations of the fractures are most influenced by the
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formation of tectonic features such as the San Juan uplift and the
Zuni uplift (cf. Fig. 1) during the Laramide Orogeny [11].
Despite the competing explanations of the origins of the
fractures, orientation measurements in various parts of the San
Juan Basin are consistent across many studies. The earliest
fracture orientation study of the San Juan Basin concluded from
aerial photography that northeast (N10E to N60E) and northwest
(N15W to N75W) trends occurred most frequently [21–24]. Their
findings are generally supported by more recent measurements
[11,12,15,19,25]. The most relevant study for the North Coalbed
Fire was carried out by Condon [15], who presents joint
orientations and coal strikes found within the Southern Ute
Indian Reservation. His findings are discussed in detail in the
ensuing section, and they are compared to the fissure orientations
that were measured over the North Coalbed Fire.
3. North Coalbed Fire
A satellite image of the area bounded by the red dotted box in
Fig. 1 is shown in Fig. 3a. The dotted rectangle depicts the region
where surface anomalies associated with the North Coalbed Fire
are observed. The lack of vegetation over the fire can be attributed
to several factors: a surface forest fire, death of vegetation due to
toxic combustion fumes emanating from the subsurface, and
intentional tree removal to prevent future forest fires. The North
Fig. 3. (a) A satellite image over the North Coalbed Fire. The red dotted box outlines the region affected by the underlying fire. A cross-section line A–A0 is used in Fig. 3b.
Satellite image is provided by Googlemaps. (b) Cross-section A–A0 showing surface topography and representative subsurface stratigraphy in the vicinity of the North
Coalbed Fire. The coalbed fire is located near the coal outcrop inside of the red dotted box. Kl ¼ Lewis Shale, Kp ¼ Pictured Cliffs Sandstone, Kf ¼ Fruitland Formation,
Kkl ¼ Kirtland Shale. [For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article.]
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coalbed fire is contained between latitude N3710105700 and
N371020 2400 and longitude W1081060 3600 and W1081060 1800 , and
has an aerial extent of approximately 600 200 m. There are signs
of coalbed fires underlying the bare patch of land south southwest
of the North Coalbed Fire, but only minor surface deformation is
observed; thus this area is not included in the surveys. The lack
of vegetation there is interpreted as largely due to surface forest
fires.
A cross-section, A–A0 is drawn (Fig. 3b) by superimposing a
USGS geological survey map over the satellite image in Fig. 3a. The
cross-section line is roughly perpendicular to the strike of the
Hogback monocline. The cross-section shows that the Fruitland
Formation crops out along the Hogback Monocline limb (cf. Fig. 1).
To the northwest of the Hogback, only the Lewis Shale—containing the Huerfanito Bentonite Bed—is observed. The region
affected by the coalbed fire is located near the coal outcrop along
the Hogback, and is circumscribed by the dotted box. In this
region, the local topography slopes between 51 and 91 to the
southeast, and the coal layer dips 61–151 in the same direction
[15]. Both the surface topography and the coalseam flatten
towards the southeast in the direction of the Central Basin
(cf. Fig. 1). The continuous and low permeability Kirtland Shale
Formation, which is absent over the North Coalbed Fire, caps the
Fruitland Formation to the southeast.
Many fissures are exposed on the surface overlying the North
Coalbed Fire. The fissures are distinguished from regional joint
sets in the same strata because fissures typically have widths on a
decimeter scale, whereas joints have apertures less than 0.5 cm
[15]. Some of these fissures emit high temperature combustion
gases, indicative of the active fire below, while others are at
ambient temperature.
