Stanford Rock Fracture Project Vol. 20, 2009 C-1

FISSURE FORMATION AND SUBSURFACE SUBSIDENCE IN A COALBED FIRE Taku S. Ide

1, David Pollard

2, and Franklin M. Orr, Jr.

3

1,3 Dept. of Energy Resources and Engineering,

2 Dept. of Geological and Environmental Sciences

Stanford University, Stanford, CA 94305

e-mail: idetaku@stanford.edu

Abstract

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, CO., 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.

Keywords:

coalbed fire, coal fire, subsidence , pre-existing

joints, fissures, numerical modeling, CO2

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 (Dai et al., 2002), where

the estimated annual loss of coal is around 200,000

tons, equivalent to a yearly emission of ~1.5Mt of CO2

(Kuenzer et al., 2005). Coalbed fires are burning in

many locations in China, Indonesia, India, and the

United States (Stracher and Taylor, 2004). 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 (DeKok,

1986). Forest fires in Indonesia in 1997 and 1998

ignited hundreds of coal fires at outcrops (Brown,

2003). 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 (DeKok, 1986, GAI

Consultants, 1983).

The particular fire examined in this study, called

the North Coalbed Fire, to distinguish it from other

active fires in the region, 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 (Williamson, 1999). Anecdotal evidences

provided by local Southern Ute Tribe members (Ide,

2007) suggest 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 digitizing

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 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

Stanford Rock Fracture Project Vol. 20, 2009 C-2

and surface deformation. The results and the limitations

of applicability of this simulation model are discussed.

San Juan Basin Geology

The San Juan Basin is an asymmetric, coal bearing

basin that covers approximately 16,800 – 19,400 square

kilometers, stretching approximately 145km west-east

and 160km north-south (Fassett, 2000, Kelso et al.,

1988). It is located near the Four Corners, and spans

across northwest New Mexico and southwest Colorado

as shown in Figure 1. The basin is well characterized

due to the abundance of both coal and coal-bed

methane resources in the Upper Cretaceous Fruitland

Formation (Figure 2). One study has estimated that a

coal-bed methane reserve of nearly 1.4 x 1012

m3 (50 x

1012

ft3) adsorbed onto 219 x 10

9 metric tons of coal

that underlies the San Juan Basin (Kelso et al., 1988).

The flat, Central Basin is bounded by several key

geologic features, which are described in detail in

previous geologic surveys of the area (Fassett, 2000,

Kelso et al., 1988, Lorenz and Cooper, 2000). 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 (Lorenz and Cooper,

2000). As Figure 1 shows, 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 (Lorenz and

Cooper, 2000), or through reactivation of western

dipping thrust faults underlying the Hogback monocline

that resulted in the uplift (Taylor and Huffman, 1988).

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 (Lorenz and Cooper, 2000). 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

(Kaiser et al., 1991).

Formations that make up the Upper Cretaceous

rocks in the San Juan Basin are described by Molenaar

(Molenaar and Baird, 1992). The Fruitland Formation,

which includes the coalbed fire, and adjacent geologic

units are depicted in the stratigraphic column in Figure

2. The left column is representative of the entire San

Juan Basin. The right column shows the top 25m 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 Sandstone (PC), which was

deposited as regressive marine sands (Condon, 1988)

parallel to the shoreline stretching northwest-southeast

(Fassett, 2000). The Fruitland Formation is a mixture of

mudstones, siltsones, carbonaceous shales and coals

deposited landward and parallel to this shoreline

(Fassett, 2000). 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 Coal Zone in the northeastern

region of the San Juan Basin (Sandberg, 1988). The

Lower Coal is burning at the North Coalbed Fire.

Figure 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 Lorenz and Cooper, 2003.

At the North Coalbed Fire, 14 boreholes were

drilled in 2007 over an area of 600m x 200m. 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 (Fassett, 1971, Sandberg,

1988). The deposition pattern suggests that the

Stanford Rock Fracture Project Vol. 20, 2009 C-3

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 (Fassett,

1988). The echelon geometry of coal deposits can make

subsurface correlations difficult in the transverse

direction (Fassett, 1988), but it has been shown that

Fruitland Formation coalbed correlation was possible

when well logs spaced less than 4km apart were

obtained (Fassett, 1971, 1988).

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 and they are

summarized in Lorenz and Cooper (2000). Ruf (2005)

suggests that the fractures formed due to post-Laramide

extension, while Taylor and Huffman (1998) describe a

Proterozoic crystalline basement with reactivated faults

that may have influenced the orientations of the

fractures in overlying strata. Lorenz and Cooper (2000)

suggest that the orientations of the fractures are most

influenced by the formation of tectonic features such as

the San Juan uplift and the Zuni uplift (cf. Figure 1)

during the Laramide Orogeny.

