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Figure 2.2: A three-dimensional state
of stress represented by Mohr’s Circles
with principal normal and principal shear
stresses labeled.
dependent, it can be shown [1] that the quantities in Eq. (2.2) are constant for a state of
stress, regardless of choice of coordinate system. Because of their directional independence,
they are called stress invariants.
I = σ +σ +σ
1 x y z
I = σ σ +σ σ +σ σ −τ2 −τ2 −τ2 (2.2)
2 x y y z z x xy yz zx
I = σ σ σ +2τ τ τ −σ τ2 −σ τ2 −σ τ2
3 x y z xy yz zx x yz y zx z xy
Furthermore, the stress invariants can be used to determine the magnitudes of the three
principal normal stresses. The cubic equation shown in Eq. (2.3) always yields three real
roots. The three solutions to this cubic are σ , σ , and σ [1].
1 2 3
σ3 −σ2I +σI −I = 0 (2.3)
1 2 3
Any state of stress can be represented graphically on a plot of shear stress vs. normal
stress, as shown in Figure 2.2. The plot in Figure 2.2 contains Mohr’s Circles, which are
named after Otto Mohr who developed this type of graphical representation. Each point on
a circle represents the state of stress in some direction. The horizontal axis intercepts, where
the shear stress is equal to zero, represent the principal normal stresses. Mohr’s diagram
also conveniently shows the maximum shear stress, which has a value equal to the radius of
the largest circle.
Materials will deform when subjected to stress. The ratio of the amount of deformation
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to the total original length of the material is called strain. That is, strain, (cid:15), is equal to ∆L/ L,
where L is the length of the unstressed material. Often it is convenient to express strains as
percentages, where percent strain, (cid:15)% = 100(cid:15).
Strength is possibly the most important consideration in engineering design, because
it is an attempt to define the limits of a component’s functional applicability. In its most
widely applicable form, strength can be defined as the applied stress at which a component
will fail to perform its intended function. This definition has led to the use of a concept
called factor of safety, FS, which is the ratio of strength to stress. Engineering designs with
a factor of safety greater than one are expected to be successful, because the stress does not
exceed the strength. Factors of safety less than one are expected to fail.
2.2.1 Elastic Moduli
Relationships between stress and strain are expressed through constitutive models. The
simplest constitutive model to describe how a material deforms under stress is to assume
that the material will deform proportionally to the load applied. This is identical to saying
that stress and strain are linearly related. This model, called the elastic model, is described
by Eq. (2.4).
σ = E(cid:15) (2.4)
Where E is called Young’s modulus. This relationship is shown graphically in Figure
2.3. The slope of the stress-strain curve of an elastic material is constant and equal to the
Young’s modulus of the material. Furthermore, elastic materials are assumed to recover
strain when they are unloaded. Elastic strains do not result in permanent deformation.
Young’s modulus relates axial stress to axial strain. Axial strains cause a material to
deform in perpendicular directions. This phenomenon, called the Poisson effect, is repre-
sented in Figure 2.4. While the amount of elongation, ∆L, due to the extensional stress in
Figure 2.4 is dictated by the Young’s modulus, the degree to which that elongation causes
narrowing of the member is described by Poisson’s ratio. Poisson’s ratio, ν, is the opposite
of the ratio of lateral strain to axial strain, as expressed in Eq. (2.5).
(cid:15)
lateral
ν = − (2.5)
(cid:15)
axial
where (cid:15) is the lateral strain and (cid:15) is the axial strain. Nearly all materials
lateral axial
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Figure 2.3: Stress-strain curve of elastic loading and un-
loading.
experience a positive lateral strain (extension) when subjected to a negative axial strain
(compression), and a negative lateral strain when subjected to a positive axial strain. The
ratio is negated to make the Poisson’s ratio generally positive.
The normal stress in the x-direction causes an x-directional strain, (cid:15) , of magnitude
x
σx/ E, as well as a strain of magnitude −ν(cid:15)
x
in the y- and z-directions. This logic can be
expanded to the other two axial directions to find expressions for the total strain in each
direction. The total strain in each direction is summarized in Eq. (2.6).
(cid:15) = 1 [σ −ν(σ +σ )]
x E x y z
(cid:15) = 1 [σ −ν(σ +σ )] (2.6)
y E y x z
(cid:15) = 1 [σ −ν(σ +σ )]
z E z x y
Young’s modulus and Poisson’s ratio are two of the six elastic moduli. Two other
elastic moduli of importance are the bulk modulus, K, and the shear modulus, G. If any
two elastic moduli are known for an isotropic, homogeneous material, then the other four
can be determined. Eqs. (2.7) and (2.8) can be used to calculate the bulk modulus and shear
modulus, respectively, if both Young’s modulus and Poisson’s ratio are known.
E
K = (2.7)
3(1−2ν)
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Figure 2.6: Pictorial representation of
shear modulus.
2.2.2 Plastic Strain
Permanent deformation is called plastic deformation. The elastic, perfectly-plastic model
is a simple plastic model which assumes that a material will behave elastically until some
yield strength is reached. The material will then begin deforming while the stress remains
at the yield strength. Elastic, perfectly-plastic behavior is represented graphically in Figure
2.7. Prior to unloading, the total strain experienced by the material consists of both elastic
strain, (cid:15) , and plastic strain, (cid:15) . Unloading of an elastic, perfectly plastic material will cause
e p
recovery of elastic strains, while some permanent, plastic strain will remain.
A select few categories of constitutive models are shown in Figure 2.8. Strain-hardening
materials deform plastically after their yield strength is reached, but they are able to support
greater loads as they deform. In contrast, materials which exhibit strain-softening behavior
will shed load while experiencing plastic deformation. Materials that experience brittle
failure lose most or all of their ability to support a load very quickly once their strength is
reached.
2.3 Rock Mass Classifications
Rock masses are complex systems with high variation between them, making them difficult
to describe quantitatively. Because each rock mass can be described uniquely, a means of
classifyingrockmassesisnecessaryinordertocategorizeandgroupthem. Thisclassification,
in addition to easing and standardizing communication regarding rock masses, is valuable
during the engineering design process.
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Table 2.1: Qualitative descriptions of
rock quality designation ranges as sug-
gested by Deere [3].
RQD % Qualitative Description
0 - 25 Very Poor
25 - 50 Poor
50 - 75 Fair
75 - 90 Good
90 - 100 Excellent
2.3.1 Rock Quality Designation (RQD)
One of the oldest rock mass classification systems which is still widely used today is the rock
quality designation (RQD) system. The RQD system, which was developed as a technique
for quantifying the percentage of recoverable core, was first described by Don Deere in 1966
[2]. The RQD value, which is calculated by analyzing core samples, is equal to the ratio of
the cumulative length of core greater than 100 mm (4 inches) to the total length of core.
Pieces greater than or equal to 4 inches in length are considered to be “sound” core, and
smaller pieces are the result of shearing, jointing, faulting, or weathering within the rock
mass. In addition to the numerical value of RQD, Deere has categorized ranges of values
and suggested qualitative descriptions, as shown in Table 2.1 [3].
When RQD was introduced, there were many existing methods for estimating the core-
recovery percentage, but RQD became the standard, and a widely used index of rock quality.
The RQD index became a standard because it is easy to measure, easy to calculate, and
nondestructive. Because of its applicability and simplicity, it has been incorporated as one
input parameter into more involved rock classification systems [4].
2.3.2 Rock Mass Rating (RMR)
One such rock mass classification system which includes the RQD among many other pa-
rameters is the rock mass rating (RMR) system. The RMR system was originally called the
“Geomechanics Classification” by Bieniawski, its developer. In addition to using previously
proven rock mass indices, RMR was designed to be functional and use a variety of important
rock and rock mass properties with appropriate weights to value their relative importance
properly [5].
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Table 2.2: Qualitative descriptions associated
withrockmasseswithRMRrangesassuggested
by Bieniawski [6].
Rating Class no. Qualitative Description
100 - 81 I Very Good Rock
80 - 61 II Good Rock
60 - 41 III Fair Rock
40 - 21 IV Poor Rock
< 20 V Very Poor Rock
Table 2.3: Quantitative estimates of rock mass strength parameters, rock
mass cohesion and rock mass friction angle, as well as an expected life of a
tunnel through a rock mass based on rock mass rating ranges as suggested
by Bieniawski [6].
Class no. Average stand-up time Cohesion (kPa) Friction Angle (◦)
I 20 yr for 15-m span > 400 > 45
II 1 yr for 10-m span 300 - 400 35 - 45
III 1 wk for 5-m span 200 - 300 25 - 35
IV 10 hr for 2.5 -m span 100 - 200 12 - 25
V 30 min for 1-m span < 100 < 15
The form of the rock mass rating system used today includes six inputs: uniaxial
compressive strength, rock quality designation (RQD), discontinuity spacing, condition of
discontinuities, presence of groundwater, and orientation of joints. In addition to passionate
support of RMR, Bieniawski gave a detailed explanation on how to determine its value here
[6]. The RMR system typically takes values between 0 and 100, like the RQD system. But
unlike the RQD system, negative values are possible with RMR. Bieniawski groups rock
masses within ranges of RMR values and assigns them qualitative descriptions, as well as
some reasonable quantitative values, as shown in Tables 2.2 and 2.3.