Four types of fissures have been observed. Examples are shown
in Fig. 4: gaping fissures, plateau/offset fissure, molehill/buckling
fissures, and narrow fissures. The gaping fissure in Fig. 4a is wide
enough for an adult to climb inside. Typical gaping fissures are
0.15–0.3 m wide at the surface and are often wider below the soil
level. Based on observations made inside of the gaping fissure in
Fig. 4a, many fissures may be connected to each other in the
subsurface. Gaping fissures are at ambient temperatures. The
surface sediment layers do not show significant rotation around
the edges of the fissure. Rather, the fissure appears to have been
pulled apart from either side. Fig. 4b is an example of a plateau
fissure. Plateau fissures have similar apertures at the surface as
gaping fissures but fissures of this type show significant
displacement and surface sediment layer rotation on one side of
the fissure. The other side of the fissure does not show much
displacement. Fig. 4c shows an example of a molehill fissure,
where surface layers of sedimentary rock are rotated to form an
apex. At molehill fissures with visible fractures at the surface,
combustion gases with temperatures as high as 290 1C (550 1F)
have been recorded. The temperatures at the fissures were
measured using a thermal gun, Raynger 3i Series, made by
Raytek. Fig. 4d is an example of a narrow fissure. Many narrow
fissures are located in the northern most portion of the field, and
these emit the hottest exhaust gases recorded in the field at about
1000 1C. Both the molehill and narrow fissures are about 0.15 m in
width. All of the fissures appear to be opening Mode I fractures
[26], as displacements are dominantly orthogonal to the fracture
surfaces.
Orientations of the fissures are systematic, and they often form
orthogonal patterns at the surface. The directions and the lengths
of 165 fissures are represented on a rose diagram in Fig. 5. Their
lengths have been made dimensionless with respect to the longest
fissure in the field, which is 75 m. The diagram shows that there
are three main fissure directions over the North Coalbed Fire and
that the longest and most frequently occurring fissures, F1, have
azimuths approximately in the N50E direction. The next most
prominent set, F2, strikes in the N35W direction, roughly
perpendicular to the first set. The third set, F3, is directed
towards the North, and these have similar lengths to the N35W
set. The fissures frequently occur together in approximately orthogonal pairs, including members of the N50E and
N35W sets.
The azimuths of the fissures were compared with observations
of joint orientations reported in Condon, 1988. Condon measured
1600 joints and coal cleats at 37 different outcrop locations on the
Southern Ute Indian Reservation. Of the 37 measurement stations,
eight are located along the Hogback Monocline and are spaced
approximately 2 km apart. Most of his measurements were for
fractures found in formations of the Upper Cretaceous, the
majority of which are in the Kirtland Shale, Fruitland Formation
and the Pictured Cliffs Sandstone. Four dominant joint sets,
labeled J1–J4, were described. Their stereonets are reproduced in
Fig. 6. A comparison of Figs. 5 and 6 shows that F1 corresponds to
J3, F2 to J4, and F3 to J2 based on similarities between the fissure
orientations and joint orientations. Typically, the joints occur in
pairs—a J1–J2 pair and a J3–J4 pair—much like the fissures F1 and
F2 that form orthogonal pairs above the North Coalbed Fire.
Condon classifies the J1–J4 joints as extension joints, due to the
lack of features such as slickenside striations that would suggest
lateral shear movement and the presence of plumose structures,
arrest lines, and twist hackle features that indicate extension
joints [15].
Whereas J1, J2 and J3 are stratigraphically continuous through
multiple beds, J4 fractures only cut through the sandstone in
interbedded sequences of sandstone and shale. Their orientation
ranges are as follows: J1 (N4E–N23E), J2 (N72W–N83W), J3
(N41E–N64E) and J4, (N24W–N49W). Joints J1, J2, and J3 have
exposed lengths of roughly 1–5 m, and are spaced 0.15–6 m. J4
exposed lengths are less than 2 m, and the spacings are more
inconsistent [15].
The fissures above the North Coalbed Fire were mapped using a
pack-mounted GPS receiver in order to place them with respect to
the topography of North Coalbed Fire site. In addition, the GPS was
used to digitize the topography and to mark the locations of
boreholes that have been drilled in the area. The GPS device used
in the survey was a Trimble ProXH, and the points recorded had
better than 1 m accuracy, with most having better than 0.5 m
accuracy after differential correction. Fig. 7a shows the digitized
representation of the surface overlying the North Coalbed Fire.