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 (Badgley,

1962, 1965, Kelley and Clinton, 1960). Their findings

are generally supported by more recent measurements

(Condon, 1988, 1997, Lorenz and Cooper, 2003, Ruf,

2005, Taylor and Huffman, 1988). The most relevant

study for the North Coalbed Fire was carried out by

Condon (1988), 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.

North Coalbed Fire

A satellite image of the area bounded by the red

dotted box in Figure 1 is shown in Figure 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 coalbed fire is

contained between latitude N37o01’57” and

N37o02’24” and longitude W108

o06’36” and

W108o06’18”, and has an aerial extent of

approximately 600 m x 200m. 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.

Figure 2: Stratigraphic columns representative of the San Juan Basin (left) and the top 25 meters 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).

A cross-section, A-A’ is drawn (Figure 3b) by

superimposing a USGS geological survey map over the

satellite image in Figure 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. Figure 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 5 and 9

degrees to the southeast, and the coal layer dips 6 to 15

degrees in the same direction (Condon, 1988). Both the

surface topography and the coalseam flatten towards

the southeast in the direction of the Central Basin (cf.

Figure 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

Stanford Rock Fracture Project Vol. 20, 2009 C-4

fissures typically have widths on a decimeter scale,

whereas joints have apertures less than 0.5 cm (Condon

1988). Some of these fissures emit high temperature

combustion gases, indicative of the active fire below,

while others are at ambient temperature.

Figure 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-A’ is used in Figure 3b. Satellite image is provided by Googlemaps. b) Cross section A-A’ 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 = Lewis Shale, Kp = Pictured Cliffs Sandstone, Kf = Fruitland Formation, Kkl = Kirtland Shale.

Four types of fissures have been observed.

Examples are shown in Figure 4: gaping fissures,

plateau/offset fissure, molehill/buckling fissures, and

narrow fissures. The gaping fissure in Figure 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 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.

Figure 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. Figure 4c shows an

example of molehill fissures, 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 290oC

(550oF) have been recorded. The temperatures at the

fissures were measured using a thermal gun, Raynger 3i

Series, made by Raytek. Figure 4d is an example of

narrow fissures, many of which are located in the

northern most portion of the field, and these emit the

hottest exhaust gases recorded in the field at about

1000oC. Both the molehill and narrow fissures are

about 0.15m in width. All of the fissures appear to be

opening Mode I fractures (Pollard and Aydin, 1988), as

displacements are dominantly orthogonal to the fracture

surfaces.

Figure 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, d) a narrow fissure venting exhaust gases exceeding 900

OC.

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 Figure 5. The length

has been made dimensionless with respect to the

longest fissure in the field, which is 75m. The diagram

shows that there are three main fissure directions over

Stanford Rock Fracture Project Vol. 20, 2009 C-5

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 1,600 joints and coal cleats at

37 different outcrop locations on the Southern Ute

Indian Reservation. Of the 37 measurement stations, 8

of them are located along the Hogback Monocline and

are spaced approximately 2km 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

through J4, were described. Their stereonets are

reproduced in Figure 6. A comparison of Figures 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 (Condon, 1988).

Figure 5: A rose diagram showing the orientation and the lengths of the fissures found above the North Coalbed Fire. The characteristic length scale is ~100m.

Figure 6 (bottom): Four stereonets reproduced from Condon, 1988. a) J1 joint b) J2 joint c) J3 joint d) J4 joint.

While 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 to 5m, and are spaced

0.15m to 6m. J4 exposed lengths are less than 2m, and

the spacings are more inconsistent (Condon, 1988).

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 meter accuracy,

with most having better than 0.5 meter accuracy after

differential correction. Figure 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

Figures 1 and 3a. The left edge of this map traces the

contact line between the Fruitland Formation and the

Pictured Cliffs Sandstone (cf. Figures 3a, 3b). 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 (Williamson, 1999). The concrete was

injected into identified openings in 2000 in an attempt

to smother the fire. Boreholes were drilled around the

Stanford Rock Fracture Project Vol. 20, 2009 C-6

grouted fissures, and thermocouples were installed to

allow monitoring of temperature changes. These

boreholes are shown as open white triangles in Figure

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 Figure 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 80ft core was obtained.

The surface information in Figure 7a can be related

to the subsurface information by creating a cross-

section along the line A-A”. This cross section shows

that the depth to coal is approximately 20 meters. 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 Figure 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

Figure 7b. Fissures that intersect the cross-section line

A-A” 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 Figure 7b connects the bottom

of the coalseam.