The RMR system was originally developed as an aide for tunnel design and support
selection [5]. While the RMR system has not changed in its essential nature or purpose
since its introduction, some modifications were made to it in its first ten to fifteen years in
existence. Since its development, the RMR system has been adapted for use in many rock
massdesignapplicationsincludingfoundationsandslopesaswellasundergroundexcavations
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other than simple tunneling [7].
2.3.3 Tunnel Quality Index (Q)
Developed around the same time as RMR, the Q-System is another rock mass classification
technique which is still used today. The Q-System incorporates the RQD value, like RMR,
but it also considers the stress state of the rock mass. Typically falling between Q = 0.001
and Q = 1000 on a logarithmic scale, the Q index is calculated as shown in Eq. (2.11) [8].
RQD J J
r w
Q = · · (2.11)
J J SRF
n a
where RQD is the rock quality designation, J is the joint set number, J is the joint
n r
roughness number, J is the joint alteration number, J is the joint water reduction factor,
a w
andSRF isthestressreductionfactor. TheQ-Systemisnotstrictlyarockmassclassification
system. The Q-System may only be applied to an underground opening within a rock mass
and not to a rock mass itself. Still in use today, the Q-System was an early attempt to
quantify and predict the response of the rock mass to being excavated [9].
2.3.4 Geological Strength Index (GSI)
The Geologic Strength Index (GSI) was introduced in an attempt to overcome some limi-
tations present in the existing classification systems. The GSI index, which ranges from 10
to 100, was created to be a direct input into numerical modeling programs. Existing clas-
sification systems were developed to account for factors such as jointing and water content
which are dealt with explicitly in modeling softwares, causing such effects to be considered
redundantly [10].
The GSI incorporates geologic makeup of the rock mass, as well as some visual char-
acteristics. Specifically, the structure of the rock mass must be defined. Originally, four
qualitative descriptions of the rock mass were defined, one of which had to be ascribed to
the rock mass. There are a total of six options now to be used for assigning a description to
the rock mass structure: intact, block, very blocky, blocky/seamy, disintegrated, and lam-
inated [10]. There are also descriptions given so that all users may arrive at the same or
similar conclusions. In addition to the structural component of the rock mass, the surface
quality of the must be described as well [11].
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Figure 2.9: Depiction showing the degree of frac-
turing expected on different length scales in a rock
mass. Used under fair use, 1995 [11].
2.4 Failure Criterion
Knowledge of the strength characteristics of in situ rock is required for practical design
purposes. The most common means of inferring the strength of rock is lab testing, which
is most commonly done on small samples of intact rock. The results of testing intact rock
samples in a lab setting cannot be assumed to be valid for rock which is not intact, so some
reduction factors are often applied [12]. A cartoon showing relevant scales of rock and the
importance of joints is shown in Figure 2.9.
The strength [13, 14, 15, 16, 17] and post-failure behavior [18] of geomaterials depend
greatly on the scale considered. Strength testing of intact rock takes many forms and is used
ubiquitously in the rock mechanics industry. Testing of rocks with a single joint, whether
natural or saw-cut, is also common in laboratories. The strength of a rock sample with a
single joint depends greatly on the orientation of the joint. For heavily jointed rock masses,
there is often a sufficient number of joints in various directions that the rock mass as a whole
can be assumed to act homogeneously [18].
The two most common means of estimating rock strength are the Mohr-Coulomb and
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theHoek-Brownfailurecriteria. Charles-AugustindeCoulombdevelopedtheMohr-Coulomb
failure criterion in the 18th Century. The Mohr-Coulomb failure criterion gives a simple,
linear relationship between shear strength and applied normal stress. The Hoek-Brown
failure criteria was adapted from an equation used to estimate the strength of concrete by
Evert Hoek and Edwin Brown for analyzing rock in the 1980’s [19]. While these two failure
criteria are the most commonly used design constraints in rock mechanics, they both ignore
the intermediate principal stress, which has been shown to have a significant and predictable
effect on failure [20].
2.4.1 Mohr-Coulomb Failure Criterion
The Mohr-Coulomb failure criterion remains one of the most widely used models for predict-
ing the failure of rocks under compression. It is widely used to predict rock failure, because it
is simple, intuitive, and accurate under many loading conditions. The Mohr-Coulomb failure
criterion predicts the shear strength, |τ|, to be a function of the applied normal stress, σ ,
n
as shown in Eq. (2.12).
|τ| = σ tanφ+c (2.12)
n
whereφandcareempiricallyderivedparameters. Theparameterφiscalledtheangleof
internal friction, and c is cohesion. The angle of internal friction is analogous to a coefficient
of friction, in that the product of it and normal stress create opposition to sliding. Cohesion
is the inherent shear strength of the rock, which can prevent failure in cases of pure shearing.
Because this shear strength estimate is a function of normal stress, the equation can
be plotted on the same axes as a Mohr’s circle, as shown in Figure 2.10. The Mohr’s circle
plotted in Figure 2.10 represents a state of stress at failure because it is intersecting the
failure envelope at the point (|τ|,σ ). Any Mohr’s circle under the failure envelope and not
n
intersecting it, is expected to be stable.
As discussed previously, the Mohr’s circle is a graphical representation of a state of
stress. Every diameter which can be drawn through the circle represents an orientation of
mutually orthogonal axes in that stress state. The horizontal diameter through the circle
would intersect at σ and σ , the principal stresses. This orientation has a shear stress
1 3
value of zero. Angles within the Mohr’s circle are double that of the actual stress state it
is representing. The principal stresses, which are 180◦ apart on the circle are perpendicular
in reality. Furthermore, the plane of failure is θ from the plane on which σ acts, and the
1
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Figure 2.10: Mohr-Coulomb failure envelope plotted with a Mohr’s circle repre-
senting a state of stress at failure (right). Representative vertical cross-section of
a laboratory rock sample with geometry and applied stresses that match the axes
plotted to the right (left).
diameter to the point of failure on the Mohr’s circle–the point at which the circle intersects
the failure plane–is 2θ from the diameter intersecting σ .
1
It is often convenient to express a failure envelope in the stress-space where the three
spatial axes are σ , σ , and σ , so that a stress state can be plotted as one point independent
1 2 3
of orientation. In the principal stress space, the Mohr-Coulomb failure envelope, shown in
Eq. (2.12), can be written conveniently in two forms: one in terms of φ (Eq. (2.13)), and one
in terms of θ (Eq. (2.14)). Where 2θ = 90◦ +φ, as can be seen in Figure 2.10.
1+sinφ cosφ
σ = σ +2c (2.13)
1 3
1−sinφ 1−sinφ
σ = σ tan2θ+2ctanθ (2.14)
1 3
A stable state of stress can reach failure in one of three simple ways: an increase in the
maximum principal stress, σ , a decrease in the minimum principal stress, σ , or the addition
1 3
of pore pressure. These three paths from a stable stress state to a state of failure are shown
in Figure 2.11 with the original state of stress being the dashed circle and the final, failed
state being the solid circle. The first two scenarios are fairly straightforward: the stress state
changes sufficiently to cause the circle to intersect the failure envelope. The third scenario
involving pore pressure involves a new concept. The presence of pore pressure within a
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Figure 2.11: Mohr’s circle showing progression to failure by increasing σ (left). Mohr’s
1
circle showing progression to failure by decreasing σ (center). Mohr’s circle showing
3
progression to failure by increasing pore pressure, p, (right).
specimen reduces the effective normal stress by the amount of pore pressure. Graphically,
this amounts to sliding the Mohr’s circle to the left by an amount equal to the pore pressure
withoutchangingthediameterofthecircle. TheexamplesshowninFigure2.11illustratethe
utility of the graphical tool developed by Mohr to accompany the failure criterion developed
by Coulomb.
The Mohr-Coulomb failure envelope for intact rock can be determined through labo-
ratory testing. At least four cylindrical rock samples should be held at various confining
stresses, typically with σ = σ , and loaded until failure. These combinations of principal
2 3
stresses at failure can then be plotted as Mohr’s circles on shear stress vs. normal stress axes.
The best-fit line that lies tangent to the Mohr’s circles representing stress states at failure
is the failure envelope. The material constants, c and θ, can then be determined from the
failure envelope [21].
In addition to intact rock, rock with joints can also be analyzed by using the Mohr-
Coulomb failure criterion. The consideration of joints adds some complexity to the Mohr-
Coulomb model, because the stability of each joint needs to be determined explicitly when
the Mohr-Coulomb criterion is used in this way. While it is possible to apply the Mohr-
Coulomb failure criterion to rock with joints, it becomes cumbersome with only a few joints
if the orientation and strength characteristics of the joints vary [22].
The Mohr-Coulomb failure criterion is simple, effective, and very widely used, but
it contains a few inherent flaws due to its simplicity. Because it is an estimate of shear
strength, tensile failure is not explained well by the Mohr-Coulomb failure criterion. This
is not a serious flaw of the Mohr-Coulomb failure criterion, because all of the widely used
failure criteria for rock are focused on the compressive region, and none of them can be
extended into the tensile region with confidence [23].