The contour map approximately represents the region bounded by
the red dotted box in Figs. 1 and 3a. The left edge of this map
traces the contact line between the Fruitland Formation and the
Pictured Cliffs Sandstone (cf. Figs. 3a and b). The dominant N50E
trending fissures are nearly parallel to the local strike of the
Hogback Monocline. The black lines represent narrow fissures that
have been grouted using a specialized concrete produced by
Goodson and Associates [7]. The concrete was injected into
identified openings in 2000 in an attempt to smother the fire.
Boreholes were drilled around the grouted fissures, and thermocouples were installed to allow monitoring of temperature
changes. These boreholes are shown as open white triangles in
Fig. 7a. Although the attempt to extinguish the fire was not
successful, the driller’s logs from 2000 provide valuable insight
into the subsurface. This particular extinguishing method failed
mainly because it was not possible to locate and fill all existing
fissures in the region. Fourteen additional boreholes were drilled
in 2007. These boreholes are marked with solid triangles in Fig. 7.
For these new boreholes, driller’s logs were obtained, and most
of the boreholes were logged using caliper, density and gamma
ray logs. In one of the boreholes, borehole 7, an 80 ft core was
obtained.
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Fig. 4. (a) A gaping fissure with an adult inside, (b) a plateau fissure, (c) a molehill fissure with a 0.15 m aperture at the apex, and (d) a narrow fissure venting exhaust gases
exceeding 900 1C.
The surface information in Fig. 7a can be related to the
subsurface information by creating a cross-section along the line
A–A00 . This cross-section shows that the depth to coal is
approximately 20 m. The cross-section is approximately
perpendicular to the prominent N50E fissures. Any boreholes
or fissures that lie close to this line are plotted along with the
surface topography in Fig. 7b. Where available, a combination of
driller’s-logs and well-logs were used to identify the depths and
thicknesses of void, ash and coalseams at each intersecting well. If
data were missing at a well, lithologies below it are left blank in
Fig. 7b. Fissures that intersect the cross-section line A–A00 are
represented using red circles. It is worth noting that in borehole
11, no signs of coal combustion were apparent. The last set of
fissures occurs up dip of borehole 11, and there are no fissures
down dip of this borehole. A black line in Fig. 7b connects the
bottom of the coal seam.
4. Formation of fissures—a conceptual model
We hypothesize that fissures are created from pre-existing
fractures in the overlying sandstone and shale that widen
when subsidence occurs. Subsidence results when the burned
coal loses structural integrity and collapses under the weight of
the overburden. In Fig. 7b, the occurrences of surface fissures
coincide with regions where void and ash were encountered
during drilling. For example, borehole 4 (solid triangle, Fig. 7b)
located near the peak of the topography contains only ash and
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Fig. 5. A rose diagram showing the orientation and the lengths of the fissures
found above the North Coalbed Fire. The characteristic length scale is 100 m.
Fig. 6. (Bottom) Four stereonets reproduced from Condon, 1988. (a) J1 joint, (b) J2
joint, (c) J3 joint, and (d) J4 joint.
coal. The lack of a void in this well suggests that subsidence
occurred, and thus both the ash and void are fully compacted.
Fissures located between boreholes 4 and 5 may have resulted
from this subsidence. Similarly, some of the void space may have
been compacted at well 5, causing a fissure to open-up down dip
of this borehole.
The notion of subsurface compaction leading to surface
deformation and fracturing is not new. It is explored in Whittaker
and Reddish’s work on subsidence related to long-wall coal
mining [27]. They describe surface profiles associated with
various subsurface subsidence configurations. Their work is based
on examples from various long-wall coal mining sites and
includes field observations, experimental, and numerical results.
In long-wall mining, the excavation front advances much like we
envision the combustion front may move through the coalseam in
a coalbed fire. Fig. 8 is a conceptual model of subsidence near a
long-wall mining process [27]. Here, tensile fractures develop in
strata immediately overlying the collapse. This figure can be also
be used to illustrate an empirical relationship presented in their
work, which shows that the ratio of the length of coal excavated
(L) to the depth (d) of excavation must typically exceed 1.4 for
maximum subsidence to occur [27]. Adjacent unmined parts of
the coalseam and a natural arch that develops above the coal
removal site may be capable of supporting most of overburden
when L/d is less than 1.4 [27]. There are two key differences
between their study and the work presented in this paper. First,
the North Coalbed Fire is burning 20 m below the surface,
whereas longwall mining typically occurs at much greater depths
[27]. Second, pre-existing vertical joints and their response to
subsurface compaction are not discussed by Whittaker and
Reddish [27].