Stanford Rock Fracture Project Vol. 20, 2009 C-7

Figure 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-A”. b) A cross-section of the North Coalbed Fire site along A-A”. Red circles indicate locations of fissures that intersect the line. Numbers above the surface represent well numbers.

Stanford Rock Fracture Project Vol. 20, 2009 C-8

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 Figure

7b, the occurrences of surface fissures coincide with

regions where void and ash were encountered during

drilling. For example, borehole 4 (solid triangle, Figure

7b) located near the peak of the topography contains

only ash and 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

(Whittakker and Reddish, 1989). 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. Figure 8 is a

conceptual model of subsidence near a long-wall

mining process (Whittaker and Reddish, 1989). 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

(Whittaker and Reddish, 1989). 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

(Whittaker and Reddish, 1989). There are two key

differences between their study and the work presented

in this paper. First, the North Coalbed Fire is burning

~20m below surface, whereas longwall mining

typically occurs at much greater depths (Whittaker and

Reddish, 1989). Second, pre-existing vertical joints and

their response to subsurface compaction are not

discussed in Whittaker and Reddish.

Figure 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. (Whittaker and Reddish, 1989)

Previous studies of coalbed fires have also

suggested that subsurface subsidence leads to the

formation of fissures at the surface (Buhrow et al.,

2004, Cao et al., 2007, Chen, 1997, Dunrud and

Osterwald, 1980, Gielisch and Kuenzer, 2003, Kuenzer,

2007a, 2007b, 2008, Litscheke, 2005, Sokol and

Volkova, 2007, Wessling, 2007, Wessling et al., 2008,

Zhang, 2007). Figure 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 (Chen,

1997), 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 (Chen, 1997). In a

coalbed fire combustion simulation model presented by

Huang et al. (2001), 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., mechanical

processes such as subsidence and fissure openings were

not considered (Wessling et al., 2008). 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 preexisting fissures, and the stiffness of

the overburden rock, we hope to aid future numerical

modeling of coalbed fires.

Stanford Rock Fracture Project Vol. 20, 2009 C-9

Figure 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)

Observations at an outcrop about 1km north of the

North Coalbed Fire shows how subsurface subsidence

can cause pre-existing fractures to open at the surface.

This outcrop exposes a fossilized coalbed fire,

subsidence, extension fractures and fissures. At this

outcrop, shown in Figure 10a, a coalseam is overlain by

10m of sandstone, shale, and siltstone. A person 1.5m

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 0.5m 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 ~1.5m.

Features at this outcrop such as Fissure 2 and the

subsided ash layer were mapped using a laser

rangefinder produced by LaserCraft Inc. (LaserCraft,

2007). The digitized version of the outcrop is

juxtaposed next to the photo of the outcrop in Figure

10b. Note how the tabular coalseam is deformed due to

collapse of the ash layer. Above the collapse, opening

fractures, much like those depicted in Figure 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 Figure 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.

Figure 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.

Stanford Rock Fracture Project Vol. 20, 2009 C-10

Numerical Modeling

Numerical models were employed to examine

whether pre-existing 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 (Crouch and Starfield, 1983). The

BEM code is a modified version of Martel’s Matlab

BEM code (Martel, 2003), which in turn is based on the

original Fortran code presented in Crouch and Starfield

(Crouch and Starfield, 1983).

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

(Berest et al., 2008, Sanz, et al., 2008). 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 (Malvern, 1960). 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 (Crouch and Starfield, 1983). 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 (Huang, 2001, Wessling, 2007,

2008).

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 (Crouch and

Starfield, 1983). Stress boundary conditions are

perturbed along the horizontal elements to simulate a

collapse as 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 (Crouch and

Starfield, 1983). 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.

Figure 11 defines the variables and applicable

dimensionless groups used in this modeling. E is

Young’s modulus, and σzz 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.

Figure 11: Definitions of variables and dimensionless groups used in the BEM model. E and σzz have units of MPa, while fd, fl, a and d have units of m.

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. Figure 10b), and simulation

results are compared to field observations.

In the first example, a 12m horizontal line of

elements that is located 10m below the surface is

deformed by applying a uniform compressive stress of

0.25MPa, which is exerted by the weight of the

overlying rock. The elastic modulus of the overburden

is 10MPa, and a maximum compaction of 1.5m is

induced at the horizontal elements. Figure 12 depicts

Stanford Rock Fracture Project Vol. 20, 2009 C-11

the distribution of the horizontal component of normal

stress, σxx, in response to the inward directed

displacement discontinuity on the horizontal elements.

The sign of σxx 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 σxx 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. Figure 12), except

vertical elements are introduced to simulate the joint.