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AsecondsignificantlimitationoftheMohr-Coulombfailurecriterionanditsapplication
is also a consequence of its simplicity. The failure envelope of many rock types is nonlinear
[24]. The shear strength for many rock types is significantly overestimated by the linear
Mohr-Coulomb failure envelope in the region with high confining stress. A more general
Mohr-Coulomb, |τ| = f(σ ), form which can be constructed by connecting tangent lines
n
to many Mohr circles at failing stress states can overcome this pitfall, while simultaneously
sacrificing the greatest strength of the linear Mohr-Coulomb criterion: its simplicity.
2.4.2 Hoek-Brown Failure Criterion
The Hoek-Brown failure criterion supplies an empirical relationship for predicting failure
which is nonlinear. The relationship, shown in Eq. (2.15), was originally developed as a
strength criterion for concrete, but was adapted by Hoek and Brown to describe rock failure
[19]. Hoek and Brown justified proposing the new relationship, by saying that it is the first
rock failure criterion which can simultaneously [25]:
• Be applied to intact rock for any stress conditions which could be expected under-
ground,
• Handle the presence of one or more joint sets within the sample, and
• Provide some insight into rock mass response.
(cid:112)
σ = σ + mσ σ +sσ2 (2.15)
1 3 c 3 c
where σ is the maximum principal stress at failure, σ is the minimum principal stress,
1 3
σ is the uniaxial compressive strength of intact rock, and m and s are empirically derived
c
material constants.
One of the first challenges faced and overcome by the Hoek-Brown criterion was the
popularityoftheMohr-Coulombcriterionatthetime. Softwarepackagesandclosed-formso-
lutions at the time required the Mohr-Coulomb constants, c and φ, as inputs. Relationships
between the Mohr-Coulomb constants and the Hoek-Brown constants, m and s, were pre-
sented a few years after the Hoek-Brown criterion was introduced. The derived relationship
is [18]:
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(cid:32)
(cid:18) (cid:19)
(cid:33)−1/2
π 1
(cid:0) (cid:1)
φ = arctan 4hcos2 + arcsin h−3/2 −1 (2.16)
6 3
where φ is the instantaneous angle of internal friction, and:
16(mσ +sσ )
c
h = 1+ (2.17)
3m2σ
c
The Hoek-Brown criterion is meant to be applicable to describe situations where the
rock or rock mass behaves isotropically. With appropriate values given to m and s, the
Hoek-Brown criterion claims to be able to describe the behavior of intact rock or highly
jointed rock masses. It is not recommended, however, to be used to explain the behavior of
rock with a single joint or a few joints, because these could not behave isotropically [26].
It was admitted from the start by the developers that an empirical relationship such as
the one shown in Eq. (2.15) is only as good as the values chosen for the constants m and
s. For easier application, relationships between the constants and the RMR value are given
[26]. These values could be applied to rock mass behavior, but not to that of intact rock.
Another significant modification occurred in 1992 when a third fitting parameter was
introduced. A modified version of the Hoek-Brown criterion was presented. The failure
criterion for intact rock remained unchanged, but a constant, a, was added to that of jointed
rock masses, which took the form [27, 28]:
(cid:18)
σ
(cid:19)a
3
σ = σ +σ m (2.18)
1 3 c b
σ
c
The Geological Strength Index was developed, among other reasons, for use with the
Hoek-Brown failure criterion. Relationships between the GSI value and the empirical con-
stants m, s, and a have been published. Furthermore, relationships between RMR and GSI
and the Q-index and GSI have also been published to make the Hoek-Brown criterion easily
accessible in addition to robust [11].
The Hoek-Brown failure criterion has seen widespread application and success in de-
scribing the behavior of intact rock and jointed rock masses since its inception. Its nonlinear
form has proven to fit more closely to lab data than the Mohr-Coulomb failure criterion.
While it does suffer from the need to fit more empirically-derived parameters than the
Mohr-Coulomb criterion, the availability of relationships between those constants and well-
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established rock mass characterization systems make choosing appropriate values for those
constants relatively easy.
2.5 Design of Underground Openings
Design approaches used for underground openings can be characterized as one of three meth-
ods: anempiricalapproach,arationalapproach,oranobservationalapproach. Theempirical
approach depends on the use of knowledge gained from previous case studies. The rational
approach requires the development of analytical solutions for the state of stress and strain
present in the subsurface during and after excavation. And an observational approach in-
volves extensive monitoring in the form of visual observations during the excavation process
so that interventions can be made when necessary to achieve a desired final form. A single
design may incorporate any or all of these three [29].
2.5.1 Analysis of Retreat Mining Pillar Stability (ARMPS) [30]
Theminingindustrynecessarilyemploysanobservationalstrategyatalltimes. Sophisticated
monitoring is used at times, but often it depends simply on visual observations. While
the observational strategy is always in use, it is a secondary strategy. Primary design of
underground mines has a focus on pillar sizing, which has historically taken an empirical
approach [31].
Aprimaryfocusofgroundcontrolinundergroundcoalmineshaslongbeenpillardesign.
It was long assumed that pillar load could be assumed to be found from the tributary area.
Pillar strength was determined from an empirical relationship. The pillar safety factor could
then be calculated to predict a satisfactory design [32]. This method could be classified
as some hybrid between a empirical strategy–determining pillar strength–and a rational
approach–calculating a factor of safety.
When using this design approach, the only variable was in the choice of empirical
relationship. Many empirically derived coal pillar strength equations have been produced
over the past century. An extensive review of empirical coal pillar strength equations was
composed in 1976 [33]. It was clear that the strength of a coal pillar is dependent upon both
the size and the shape of the pillar. The dependence of coal pillar strength on shape and size
was reiterated in a more recent review of empirically derived strength equations published
some twenty years later [34]. A comprehensive list of coal pillar strength equations was
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compiled in a recent paper [35], which listed over a dozen equations.
In addition to the difficulty faced when deciding on a strength equation, it was realized
that estimating pillar load from the tributary area leads to erroneous results [36]. Assuming
thetributaryareaforfindingpillarloadresultsinthetheoreticalmaximumloadonthepillar.
The actual pillar load is considerably less. Excavating material to create pillars causes some
convergence within the seam. The overburden tends to have some capacity to support itself,
and the load is instead distributed to barrier pillars, intact rock, and gob.
The Analysis of Retreat Mining Pillar Stability (ARMPS) [30], represents further de-
velopment into a combination empirical-rational approach to underground coal mine design.
ARMPS was formulated from ALPS, Analysis of Longwall Pillar Stability. Since its incep-
tion, ARMPS has become an industry standard in the United States.
ARMPS calculates the load on the active mining zone (AMZ), which depends on the
loading condition. The strength of the pillars, S , is assumed to follow the Mark-Bieniawski
P
pillar strength formula:
(cid:20) (cid:18)
w
w2(cid:19)(cid:21)
S = 6.2MPa 0.64+ 0.54 −0.18 (2.19)
P
h hL
A stability factor is then calculated, which is the ratio of the load bearing capacity of
the pillars within the active mining zone to the load on those pillars. The value of ARMPS is
tied to the large database of cases which it uses to set safe thresholds for its stability factor.
Rather than assuming a factor of one to be the threshold between unsafe designs and safe
ones, ARMPS uses its extensive database to set the threshold at a stability factor of 1.5 [34].
ARMPS uses mine geometry alone to suggest which designs may be stable and which
may not be. Overburden thickness, the pillar array, and the loading condition are the only
inputs. Its simplicity, ease of use, and large database have led to its ubiquity in underground
coal mine design, but it does not include site-specific characteristics.
2.5.2 Ground Response Curve
Theconvergence-confinementmethod(CMM),ananalyticaltechnique, wouldbeclassifiedas
a rational approach to the design of underground openings. The CCM has seen widespread
use in civil engineering for determining the response of the subsurface during tunneling. The
stress and strain response around the opening can be determined after some simplifying
assumptions are made. Originally, those assumptions were [37]:
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Figure 2.12: Vertical cross-section of a
circular tunnel of radius, R, with inter-
nal pressure, p , which is analyzed for the
0
convergence-confinement method (CM).
• Opening has a circular vertical cross-section
• Stress field is hydrostatic
• Homogeneous and isotropic rock mass
Becauseofthehydrostaticstressfieldandthecircularopeningassumptions,theproblem
becomes two-dimensional. First in the radial direction, the problem can be depicted in a
vertical cross-section, as shown in Figure 2.12. Following the assumption of a hydrostatic
stress state, the state of stress in the rock mass prior to excavation is σ = σ = σ = p ,
1 2 3 0
where p is the in situ stress. Rather than being viewed in three orthogonal directions,
0
the CCM approach considers only the internal pressure of the tunnel, p , and the external
i
pressure of the tunnel, p , where p = p = p prior to excavation. As such, determining
e i e 0
the stress and strain response around the opening involves determining the expected radial
convergence given a reduction in internal radial pressure.
The solution for determining the stress-strain response in an axial-symmetric element
of rock, which was originally published over seventy years ago, can be found here [29].
Solutions for both elastic and elastic-plastic materials are also given. A typical stress-strain
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Figure 2.13: Typical ground reaction curve (GRC) as determined via
the convergence-confinement method (CCM).
curve representing the response of the rock mass, called the ground response curve (GRC),
can be seen in Figure 2.13.
The curve begins on the stress-axis at the value of the in situ stress state, p . As the
0
tunnel is being excavated, the pressure inside of the tunnel is reduced, which causes radial
convergence. This relationship between internal radial pressure and radial convergence is
represented by the GRC.