Previous studies of coalbed fires have also suggested that
subsurface subsidence leads to the formation of fissures at the
surface [28–40]. Fig. 9 is from one such study of a Coalbed Fire in
China, where subsidence apparently played a significant role in
opening surface fissures indicated by the arrows. Most of these
studies did not examine whether fissures resulted from the
widening of pre-existing joints in the region. In Chen’s work [29],
it is shown that fissure orientations coincide with joint
orientations in the sandstones overlying the coalbed fire in
Ruqigou, China. In this study, however, relationships between
variables such as the location and magnitude of subsidence and
the widths of surface fissures were not established [29]. In a
coalbed fire combustion simulation model presented by Huang
[41], the fissures were modeled as fixed boundary conditions,
through which exhaust gases can escape and fresh oxygen can
enter, irrespective of the location of the combustion front.
Similarly, in the numerical model of Wessling et al. [40],
mechanical processes such as subsidence and fissure openings
were not considered. By establishing a first order relationship
between combustion front location and fissure opening width as a
function of governing variables such as depth, length of collapse,
proximity of pre-existing fissures, and the stiffness of the
overburden rock, we hope to aid future numerical modeling of
coalbed fires.
Observations at an outcrop about 1 km north of the North
Coalbed Fire shows how subsurface subsidence can cause preexisting fractures to open at the surface. This outcrop exposes a
fossilized coalbed fire, subsidence, extension fractures and
fissures. At the outcrop, shown in Fig. 10a, a coalseam is
overlain by 10 m of sandstone, shale, and siltstone. A person
1.5 m tall standing to the right is used as a scale. There are two
prominent features at the outcrop: the fissure that runs down
the middle of the outcrop, and the deformed ash layer towards the
bottom of the outcrop. The fissure down the middle of the
photograph is labeled as Fissure 2, and this fissure has an opening
of around 0.5 m at the surface. When the coalseam was consumed
by a combustion front moving from the right to left, we suggest
the ash deformed by compaction under the weight of the
overburden. The maximum collapse recorded at the outcrop
is 1.5 m.
Features at this outcrop such as Fissure 2 and the subsided ash
layer were mapped using a laser rangefinder produced by
LaserCraft Inc. [42]. The digitized version of the outcrop is
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Fig. 7. (a) A contour map of the North Coalbed Fire site, fissures and wells created using a pack-mounted GPS. Red lines are gaping fissures, green lines are plateau/offset
fissures, magenta lines are molehill/buckling fissures, and blue lines are narrow fissures. The cross-section is created along A–A00 . (b) A cross-section of the North Coalbed
Fire site along A–A00 . Red circles indicate locations of fissures that intersect the line. Numbers above the surface represent borehole numbers. [For interpretation of the
references to color in this figure legend, the reader is referred to the webversion of this article.]
Fig. 8. A conceptual model of subsidence associated with long wall mining. Tensile
stress fractures associated with the collapse are shown. L signifies the length of
coal excavated, and the d the depth below the surface of the seam being mined
[27].
Fig. 9. A picture of a subsided area and fissures nearby (indicated by arrows) in a
coalbed fire at the Wuda Syncline, Inner Mongolia Autonomous Region, China.
(Courtesy of Chris Hecker, ITC, 2008.)
juxtaposed next to the photo of the outcrop in Fig. 10b. Note how
the tabular coalseam is deformed due to the collapse of the ash
layer. Above the collapse, opening fractures, much like those
depicted in Fig. 8, were observed. In addition, four fissures with
more modest openings were mapped over the collapse. In
subsequent sections, when we compare numerical solutions to
our measurements at this outcrop, we assume that Fissure 2 in
Fig. 10b widened largely due to the collapse of the combusted coal
layer and that the weathering process to expose the outcrop did
not significantly enhance the opening.