The vertical elements are placed at x = -12m, where

tensile stresses found in the first case (cf. Figure 12).

Figure 13 shows the model geometry and the resulting

normal horizontal stress (σxx) distributions when a

horizontal collapse occurs near the vertical fracture. A

comparison of Figures 12 and 13 shows that if a vertical

joint exists off to the side of the compaction zone, σxx

relaxes and becomes less tensile as the joint opens.

Figures 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 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 pre-existing 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 Figure 11. Four

dimensionless groups are chosen to represent the

relationships between the variables. Π1, or E/σxx, is the

ratio of Young’s modulus of the rock to the stress

imposed along the horizontal elements to induce

subsidence. Π2, or fd/d, is the ratio of the height of the

vertical fracture to the depth at which compaction

occurs. Π3, or a/d, is the ratio of the horizontal length of

subsidence to the depth. Finally, Π4, 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 other words, the

joint opens. Simulation results show that this

dimensionless length does not vary with respect to Π1,

and thus the following analyses are limited to

Figure 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. Figure 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.

Stanford Rock Fracture Project Vol. 20, 2009 C-12

demonstrating the dependence of the dimensionless

length scale on Π2, Π3, and Π4. 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.

Figure 15 is a plot of the relationship between the

dimensionless opening (Umax Opening / Umax Collapse)

and Π4 (fl/d). Each line represents a different value of

Π2 (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, Π3,

the ratio between the two variables is constant.

Variables a and d are specified such that Π3 = 1.0.

Figure 15 shows that for a constant value of Π2, or for a

fixed height of the fracture, a maximum horizontal

displacement at the surface is observed when Π4~0.8.

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 Figure 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. Figure 15 also shows that when Π2,

or the height of the pre-existing joint, increases, the

magnitude of the opening also increases. Based on the

results, when Π3 = 1.0, the maximum fissure opening is

observed when the pre-existing joint is located at Π4 ~

0.8 and is stratigraphically continuous down to the

collapse horizon, or Π2 = 1.

Figure 16 is a similar plot. It shows how the

dimensionless length scale (Umax Opening / Umax

Collapse) depends on Π4 (fl/d) for varying values of Π3

(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 Π2

(fd/d) is 1.0. The figure shows that for a fixed value of

Π3, 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 0.5<fl<1.0 depending on the value of

Π3. As Π3 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

Π3 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.

Figure 15 (above): Dimensionless length vs. Π4 (fl/d). Each line represents a different value of Π2 (fd/d), while Π3 (a/d) is kept constant at 1.0.

Figure 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.

Stanford Rock Fracture Project Vol. 20, 2009 C-13

Figure 16 (below): Dimensionless length vs. Π4 (fl/d). Each line represents a different value of Π3 (a/d), while Π3 (fd/d) is kept constant at 1.0.

We investigate whether the relationship between

the subsidence and fissure opening at the outcrop in

Figures 10a and 10b can be predicted using this

numerical model. In this simulation only the most

prominent fissure at the outcrop, indicated on Figure

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 2.5m 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 10MPa,

which is one to three orders of magnitude lower than

published elastic moduli of various shales and

sandstones. The length of subsidence is approximately

12m at the outcrop, although the exact length is not

known due to limited exposure at the outcrop.

The subsidence occurs approximately 10m 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

(Whittaker and Reddish, 1989). The collapsing ash

layer is modeled using tilted elements with

appropriately defined stress boundary conditions. The

depth where the collapse occurs is approximately 10m,

maximum subsidence is approximately 1.5m, and a

0.5m 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. Figure 17a shows the geometry of the model

and Figure 17b is the σxx stress distribution map

resulting from the collapse when a downward stress of

0.25 MPa is defined along the horizontal elements.

Figure 17: a) Geometric representation of the two prominent features found at the outcrop (cf. Figure 10). b) Tensile stresses dominate around the diagonally oriented joint, which is stratigraphically continuous down to the depth of collapse. fd~10m, d~10m, a~12m, fl~2.5m.

Figure 18: A conceptual model depicting the mechanism of how pre-existing joints above the North Coalbed Fire open up to form a fissure.

Stanford Rock Fracture Project Vol. 20, 2009 C-14

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 Figure 16 to obtain the dimensionless length

scale. Based on the model assumptions, appropriate

dimensionless values are calculated as follows: Π2 =

fd/d ~ 1, Π3 = a/d ~ 1.2, Π4 = fl/d ~ 0.25. 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 = 0.5m and

UmaxCollapse = 1.5m, 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 pre-exisiting joints that are located above existing

coalbed fires can open when they are in regions of

tensile stress induced by the subsidence. Figure 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 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.

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

acknowledge: 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 to make this

research possible.

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