Convergence of the opening is elastic until some critical pressure, p , is reached, after
cr
which the convergence becomes plastic. Plastic radial convergence will continue as the
internalpressureisreduceduntilnomoresupportisrequiredtopreventfurtherconvergence–
represented by the intersection of the GRC with the horizontal axis. It could also be the
case that the self-supporting capacity of the rock is lost and the curve would never intersect
the horizontal axis. If the critical pressure is never reached, then the response will be purely
elastic [38].
Other than considering the radius, the only other relevant spatial dimension with the
original simplifying assumptions for the problem is in the direction of the tunnel axis. When
the tunnel face is very far from an analyzed region, the internal pressure is equal to the
in situ pressure. As the tunnel excavation approaches, the internal radial pressure reduces
because of the presence of the excavation. There is a reduction in radial pressure in a region
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Figure2.14: Typicalgroundreactioncurve(GRC)andlineardisplace-
ment profile (LDP) as determined via the convergence-confinement
method (CCM).
some distance ahead of the excavation face. The relationship between the axial distance
from the excavation face and the radial convergence, called the linear displacement profile
(LDP), is shown in Figure 2.14 [39].
The LDP shows that there is radial convergence ahead of the tunnel face. Radial
convergence has been measured as much as one radius ahead of the excavation face. This
convergence increases steadily up to the excavation face where approximately one-third of
the total expected convergence is expected. No more convergence is expected at a greater
distance that 1.5 diameters away from the excavation face [11]. These are obviously very
rough estimates, especially when considering the fact that not all rock masses have sufficient
self-supporting capacity to force intersection of the GRC with the horizontal axis.
Not only is the CCM a relatively easy solution to achieve, the GRC has uses during
support selection and installation. The support pressure-radial convergence curve is anal-
ogous to a stress-strain curve. The stress-strain characteristic curves of supports may be
plotted along with the GRC and LDP on these plots [40].
After a support is installed, its own strain increment will match that of the tunnel.
The applied stress on the support will increase according to the support characteristic curve
(SCC), which is simply the stress-strain curve of the support. Loading will increase until
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either the SCC intersects the GRC or the support fails. When the SCC intersects the GRC,
the support is supplying the internal radial pressure required to prevent further convergence,
so equilibrium is reached. This relationship between the SCC and GRC has obvious impli-
cations for support selection. Furthermore, the LDP gives some indication of the timing
available for support installation. Obviously, supports may not be installed until the open-
ing has been excavated. The earliest time available for support installation is dependent
upon the mode of excavation in use as well as the support chosen [41].
In addition to the circular, hydrostatic, isotropic solution described here, solutions for
many other simplifying assumptions have been determined. Some of the first variations on
the original solution were to generalize it to include non-hydrostatic stress states. Initial
solutions assumed the rock mass to be a Mohr-Coulomb material [42, 43], but some later
solutions involved Hoek-Brown materials [44, 45, 46]. An extensive history of GRC solutions
through 1983 are given here [37].
Closed-form solutions nearly exclusively assume a circular vertical cross-section. While
this simplifying assumption is applicable in many tunneling operations, it is too simple to
be applied to mining. Analytical solutions of increasing complexity are quite rare, and are
still limited in application because they are too simple [47].
Using the convergence-confinement method to solve for the ground response curve can
only apply to the simplest geometries. And it was originally concerned with determining the
ground response due only to a reduction in the internal pressure of the future tunnel related
to excavation. Numerical modeling has seen ever increasing use in recent decades because
of technological advances made to computing. These numerical models can provide a means
of estimating the ground response curve for very complex geometries, while incorporating
site-specific characteristics.
A majority of studies related to ground control in mining involving numerical modeling
useItasca’sFLAC3D(FastLagrangianAnalysisofContinuain3-Dimensions)[48]. FLAC3D
is an explicit, finite-difference modeling program. Unlike its competitors, this explicit mod-
eling scheme allows extreme flexibility and accurate results well into the plastic region of
material response.
The ground response curve concept has been used to study various loading conditions
expected during longwall mining [49, 50, 51]. An excellent example of the power and versa-
tility of numerical models when applied to mining applications is shown in [49]. Numerical
models were used in [49] to determine the response in a longwall gate road to increased
loading from a passing longwall–a geometry and loading condition far too complex for CCM.
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There has been limited study of the ground response in room-and-pillar coal mines
using numerical models. [52] used explicitly modeled coal pillars within a panel. The elastic
modulus of the pillar material was reduced to determine the response of the surrounding
rock at mid-panel.
Difficulties are met when explicitly modeling pillars within a panel-scale model. An
element size sufficiently small to represent the pillars to adequate realism would be pro-
hibitively fine at the panel scale. A considerably coarser mesh is typically chosen for models
which represent much larger spatial extents. The FLAC3D developers have recommended
against using zones of significantly different sizes in a single simulation. The solution scheme
used in FLAC3D results in slow execution times when model geometries include zones of
significantly different sizes [53].
A method has been proposed which follows pillar behavior on the small-scale, accounts
for the panel response on the large-scale, and is computationally reasonable [54]. This study,
performed in a trona room-and-pillar mine in Wyoming, details a two-scale approach to
modeling room-and-pillar panels. First, the loading response of pillars is simulated in small-
scale models. Then, a large, panel-scale model is developed which accounts for the pillar
response, but only models the pillar explicitly with a fictitious material.
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Works Cited
[1] Norman E Dowling. Mechanical behavior of materials: engineering methods for defor-
mation, fracture, and fatigue. Prentice hall, 1993.
[2] DU Deere, AJ Hendron, FD Patton, and EJ Cording. Design of surface and near-
surface construction in rock. In The 8th US Symposium on Rock Mechanics (USRMS).
American Rock Mechanics Association, 1966.
[3] DU Deere. Geological considerations. Rock mechanics in engineering practice, pages
1–20, 1968.
[4] DU Deere and DW Deere. The rock quality designation (RQD) index in practice. In
Symposium on Rock Classification Systems for Engineering Purposes, 1987, Cincinnati,
Ohio, USA, 1988.
[5] ZT Bieniawski. Engineering classification of jointed rock masses. Civil Engineer in
South Africa, 15(12), 1973.
[6] ZT Bieniawski. The geomechanics classification in rock engineering applications. In 4th
ISRM Congress. International Society for Rock Mechanics, 1979.
[7] ZT Bieniawski. Engineering rock mass classifications: a complete manual for engineers
and geologists in mining, civil, and petroleum engineering. John Wiley & Sons, 1989.
[8] N. Barton, R. Lien, and J. Lunde. Engineering classification of rock masses for the
design of tunnel support. Rock mechanics, 6(4):189–236, 1974.
[9] NGI. Using the Q-system: rock mass classification and support design. Norwegian
Geotechnical Institute, Oslo, April 2013.
[10] V Marinos, P Marinos, and Evert Hoek. The geological strength index: applications
and limitations. Bulletin of Engineering Geology and the Environment, 64(1):55–65,
2005.
[11] E Hoek, PK Kaiser, and WF Bawden. Support of underground excavations in hard rock.
AA Balkema, Rotterdam, 1995.
[12] AJ Hendron. Mechanical properties of rock. Rock Mechanics in Engineering Practice,
pages 21–53, 1968.
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[13] Nick Barton. Shear strength criteria for rock, rock joints, rockfill and rock masses:
Problemsandsomesolutions. Journal of Rock Mechanics and Geotechnical Engineering,
5(4):249 – 261, 2013.
[14] Nick Barton and Stavros Bandis. Effects of block size on the shear behavior of jointed
rock. In The 23rd US Symposium on Rock Mechanics (USRMS). American Rock Me-
chanics Association, 1982.
[15] Seong-Tae Yi, Min-Su Kim, Jin-Keun Kim, and Jang-Ho Jay Kim. Effect of specimen
size on flexural compressive strength of reinforced concrete members. Cement and
Concrete Composites, 29(3):230–240, 2007.
[16] JN van der Merwe. A laboratory investigation into the effect of specimen size on the
strength of coal samples from different areas. Journal of the South African Institute of
Mining and Metallurgy, 103(5):273–279, 2003.
[17] Z.T. Bieniawski. The effect of specimen size on compressive strength of coal. Interna-
tional Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 5
(4):325 – 335, 1968.
[18] Evert Hoek. Strength of jointed rock masses. Geotechnique, 33(3):187–223, 1983.
[19] Evert Hoek and Paul Marinos. A brief history of the development of the Hoek-Brown
failure criterion. Soils and rocks, 2:1–8, 2007.
[20] GA Wiebols and NGW Cook. An energy criterion for the strength of rock in polyax-
ial compression. In International Journal of Rock Mechanics and Mining Sciences &
Geomechanics Abstracts, volume 5 (6), pages 529–549. Elsevier, 1968.
[21] R Ulusay. The ISRM Suggested Methods for Rock Characterization, Testing and Moni-
toring: 2007-2014. Springer, 2015.
[22] Q Xu, J Chen, J Li, C Zhao, and C Yuan. Study on the constitutive model for jointed
rock mass. PloS one, 10(4), 2015.
[23] ZF Zhang and J Eckert. Unified tensile fracture criterion. Physical review letters,
94(9):094301, 2005.