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Fig. 10. (Left) A picture of an outcrop near the North Coalbed Fire with an exposed fossilized coalbed fire, subsidence and associated surface fissures; (right) Some features
from the same outcrop mapped using a Laser Range Finder. The major features are depicted using thicker lines.
5. Numerical modeling
Numerical models were employed to examine whether preexisting joints could pull open to form fissures when subjected to
the stresses due to the overburden weight and those induced by a
subsurface collapse. The mechanical effects of subsurface subsidence on the jointed strata overlying the coal were modeled
using a Boundary Element Method (BEM) formulation for a line
source of displacement discontinuity in an elastic half-plane. This
problem formulation is an adaptation of the displacement
discontinuity method [43]. The BEM code is a modified version
of Martel’s Matlab BEM code [44], which in turn is based on the
original Fortran code presented in Crouch and Starfield [43].
Several key assumptions are made in this model, including an
elastic homogeneous medium with a reduced stiffness coefficient,
infinitesimal strain, a state of plane strain, and a flat traction free
surface. The rock above the collapsing coalseam is modeled using
a reduced stiffness coefficient in place of explicitly modeling each
fracture and joint in the overburden. The use of reduced stiffness
coefficients compared to the values measured in experiments is
justified in the previous literature on fractured rock deformation
[45,46]. Hooke’s Law is used to relate stress and strain, while the
infinitesimal strain assumption dismisses higher order displacement derivative terms in the relationship between strain and
displacement [47]. The infinitesimal strain assumption admits the
use of the method of superposition, which is used to calculate
stress and displacement distributions in the domain and to create
a half-plane surface. The plane strain assumption restricts any
displacement perpendicular to the plane of the model [43].
Finally, a flat surface is modeled rather than the actual topography
over the coalbed fire outcrop for simplification. Although these
assumptions lead to a model that, at best, approximates the
deformation of jointed rock over a coalbed fire, it nevertheless
helps to build an intuitive understanding between subsidence and
fissure opening, which has not been explored in today’s coalbed
fire modeling literature [36,40,41].
In the BEM code, discretized horizontal elements are used to
model the coalseam, and discretized vertical traction free
elements are used to model pre-existing joints in the overburden.
The infinite plane is transformed into a half-plane by introducing
the principle of superposition to create a traction free boundary
condition along the x-axis [43]. Stress boundary conditions are
perturbed along the horizontal elements to simulate a collapse as
Fig. 11. Definitions of variables and dimensionless groups used in the BEM model.
E and szz have units of MPa, while fd, fl, a and d have units of m.
the coal burns, and the elastic domain is deformed as a result of
this perturbation. Stresses and displacements that arise at any
point in the domain can be calculated by combining the
contribution of stresses and displacements from each element
[43]. The stress distribution in the elastic material is a function of
the location and orientation of the boundary elements and the
boundary conditions on them.
Fig. 11 defines the variables and applicable dimensionless
groups used in this modeling. E is Young’s modulus, and szz is the
normal compressive stress defined along the horizontal elements
to simulate the downward pressure due to the overburden. These
variables both have units of stress (MPa). All other variables have
units of length (m), and they are defined as follows: fd is the
height of the vertical fracture, fl is the distance between the
vertical fracture and the edge of the horizontal collapse, d is
the depth, and a is the horizontal length of the collapse.
We first introduce a domain with no vertical joints in order to
illustrate the stress distribution that arises as a result of collapse
of a continuous overburden. We then introduce a vertical fracture,
and compare how it reacts to a subsidence event when located in
regions of induced tensile stress. This is followed by a sensitivity
analysis to demonstrate the behavior of vertical joints with
respect to various model variables. Finally, a BEM model is
constructed from the outcrop mapped using the laser range finder
(cf. Fig. 10b), and simulation results are compared to field
observations.