[24] John Conrad Jaeger and Neville GW Cook. Fundamentals of rock mechanics. Chapman
& Hall, London, 3rd edition, 1979.
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[25] EvertHoekandEdwinTBrown. Underground excavations in rock. InstitutionofMining
and Metallurgy, 1980.
[26] Evert Hoek and Edwin T Brown. The Hoek-Brown failure criterion-a 1988 update. In
Proc. 15th Canadian Rock Mech. Symp, pages 31–38. Toronto, Dept. Civil Engineering,
University of Toronto, 1988.
[27] E Hoek, D Wood, and S Shah. A modified Hoek-Brown failure criterion for jointed rock
masses. In Eurock, volume 92, pages 209–13, 1992.
[28] Sandip Shah. A study of the behaviour of jointed rock masses. PhD thesis, University
of Toronto, 1992.
[29] Pierpaolo Oreste. The convergence-confinement method: roles and limits in modern
geomechanical tunnel design. American Journal of Applied Sciences, 6(4):757, 2009.
[30] C. Mark and F.E. Chase. Analysis of retreat mining pillar stability (armps). In
Proceedings-New Technology for Ground Control in Retreat Mining. Pittsburgh, PA: US
Department of Health and Human Services, Public Health Service, Centers for Disease
Control and Prevention, National Institute for Occupational Safety and Health, DHHS
(NIOSH) Publication, pages 17–34, 1997.
[31] BN Whittaker, T Unlu, DJ Reddish, and Smith SF. Pillar design aspects for stability in
deepcoalmines. Assessment and Prevention of Failure Phenomena in Rock Engineering,
1993.
[32] C Mark. State-of-the-art in coal pillar design. Transactions-Society for Mining Metal-
lurgy and Exploration Incorporated, 308:123–128, 2000.
[33] WA Hustrulid. A review of coal pillar strength formulas. Rock Mechanics, 8(2):115–145,
1976.
[34] Christopher Mark and Timothy M Barton. Pillar design and coal strength. In
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Department of Health and Human Services, Public Health Service, Centers for Disease
Control and Prevention, National Institute for Occupational Safety and Health, DHHS
(NIOSH) Publication, pages 49–59, 1997.
[35] M Jawed, RK Sinha, and S Sengupta. Chronological development in coal pillar design
for bord and pillar workings: A critical appraisal. Journal of Geology and Mining
Research, 5(1):1–11, 2013.
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[36] H Wagner. Pillar design in coal mines. JS Afr Inst Min Metall, 80:37–45, 1980.
[37] Edwin T Brown, John W Bray, Branko Ladanyi, and Evert Hoek. Ground response
curves for rock tunnels. Journal of Geotechnical Engineering, 1983.
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[38] DiegoLopeAlvarez. Limitationsofthegroundreactioncurveconceptforshallowtunnels
under anisotropic in-situ stress conditions. Master’s thesis, Universitat Polit`ecnica de
Catalunya, 2012.
[39] N Vlachopoulos and MS Diederichs. Improved longitudinal displacement profiles for
convergenceconfinementanalysisofdeeptunnels. Rock mechanics and rock engineering,
42(2):131–146, 2009.
[40] Thomas M Barczak. Optimizing secondary roof support with the niosh support tech-
nology optimization program (stop). In Proceedings of 19th International Conference
on Ground Control in Mining, Morgantown, WV, pages 74–84, 2000.
[41] Thomas M Barczak, Thomas P Mucho, and Dennis R Dolinar. Design methodology for
standing secondary roof support systems. Proceedings, New Technology for Coal Mine
Roof Support, pages 133–150, 2000.
[42] JJK Daemen and C Fairhurst. Influence of failed rock properties on tunnel stability.
In The 12th US Symposium on Rock Mechanics (USRMS). American Rock Mechanics
Association, 1970.
[43] JW Bray. A study of jointed and fractured rock. part ii–theory of limiting equilibrium.
Rock mechanics and engineering geology, 5(4):197–216, Dec 1964.
[44] CCarranza-TorresandCFairhurst. Applicationoftheconvergence-confinementmethod
oftunneldesigntorockmassesthatsatisfytheHoek-Brownfailurecriterion. Tunnelling
and Underground Space Technology, 15(2):187–213, 2000.
[45] C Carranza-Torres and Ch Fairhurst. The elasto-plastic response of underground ex-
cavations in rock masses that satisfy the Hoek-Brown failure criterion. International
Journal of Rock Mechanics and Mining Sciences, 36(6):777–809, 1999.
[46] Kyung-Ho Park, Bituporn Tontavanich, and Joo-Gong Lee. A simple procedure for
ground response curve of circular tunnel in elastic-strain softening rock masses. Tun-
nelling and Underground Space Technology, 23(2):151–159, 2008.
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[47] H Yavuz. Support pressure estimation for circular and non-circular openings based on
a parametric numerical modelling study. Journal-South African Institute Mining and
Metallurgy, 106(2):129, 2006.
[48] Itasca Consulting Group, Inc., Minnesota. Fast Lagrangian Analysis of Continua in
3-Dimensions, version 5.0, manual, 2013.
[49] Essie Esterhuizen and Tom Barczak. Development of ground response curves for long-
wall tailgate support design. In Golden Rocks 2006, The 41st US Symposium on Rock
Mechanics (USRMS). American Rock Mechanics Association, 2006.
[50] Thomas M Barczak. A retrospective assessment of longwall roof support with a focus
on challenging accepted roof support concepts and design premises. In Proceedings of
the 25th international conference on ground control in mining, Morgantown, WV, pages
232–243, 2006.
[51] Thomas M Barczak, GS Esterhuizen, John Ellenberger, and P Zhang. A first step
in developing standing roof support design criteria based on ground reaction data for
Pittsburgh seam longwall tailgate support. In Proceedings of the 27th International
Conference on Ground Control in Mining, pages 349–359, 2008.
[52] Essie Esterhuizen, Chris Mark, and Michael Murphy. The ground response curve, pillar
loading and pillar failure in coal mines. In 29th International Conference on Ground
Control in Mining, 2010.
[53] Inc. Itasca Consulting Group. Flac3d training course - basic concepts and recommended
procedures, 2015.
[54] M Board, B Damjanac, and M Pierce. Development of a methodology for analysis of
instability in room and pillar mines. In Deep Mine 07, Proceedings of the Fourth In-
ternational Seminar on Deep and High Stress Mining, pages 273–282. Perth, Australia,
2007.
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Chapter 3
Modeling the Ground Response Curve
for a Room-and-Pillar Coal Panel
3.1 Abstract
The response of the overburden to excavations made within a coal seam has significant
implications on the stability of mine workings. A useful tool for analyzing the reponse of
a rock mass to underground excavations, called the ground response curve, was developed
for the tunneling industry approximately seventy years ago. While mine geometries are far
too compex for analytical solutions to the ground response curve to be developed, numerical
modeling may be used instead. Numerical modeling is used in this study to solve for the
ground response curve for a room-and-pillar coal mine panel in the eastern US. The ground
response curves obtained are compared to stress-strain curves for pillars within the panel to
estimate panel stability.
3.2 Introduction
Coal mines provide a unique set of challenges toward safe design. The complexity arises from
the soft nature of coal and the high variability among coal measure rocks. The rock types
present around coal seams often range from strong, competent sandstones to weak, lami-
nated shales. Ground control in these environments begins with pillar sizing. Larger pillars
obviously offer more support, but at the cost of leaving a valuable resource underground.
36
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Figure 3.1: Injuries due to fall of roof or rib between
2006 and 2014. This includes fatal injuries, non-fatal
injuries with days lost, and injuries with no days lost
[1].
Ground control is a primary design consideration during the development of under-
ground coal mines. Poor ground conditions can negatively affect ventilation and haulage.
Extremely poor ground conditions or poor designs can result in catastrophe. Over 16% of
all reported incidents in underground coal mines from 2006 to 2014 were due to fall of roof
or rib [1]. A chart of the total number of injuries attributed to ground control issues in
underground coal mines in the US is shown in Figure 3.1. There has been a downward trend
in the number of incidents of late, but safer conditions are certainly possible.
The ground response curve is a useful tool to aid in understanding the stability of
underground openings. Developed for the tunneling industry, the ground response curve
was originally determined using the convergence-confinement method (CCM). In its original
form, CCM simply predicted the relationship between reduced radial pressure inside of a
tunnel due to excavation and the radial convergence of that excavation [2]. A depiction of a
ground response curve is shown in Figure 3.2.
Ground response curves (GRC) are plotted on pressure-convergence axes. The curve
beginsonthepressure-axisatavalueequaltotheinsitustressstate. Astheinternalpressure
of the rock mass is reduced due to an approaching excavation, convergence is expected. The
GRC represents the internal pressure required to prevent further convergence. The curve has
great utility for estimating not only the self-supporting strength of an underground opening,
but also the type of support which should be applied [3].
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Figure 3.2: Ground reaction curve (GRC) with two possible outcomes
shown. The solid line represents stable convergence, and the dashed
line represents unstable convergence.
The convergence-confinement method (CCM), when applied to circular tunnels, often
predicts stable convergence [2]. Stable convergence is represented by the solid line-type in
Figure 3.2. The curve with the solid line-type shows convergence associated with an under-
ground opening which has sufficient self-supporting capacity to limit convergence naturally.
That is, without the installation of artificial support, the total convergence of the excava-
tion is expected to be the intersection of the GRC and the convergence-axis, where internal
pressure is zero.
Working sections in retreating room-and-pillar mines are not expected to experience
stable convergence [4]. The dashed line-type in Figure 3.2 shows an underground opening
which is expected to experience unstable convergence. The minimum point in the curve
represents a loss of self-supporting capacity of the rock mass around the excavation. Full
collapse of the opening is expected after the rock mass no longer has the integrity to support
its own weight. This is represented by the increasing slope of the GRC where the internal
pressure required to prevent future convergence approaches the original lithostatic stress.
The geometry of underground mine openings tends to be far more complex than those
in the tunneling industry. However, the ground response curve concept may still be applied.
Analyticalsolutionsforthegroundresponsecurveareoftennotpossibleforminingscenarios,
but the curve itself may still be determined through numerical modeling [5]. The numerical
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Figure 3.3: Contour map showing depth of cover over room-and-pillar panel 2E.
The marked drillhole locations represent the locations of the two holes drilled into
the roof for installation of the seismic array from which core samples were collected
and tested for rock mechanics properties.
modeling performed in this study was completed in FLAC3D [6]
3.3 Site Description
This study included characteristics specific to a room-and-pillar coal mine located in the
central Appalachian coal fields of the Eastern United States. The room-and-pillar mine
panel studied here was numbered “Panel 2E” by the mine operators. As shown in Figure
3.3, the depth of cover over Panel 2E ranged from approximately 700 to 1000 feet. Panel 2E
was a seven-entry panel containing rectangular pillars. Entries were cut to a height between
six and seven feet. The barrier pillars on either side are approximately 140-feet wide.
The mined seam was the Jawbone. Coal thickness in the studied mine sections was
approximately five feet, and approximately six inches of parting was present. Rib sloughage
wascommonlyobservedtooccurtoadepthofsixinchestoafootintotherib. Thesloughage
was likely due to the degree of fracturing within the seam, which is depicted in Figure 3.4.
Both the roof and floor are comprised of shaley material. Two holes were drilled into
the roof for the installation of triaxial geophones. The location of the holes that were drilled
is shown in Figure 3.3. Core samples of the roof were collected during the drilling of these
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Table3.2: Firstestimateofmaterialprop-
erties of the roof rock used in numerical
models. The values listed are obtained
from laboratory testing or literature avail-
able on numerical modeling input param-
eters.
Parameter Unit Value
Young’s modulus GPa 23.2
Compressive strength MPa 80
Angle of internal friction ◦ 30
Cohesion MPa 14.8
Tensile strength MPa 4.6
Bedding friction angle ◦ 10
Bedding cohesion MPa 2.96
Bedding tensile strength MPa 0.46
3.4.1 The Pillar Response
Small-scalepillarmodelswereconstructedwithrepresentativematerialsoftheroofandfloor.
Coal was modeled as a Hoek-Brown material, while the roof and floor were modeled using
the ubiquitous joint constitutive model. These models were loaded while the stress-strain
response of the pillar material was measured and recorded.
A range of reasonable properties of the coal material were found in the literature [8, 9].
Values throughout this range were tested as inputs into the numerical models and the stress-
strain response was measured. Model calibration at this stage was performed by comparing
the peak strength of various square pillar dimensions against the empirical Bieniawski pillar
strength equation [10]:
(cid:20) (cid:21)
W
p
S = S 0.64+0.36 (3.1)
P i
H
p
Square pillars with width-to-height ratios of 6 and 8 were tested in this way to find
appropriate values for coal as a Hoek-Brown material. These pillars were modeled with
an elastic roof and floor to focus on the coal material, and to minimize the effect of the
surrounding material. The stress-strain curves of the two pillar dimensions tested are shown
in Figure 3.6. The peak strength values obtained are within approximately ten percent of
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Figure 3.6: Stress-strain response of the two square
pillars–of width to height ratios equal to six and eight–
with elastic roof and floor.
the values suggested by Eq. (3.1).
After finding appropriate coal material properties, those material properties were mod-
eled with a more realistic roof and floor material. The roof and floor were modeled as jointed
Mohr-Coulomb materials by using the ubiquitous joint constitutive model within FLAC3D.
The material properties listed in Table 3.2 were used as inputs. The ubiquitous joint con-
stitutive model considers the effect of a specified joint strength and orientation anywhere
within the roof and floor material without explicitly representing any joints.
A pillar matching those cut in the room-and-pillar Panel 2E was modeled in FLAC3D
with ubiquitously jointed shale material as the roof and floor while the stress-strain response
was recorded. The stress-strain curve of this pillar is shown in Figure 3.7. Stress and strain
values were calculated as averages over the entire pillar area.
Calibration of the model was performed at this stage in two forms. The pillar peak
strength was matched to the Mark-Bieniawski empirical pillar strength relationship [11].
The pillar response was also matched to underground observations. Visual observations
were limited in Panel 2E to the degree of rib sloughage. Rib sloughage of six inches to one
foot was commonly reported throughout the panel. This rib sloughage was matched to the
failed state of the pillar-scale models.
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Figure 3.7: Stress-strain response of a rectangular pillar with roof and
floor properties listed in Table 3.2.
3.4.2 The Overburden Response
The response of the overburden to excavations made within the seam was modeled by con-
structing thin vertical cross-sections of the rock mass. These vertical cross-sections included
material from the floor up to the surface. The models were allowed to reach equilibrium with
gravity loading and horizontal stresses considered. The vertical pressure within the seam
was then reduced gradually to represent excavation of the openings. The vertical pressure
of the roof on the seam as well as the convergence of the seam was measured throughout
the excavation process. An example ground response curve as obtained from this modeling
method is shown in Figure 3.8.
Roof and floor material was assumed to follow the built-in ubiquitous joint constitutive
model in FLAC3D. A user-defined joint strength and orientation is considered implicitly
throughout the modeled roof and floor material. The ubiquitous joint model is the most
efficient method for including the presence of a series of joints or laminations in FLAC3D.
The curve starts as the in situ vertical stress value on the internal pressure-axis. As the
internal pressure within the seam is reduced, convergence occurs. This curve never reaches
the horizontal axis, so unstable convergence is expected.
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Figure 3.8: Ground response curve of Panel 2E.
3.5 Results and Discussion
The ground response curve is a useful tool for analyzing the stability of underground exca-
vations. While unstable convergence is predicted from the curve obtained here, this is only
expected to occur after full extraction. Further convergence can be prevented at any point
with the application of a vertical stress which matches that described by the curve.
An altered pillar stress-strain response curve is plotted superimposed on the GRC in
Figure 3.9. The stress-strain response of the pillar is reduced by a factor of (1−ER), where
ER is the extraction ratio of the panel. This is done to average the stress a pillar applies to
the roof over the entire tributary area.
Convergence within the mined-out panel is expected to stop at the intersection point
of the altered pillar stress-strain curve and the ground response curve. At this point, the
pillars are supplying the internal pressure required to prevent further convergence of the
excavation.
3.6 Conclusions
The ground response curve of the rock mass surrounding a room-and-pillar coal mine has
beenestimatedusingFLAC3D.TheGRCwasestimatedbygradualreductionofthepressure
within the future underground opening. This method is a similar procedure to the analytical
solution determined from the convergence-confinement method.
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Works Cited
[1] Mine safety and health administration.
[2] Edwin T Brown, John W Bray, Branko Ladanyi, and Evert Hoek. Ground response
curves for rock tunnels. Journal of Geotechnical Engineering, 1983.
[3] Pierpaolo Oreste. The convergence-confinement method: roles and limits in modern
geomechanical tunnel design. American Journal of Applied Sciences, 6(4):757, 2009.
[4] B Damjanac, M Pierce, and M Board. Methodology for stability analysis of large room-
and-pillar panels. In 48th US Rock Mechanics/Geomechanics Symposium. American
Rock Mechanics Association, 2014.
[5] Essie Esterhuizen, Chris Mark, and Michael Murphy. The ground response curve, pillar
loading and pillar failure in coal mines. In 29th International Conference on Ground
Control in Mining, 2010.
[6] Itasca Consulting Group, Inc., Minnesota. Fast Lagrangian Analysis of Continua in
3-Dimensions, version 5.0, manual, 2013.
[7] William J Conrad. Microseismic monitoring of a room and pillar retreat coal mine in
southwest virginia. Master’s thesis, Virginia Polytechnic Institute and State University
(Virginia Tech), 2016.
[8] Essie Esterhuizen, Chris Mark, and Michael M Murphy. Numerical model calibration
for simulating coal pillars, gob and overburden response. In Proceeding of the 29th
international conference on ground control in mining, Morgantown, WV, pages 46–57,
2010.
[9] Jienan Pan, Zhaoping Meng, Quanlin Hou, Yiwen Ju, and Yunxing Cao. Coal strength
and young’s modulus related to coal rank, compressional velocity and maceral compo-
sition. Journal of Structural Geology, 54:129–135, 2013.
[10] Z.T. Bieniawski. The effect of specimen size on compressive strength of coal. Interna-
tional Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 5
(4):325 – 335, 1968.