In the first example, a 12 m horizontal line of elements that is
located 10 m below the surface is deformed by applying a uniform
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compressive stress of 0.25 MPa, which is exerted by the weight of
the overlying rock. The elastic modulus of the overburden is
10 MPa, and a maximum compaction of 1.5 m is induced at
the horizontal elements. Fig. 12 depicts the distribution of the
horizontal component of normal stress, sxx, in response to the
inward directed displacement discontinuity on the horizontal
elements. The sign of sxx at the surface is indicated by the words
tensile (+) and compression (). The blue solid line along the
bottom of the figure indicates the horizontal elements subject to
subsurface subsidence. We suggest that this inward directed
relative motion is similar to what would occur as compaction of
the coalseam developed during burning. Directly above the
elements at the surface sxx is compressive. The greatest
concentrations of surface tensile stresses emanate diagonally
upward from the ends of the line of collapse.
A modification to the first simulation investigates the effects of
the collapse on traction free vertical joints. The setting and the
parameter values are the same as the first simulation (cf. Fig. 12),
except vertical elements are introduced to simulate the joint. The
vertical elements are placed at x ¼ 12 m, where tensile stresses
found in the first case (cf. Fig. 12). Fig. 13 shows the model
geometry and the resulting normal horizontal stress (sxx)
distributions when a horizontal collapse occurs near the vertical
fracture. A comparison of Figs. 12 and 13 shows that if a vertical
joint exists off to the side of the compaction zone, sxx relaxes and
becomes less tensile as the joint opens.
Figs. 14 compares the horizontal displacements between the
two cases discussed in this section, the model without vertical
fracture and the model with the vertical fracture. The horizontal
89
displacements at the surface have been made dimensionless by
the maximum vertical subsidence induced along the horizontal
elements. Here a positive displacement signifies a movement to
the right, and a negative displacement indicates a movement to
the left. Horizontal surface displacements are continuous when
there are no vertical fractures since the domain is modeled as an
elastic medium. In contrast, surface displacements are perturbed
during the subsidence when a fracture is located within the
tensile region. The right side of the fracture—the edge closer to
the induced subsidence—displaces towards the region of the
collapse horizontal elements, while the left side does not displace
as much, so the model fracture opens. This result shows how preexisting joints in tensile regions may widen to form fissures.
A sensitivity study was undertaken to explore how the opening
of vertical joints are influenced by the governing variables
presented in Fig. 11. Four dimensionless groups are chosen to
represent the relationships between the variables. P1, or E/sxx, is
the ratio of Young’s modulus of the rock to the stress imposed
along the horizontal elements to induce subsidence. P2, or fd/d, is
the ratio of the height of the vertical fracture to the depth at which
compaction occurs. P3, or a/d, is the ratio of the horizontal length
of subsidence to the depth. Finally, P4, or fl/d, is the ratio of the
distance between the vertical fracture and the edge of the
collapsed region to the depth. These groups are plotted against a
dimensionless length scale, UmaxOpening/UmaxCollapse, which
relates the horizontal displacement of the joint at the surface to
the maximum vertical subsurface subsidence along the horizontal
elements. Here, a negative dimensionless length means that the
edges of the vertical elements displace away from each other, or in
Fig. 12. Subsidence along horizontal elements (blue solid line, bottom center) and resulting stress distributions in the domain. Tensile stresses emanate diagonally upwards
from the edge of the horizontal elements. Colorbar in MPa. [For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this
article.]
Fig. 13. A vertical joint located to the left of the collapsed region. Tensile stresses near the vertical joint are relaxed due to the traction free elements.
Fig. 14. Horizontal displacements at the surface for cases with no fracture (solid line) and with a fracture (dotted line). The model with a fracture in the domain shows a
displacement discontinuity indicating an opening.
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other words, the joint opens. Simulation results show that this
dimensionless length does not vary with respect to P1, and thus
the following analyses are limited to demonstrating the dependence of the dimensionless length scale on P2, P3, and P4. The
results presented from the sensitivity analyses can be used, on a
first order basis, to estimate the location and the magnitude of
the subsidence when the only the widths of the surface fissures
are known.