[11] C. Mark and F.E. Chase. Analysis of retreat mining pillar stability (armps). In
Proceedings-New Technology for Ground Control in Retreat Mining. Pittsburgh, PA: US
Department of Health and Human Services, Public Health Service, Centers for Disease
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Figure 4.1: Injuries due to fall of roof or rib between
2006 and 2014. This includes fatal injuries, non-fatal
injuries with days lost, and injuries with no days lost
[3].
highly variable, often laminated rock present above and below coal seams. Underground
coal mine ground control starts with proper pillar sizing. Larger pillars, while offering
more support, reduce coal production. The sizing of pillars, more than any other design
consideration, is a balance between revenue and cost.
Control of the ground is a primary design consideration during the development of
underground coal mines. Poor ground conditions will at least add cost to ventilation and
haulage needs. Increasingly bad ground conditions can prevent future raw material extrac-
tion or even cause injury or death to mine workers. Over 16% of all reported incidents in
underground coal mines from 2006 to 2014 were due to fall of roof or rib [3]. A chart of the
total number of injuries attributed to ground control issues in underground coal mines in
the US is shown in Figure 4.1. There has been a downward trend in the number of incidents
of late, but safer conditions are certainly possible.
Room-and-pillar coal mine stability has two scales to consider. Stability must be main-
tained at the pillar scale and at the mine-wide scale. Mine-wide stability is largely a function
of the response of the overburden to excavations made within the panel. Pillar sizing and
the performance of the pillars has great implications on panel stability [4].
Numerical modeling was performed to explore the interaction between the overburden
and the pillars on a large, panel-wide scale. To accomplish this, the interaction between the
roof, pillars, and the floor was first studied on a small scale. The results of these pillar-scale
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models were then used in a panel-scale study to assess mine-wide stability. This two-step
approachallows for computationallyefficient modeling while consideringboththe small scale
and the large scale [5].
4.3 Overview of Two-Scale Modeling Approach
A two-scale modeling approach for modeling room-and-pillar mines in FLAC3D has been
suggested in the literature [5]. This approach is ideal for analyzing the interaction between
the large-scale and the small-scale responses during excavation. The two-scale approach has
been used to estimate the stress on pillars in a room-and-pillar trona mine. The ground
response curve has also determined using this method.
Acomputationallyefficientroom-and-pillarpanel-scalemodelrequiresdiscretizationtoo
coarse for accurate representation of the pillar scale. Accurate representation of pillar-scale
behavior in a room-and-pillar mine requires discretization too fine to be extended to large-
scale models while remaining computationally efficient. The two-scale modeling approach
employed here allows for pillar-scale behavior to be represented in a panel-scale model in a
computationally efficient manner.
This two-scale, two-step approach starts with a pillar-scale model. Coal pillar behavior
depends greatly on the shape and size of the pillar itself, as well as the interaction between
the coal and the roof and floor material. To represent the coal pillar behavior accurately, a
coalpillarismodeledalongwithsufficientextentofroofandfloormaterial. Thesemodelsare
loaded until failure. During loading, the stress-strain response of the roof-pillar-floor system
was recorded. Calibration of the pillar-scale model took place at this stage by matching
model outputs to observations made underground.
The stress-strain curve recorded during pillar loading at the small-scale is later used to
represent the seam in a large-scale model. Many shapes and sizes of pillars are often used for
room-and-pillar mines, which are all expected to behave differently when loaded. Each pillar
in a room-and-pillar panel need not be modeled independently. Instead, unique patterns of
pillars should be identified and modeled. Each pillar pattern which is modeled has a spatial
extent to which it may be assumed to represent similar pillars in a reasonable manner. If
pillar shape and size are uniform in a room-and-pillar panel and the roof and floor conditions
are consistent, then only one small-scale model is required. If not, multiple pillar patterns
should be modeled with their corresponding roof and floor conditions.
The stress-strain curves obtained during these small-scale models may then be used as
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Figure 4.2: Contour map showing depth of cover over room-and-pillar panel 2D,
center frame. The drillhole location marked is Core Hole 679, which was drilled
from the surface prior to mine development.
inputs in larger scale models. Instead of representing pillar geometry explicitly, which would
require a discretization too fine to be computationally reasonable, the material within the
coal seam is modeled using a fictitious material which is made to represent the mined-out
coal seam. The fictitious material used to represent the coal seam acts as a surrogate for the
small-scale room-and-pillar geometry. It responds as the actual seam is expected to during
the excavation process while allowing coarse enough discretization to be computationally
efficient in large-scale models.
4.4 Site Description
This study included characteristics specific to a room-and-pillar coal mine located in the
central Appalachian coal fields of the Eastern United States. As shown in Figure 4.2, the
depth of cover over the studied panel ranged from approximately 700 to almost 1100 feet.
The panel which was the focus of this study is denoted “Panel 2D” by the mine operators.
Panel 2D was a seven-entry panel with rectangular pillars. The barrier pillars on either side
of Panel 2D are approximately 140-feet wide.
AcoreholewasdrilledfromthesurfacedirectlyabovePanel2Dpriortothedevelopment
of the mine. The location of this exploratory core hole, Core Hole 679, is shown in Figure
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Figure 4.5: An example of a coal pillar geometry in
FLAC3D. The pillar shown is one quarter of a pillar
which has a width to height ratio of 8.
(cid:18)
σ
(cid:19)a
3
σ = σ +σ m (4.1)
1 3 c b
σ
c
The stress-strain response of the pillars was recorded during loading. Stress-strain
curves for the two models which most closely match the peak strength as suggested by the
empirical Bieniawski equation are shown in Figure 4.6. The square pillar with width-to-
height ratio of 6 shows strain-softening behavior, while the pillar with width-to-height ratio
of 8 shows perfectly plastic, approaching strain-hardening post-peak behavior, as expected
from laboratory tests [10]. The material parameters used for these two models were used for
subsequent pillar-scale numerical models.
During this stage of modeling, calibration was performed by attempting to match the
peak strength of the modeled pillar to the empirically derived, Bieniawksi coal pillar strength
equation [11]. This calibration method has been used previously [9]. The pillar strength,
S , of a square pillar as given by the Bieniawski formula is [12]:
P
(cid:20) (cid:21)
W
p
S = S 0.64+0.36 (4.2)
P i
H
p
where W is the pillar width and H is the pillar height.
p p
The peak strength results from the numerical models is listed with strengths predicted
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Figure 4.6: Stress-strain response of the two square
pillars–of width to height ratios equal to six and eight–
with elastic roof and floor.
Table 4.2: Peak strength of two numerically modeled
square coal pillars and the predicted strength from the
Bieniawski equation.
Width to Pillar strength estimation method
height ratio Bieniawski Equation Numerical Model
6 17.3 MPa 18.9 MPa
8 21.8 MPa 22.9 MPa
by the Bieniawski equation in Table 4.2. A difference of approximately ten percent exists
between the results of the numerical models and the peak strength values predicted by the
Bieniawski equation. The material property values obtained here are not the sole combina-
tion of values which would produce results within a reasonable range of the values predicted
by the Bieniawski equation, but they both match empirical results and are known to be well
within reasonable ranges.
Thematerialpropertyvaluesobtainedforthecoalpillarfromthenumericalmodelingof
thesquarepillarswereassignedtonumericalmodelsofpillarsmatchingthedimensionsofthe
rectangularpillarscutinPanel2D.ThevalueobtainedwascomparedtotheMark-Bieniawski
strength equation, Eq. (4.3) [13]. The peak strength values obtained for the rectangular
pillar models were within approximately ten percent of the strength value predicted by the
Mark-Bieniawski equation.
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Table 4.3: First estimates of material
properties of the roof rock used in numeri-
cal models. The values listed are obtained
from laboratory testing or literature avail-
able on numerical modeling input param-
eters [9].
Parameter Unit Value
Young’s modulus GPa 23.2
Compressive strength MPa 80
Angle of internal friction ◦ 30
Cohesion MPa 14.8
Tensile strength MPa 4.6
Bedding friction angle ◦ 10
Bedding cohesion MPa 2.96
Bedding tensile strength MPa 0.46
is shown in Figure 4.7. The stress and strain values plotted are determined from average
stress and strain across the area of the pillar. Only one quarter of the pillar was modeled to
obtain this stress-strain curve.
Calibration of the model is necessary at this stage. An initial stage of calibration was
performed when the peak strength of two sizes of modeled square coal pillars were matched
to empirically determined pillar strengths. These coal strength properties also matched
empirical strength equations for rectangular pillars. Calibrating models by matching them
to underground observations is another common practice. Visual observations at the studied
site were limited to the degree of rib sloughage, which was reported to be six inches to one
foot. Rib sloughage was identified in the models by analyzing the “state” of the zones in the
coal pillar.
4.5.2 Large-Scale Modeling
The stress-strain curves obtained from loading the pillar-scale models in FLAC3D was used
as an input in the large-scale models. A fictitious material was used to represent the seam
during excavation. The fictitious material modeled within the seam was made to follow the
stress-strain response of the panel itself to being excavated. Using this fictitious material, a
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Figure 4.7: Stress-strain response of a rectangular pillar with roof and
floor properties listed in Table 4.3.
much coarser, and, therefore, much more efficient large-scale model could be created.
Large models with a lateral extent sufficient to encompass the entire room-and-pillar
panel were constructed. These models extended vertically from below the mined seam to the
surface. Discretizationofthemodelswasfarcoarserthanrequiredforaccuraterepresentation
of the pillar geometry explicitly. The panel-scale model geometry is shown in Figure 4.8.