Fig. 15 is a plot of the relationship between the dimensionless
opening (Umax Opening/Umax Collapse) and P4 (fl/d). Each line
represents a different value of P2 (fd/d). In the following
discussion,
the
maximum vertical
subsidence
length,
UmaxCollapse, depth, d, and length of subsidence, a, will be fixed
to simplify our analysis. As a consequence of fixing both d and a,
P3, the ratio between the two variables is constant. Variables a
and d are specified such that P3 ¼ 1.0. Fig. 15 shows that for a
constant value of P2, or for a fixed height of the fracture, a
maximum horizontal displacement at the surface is observed
when P40.8. The fissure width reaches a maximum when it is
located diagonally above and to the side of the zone of
compaction, consistent with where a concentration of tensile
stresses was observed in Fig. 12. The fissure opening decays to 0 as
the vertical joint moves farther away from the region of
subsidence regardless of the height of the fracture. This result is
reasonable since the stresses associated with the subsidence
decay with increasing distance. Fig. 15 also shows that when P2,
or the height of the pre-existing joint, increases, the magnitude of
the opening also increases. Based on the results, when P3 ¼ 1.0,
the maximum fissure opening is observed when the pre-existing
joint is located at P40.8 and is stratigraphically continuous
down to the collapse horizon, or P2 ¼ 1.
Fig. 16 is a similar plot. It shows how the dimensionless length
scale (Umax Opening/Umax Collapse) depends on P4 (fl/d) for varying
values of P3 (a/d) with both the maximum subsidence distance
(UmaxCollapse) and depth (d) fixed. In addition, fd, the height of the
fracture, is fixed and defined such that P2 (fd/d) is 1.0. The figure
shows that for a fixed value of P3, which represents the length over
which the collapse occurs, the fissure opening again depends
strongly on the location of the vertical joint. The fissure opening
decays to 0 far away from the subsidence and is the widest between
0.5oflo1.0 depending on the value of P3. As P3 increases, the
horizontal displacement at the surface increases, which makes
sense since a longer subsidence length leads to a greater tensile
stress emanating upwards towards the surface. The location where
the maximum fissure opening is observed moves closer to the edge
of the horizontal compaction when P3 increases. In other words,
the region of tensile stresses that extends upwards towards the
surface lies more directly above the horizontal compaction as the
length of subsidence increases when depth is constant.
We investigate whether the relationship between the subsidence and fissure opening at the outcrop in Fig. 10a and b can be
predicted using this numerical model. In this simulation only the
most prominent fissure at the outcrop, indicated on Fig. 10b, is
explicitly modeled using traction free elements. This fissure at the
outcrop is slightly oblique and appears to be stratigraphically
continuous down to the depth of the collapse. The bottom of this
fissure is located approximately 2.5 m left of the edge of the
collapsed zone. All other fissures and tensile stress fractures at the
outcrop are incorporated into the model by reducing the bulk
stiffness of the rock to 10 MPa, which is one to three orders of
magnitude lower than published elastic moduli of various shales
and sandstones. The length of subsidence is approximately 12 m
at the outcrop, although the exact length is not known due to
limited exposure at the outcrop. The subsidence occurs approximately 10 m below the surface. This ratio of length of collapse/
depth is close to the critical extraction value of 1.4 observed for
collapses associated with long-wall mining operations [27]. The
collapsing ash layer is modeled using tilted elements with
appropriately defined stress boundary conditions. The depth
where the collapse occurs is approximately 10 m, maximum
subsidence is approximately 1.5 m, and a 0.5 m surface opening of
the vertical fracture was observed at the outcrop.
When a collapse is induced in the numerical model, tensile
stresses are relaxed around the vertical fissure by opening. Fig. 17a
Fig. 15. Dimensionless length vs. P4 (fl/d). Each line represents a different value of P2 (fd/d), while P3 (a/d) is kept constant at 1.0.
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91
Fig. 16. Dimensionless length vs. P4 (fl/d). Each line represents a different value of P3 (a/d), while P3 (fd/d) is kept constant at 1.0.
Fig. 17. (a) Geometric representation of the two prominent features found at the outcrop (cf. Fig. 10). (b) Tensile stresses dominate around the diagonally oriented joint,
which is stratigraphically continuous down to the depth of collapse. fd10 m, d10 m, a12 m, and fl2.5 m.
shows the geometry of the model and Fig. 17b is the sxx stress
distribution map resulting from the collapse when a downward
stress of 0.25 MPa is defined along the horizontal elements. The
dimensionless opening, UmaxOpening/Umax Collapse is around 0.23
when these parameters are used to simulate the fissure opening
and the collapse. Alternatively, this value could have been
obtained by calculating appropriate dimensionless variables, and
using Fig. 16 to obtain the dimensionless length scale. Based on
the model assumptions, appropriate dimensionless values are
calculated as follows: P2 ¼ fd/d1, P3 ¼ a/d1.2, P4 ¼ fl/d0.25.
Although this method approximates the coalseam and the traction
free fracture to be horizontal and vertical, respectively, it
nevertheless gives a dimensionless length scale of approximately 0.23. Both of these values are consistent with the
UmaxOpening/UmaxCollapse observed at the outcrop. At the
outcrop, UmaxOpening ¼ 0.5 m and UmaxCollapse ¼ 1.5 m, giving a
length scale ratio of 0.3. The discrepancy is attributed to relatively
simple assumptions associated with this numerical model. In
future modeling efforts, these assumptions will be made more
realistic.
The results from the numerical simulation suggests that preexisting joints that are located above existing coalbed fires can
open when they are in regions of tensile stress induced by the
subsidence. Fig. 18 is a conceptual model of how the propagation
of the combustion front at the North Coalbed Fire can lead to
opening of fissures at the surface. The figure accounts for the local
geology, geometry and the findings from the numerical
investigations. In the figure, the lithology above the coalbed fire
is characterized as either shales or sandstones. At the site, shales
are often softer than the sandstones. In this conceptual model, the
coalseam is transformed into a layer of ash as the thin combustion
front propagates through the lower coal. The overlying strata
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Fig. 18. A conceptual model depicting the mechanism of how pre-existing joints above the North Coalbed Fire open up to form a fissure.
collapse, and a pre-existing joint opens up to form a surface
fissure. The underlying Pictured Cliffs sandstone remains intact.
Opened fissures above the fire may act as conduits that connect
the surface and the coalseam. These fissures allow combustion
gases to escape from the combustion zone, and enable fresh
oxygen to reach the coalseam in order to keep the combustion
alive.
6. Conclusions
At the surface above the North Coalbed Fire, which burns along
the Hogback Monocline in the San Juan Basin, numerous fissures
form orthogonal patterns. Some of these fissures vent hot exhaust
gases from the subsurface, an indication of a burning coalseam in
the subsurface. A combination of available geologic data from
previous surveys, observations and measurements from the field
allows identification of a mechanism for the formation of surface
fissures. The hypothesis is that pre-existing joints in the strata
overlying the North Coalbed Fire widen to form fissures when the
underground coalseam combusts and then compacts as its
structural integrity is lost. Previous literature has suggested or
described relationships between surface deformation and subsurface subsidence, but no work has established first order functional
relationships between variables that govern fissure widening and
subsurface subsidence in a coalbed fire. In this study, a simple
BEM model was formulated to simulate the collapse of the
coalseam and the opening of pre-existing vertical fractures.
Results show that the aperture of the fissures at the surface
depends strongly on where the vertical fracture is located with
respect to the subsurface subsidence. The sensitivity analyses
performed using this simulator also demonstrate the relationships
amongst the governing variables defined in this study. Those
relationships can be used to estimate the location and subsidence
magnitude based on the fissure locations and width measured at
the surface. The model was tested using a dataset obtained from a
near by outcrop that showed evidences of subsidence in a
combusted coalseam and an opening of a vertical fracture above.
Many assumptions were made in the simple numerical simulation, and thus there is some discrepancy between the model
results and measured values.
Acknowledgments
The authors of this paper would like to thank: Bill Flint of the
Southern Ute Indian Tribe for facilitating fieldwork details and his
help in securing funding; the Southern Ute Indian Tribe for their
gracious hospitality, allowing us to access their land and their
continued support; Jonathan Begay, Kyle Siesser and Ashley
Neckowitz for their help in the field and the Stanford Global
Climate and Energy Project and its contributors for their funding
that made this research possible.
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