The material modeled within the seam was made to follow an altered version of the
stress-strain response recorded from the pillar-scale models. The stress-strain relationship
of the fictitious material, σ ((cid:15)), is related to the stress-strain relationship of the actual coal
f
pillars, σ ((cid:15)), by:
p
σ ((cid:15)) = (1−ER)σ ((cid:15)) (4.4)
f p
where ER is the extraction ratio within the panel. The factor (1−ER) is equal to the
ratio of the pillar area divided by the tributary area, so multiplying the stress applied to the
pillars by a factor of (1−ER) has the effect of distributing the stress on a single pillar to
the tributary area of the pillar [14]. This results in the appropriate amount of stress being
applied to the coarse, fictitious material within the panel.
The adjustment made to the stress-strain relationship shown in Eq. (4.4) forces the
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pillar array within the seam would, the response of the overburden to the excavation is
realistic. The material within the seam is loaded as the overburden relaxes over the panel
and a pressure arch forms above the panel.
4.6 Results and Discussion
An in situ stress state was applied to the model geometry shown in Figure 4.8. A vertical
stress, σ , representing the lithostatic pressure was applied to the model. The horizontal
v
stresses which were applied followed recommendations from the literature, which suggested
that the horizontal stresses in the region of the studied mine site are approximately 1.2σ
v
[15]. The initial model geometry with this stess state was allowed to reach equilibrium.
The in-seam vertical stress was reduced by the factor shown in Eq. 4.6, which creates
unbalanced forces. Load from the overburden weight is applied to the material within the
seam. Pressure arches form above the mined-out panel. After the model is allowed to regain
equilibrium, the stability of the mined seam and the surrounding rock mass can be assessed.
The vertical stress on the zones in the panel can easily be determined from FLAC3D.
This vertical load can be converted to the actual stress on the pillars by dividing the vertical
stress by (1−ER). The load on the pillars in the panel is shown in Figure 4.9.
The panel shown in Figure 4.9 has the same orientation as that shown in Figure 4.2.
Much of the variation in vertical stress on the pillars can be explained by the depth of cover
(Figure 4.2), as should be expected. In addition to the mined-out panel, the barrier pillars
on either side of the panel are included in this diagram. It can be seen that the barrier pillars
took on increased load when the seam was excavated.
In addition to the stress on the pillars, stability of the mine can easily be quantified.
The metric chosen for quantifying panel stability is similar to the ARMPS stability factor
[13]. The ratio of the pillar strength to pillar stress is shown in Figure 4.10. The strength
is assumed to follow the empirical Mark-Bieniawski strength equation, Eq. (4.3). The stress
on the pillars is that calculated from the two-scale modeling approach, as shown in Figure
4.9.
The resulting safety factors are similar to those found by the ARMPS method. With
thispillargeometry, ARMPSestimatesthestabilityfactorofthepaneltobebetween2.3and
3.1, depending on the depth of cover. The range of stability factors determined by ARMPS
is very similar to the range of safety factors determined from numerical modeling with the
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Figure 4.11: Safety factor of the pillars in Panel 2D assuming weaker laminations in
the roof and floor material. Strength is found from the empirical Mark-Bieniawski
strength equations, and stress is determined from the two-scale modeling approach.
roof and floor properties listed in Table 4.3. Because ARMPS has been used for nearly two
decades with great success, a close match between ARMPS and the two-scale approach is a
strength.
Results of the two scale approach, however, suggest that the geologic make-up of the
overburden can significantly impact pillar safety factor. The same two-scale, two-stage anal-
ysis was performed with a more competent overburden. The shale strata in previous simu-
lation were replaced with more competent sandstone to obtain the results shown in Figure
4.11.
TheresultsdisplayedinFigures4.10and4.11suggestthatvariationswithinthematerial
properties of the strata overlying a coal mine can considerably affect stability, as should be
expected. Increasing the percentage of competent strata above a coal seam affected the
safety factors by 10%. Inclusion of site-specific material properties adds to the reliability of
these results.
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4.7 Conclusions
A two-scale modeling approach has been outlined which can be applied to room-and-pillar
coal mine stability. The two-scale approach is a computationally efficient means of con-
sidering pillar-scale behavior in panel-scale models. Small-scale models were created which
representuniquepatternsofpillargeometrywithinthestudiedcoalminepanel. Thesepillars
are loaded significantly into the plastic region while their stress-strain response is recorded.
These stress-strain curves are then used in much larger scale models with a much coarser
model discretization–too coarse for explicit representation of the pillars. The material within
the seam of these large-scale models is made to respond as the pillars within the seam do in
the small-scale models.
This two-step, two-scale modeling process easily provides a means of estimating stress
on the pillars during development. The results obtained from this two-step process have
been shown to match well with the results given by ARMPS. Matching ARMPS, an in-
dustry standard in design, suggests that the results are reasonable. Varying the material
properties of the strata overlying the room-and-pillar panel in this two-scale, two-step pro-
cess can significantly impact the resulting safety factors. And the inclusion of site-specific
characteristics adds to the reliability of the results.
4.8 Acknowledgment
This work was supported by NIOSH (contract 200-2011-40313) through the Capacity Build-
ing and Ground Control Research for the Mining Industry initiative.
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Chapter 5
Probabilistic Approach to Coal Pillar
Design
5.1 Abstract
The classical approach to engineering design involves the purely deterministic calculation of
the factor of safety–the ratio of strength to stress. The factor of safety is an easy calculation
to perform in many circumstances, and it is very easy to interpret the results. The simplicity
of the method is both a strength and a weakness. The results of the deterministic factor of
safety calculation are simple to determine and interpret, but it has no ability to account for
the uncertainty and variability present in the inputs.
Uncertainty is prevalent in geotechnical engineering applications. This uncertainty can
stemfromspatialvariability, poorsampling, adynamicallychangingenvironment, etc. Prob-
ability analyses allow input parameters to take the form of a distribution rather than a single
value, making them uniquely equipped to handle the uncertainty inherent in geotechnical
engineering design considerations. A stochastic approach also has the benefit of resulting in
a probability of failure, which is more meaningful than a factor of safety.
Though stochastic modeling is becoming more common in many geotechnical applica-
tions, it is still not widely used for coal pillar design. The objectives of this study are to
justify the concept of using a stochastic approach to coal pillar design and to compare the
results of a simple stochastic analysis to those of standard industry practice.
Asimplesyntheticstudywasperformedtocomparetheresultsofaprobabilisticanalysis
of coal pillar design to the results obtained from running ARMPS, published by NIOSH.
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Normal distributions were assigned to each input parameter required to determine the factor
of safety of a single coal pillar. The probability of failure resulting from the synthetic study
was found to be more conservative than the ARMPS stability factor.
A probabilistic approach to coal pillar design is discussed in comparison to the tra-
ditional deterministic approach. The effective handling of uncertainty and the increased
meaning of the inputs and outputs inherent to a probabilistic approach are determined to
be the greatest strengths of the method.
5.2 Introduction
The method of engineering design is the process of choosing the appropriate components to
make a functional structure that is sufficiently safe. Engineering design typically involves
an iterative, purely deterministic approach where a multitude of inputs are adjusted until
the optimal design is reached. This deterministic approach to assess safety and durability
generally results in a factor of safety (FS) value, as calculated by:
STRENGTH
Factor of Safety = (5.1)
STRESS
The factor of safety is a very easy calculation to perform in many circumstances, and
it is very easy to interpret the results. If the strength of a component or a structure is
greater than the stress expected to be applied to the component or structure, then the factor
of safety will be greater than one and the component or structure is expected not to fail.
However, if the stress exerted on the component or structure exceeds the strength, then the
factor of safety will be less than one and the component or structure is expected to fail.
The greatest strength of deterministic factor of safety calculation is also its greatest
weakness: it is extremely simple. Its ubiquity in engineering design calculations can also be
attributed to a general unwillingness to change. Because of its simplicity, the deterministic
approach to factor of safety calculations is completely lacking in uncertainty quantification.
For the deterministic approach to be used, it must be assumed that the exact inputs
are known. If the exact inputs are known, then the exact solution can be determined. The
deterministicapproachisaverysimpleapproachtoengineeringdesign. Thegreateststrength
of deterministic factor of safety calculation is also its greatest weakness: it is extremely
simple. Because of its simplicity, the deterministic approach to factor of safety calculations
is completely lacking in uncertainty quantification.
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Uncertainty quantification is an important practice in all engineering practices. This
is especially true when regarding geotechnical engineering. A high level of uncertainty is
involved with engineering geotechnical structures. A common method of skirting the issue
of uncertainty quantification is to take a conservative approach to design. The conservative
approach involves underestimation of the strengths and/or overestimation of the stresses in
an attempt to guarantee a safe design. Using a conservative approach for engineering design
does not guarantee safety, can lead to over design of components and structures, and removes
meaning from the term factor of safety by introducing intentionally arbitrary inputs.
This conservative approach has led to design standards that require factors of safety
for elevator. Elevators must be over designed to some degree because of the likelihood of
misuse and the dire consequences of failure, but many engineering structures do not require
the over design which is typically present. Intentionally designing to a factor of safety much
greater than one indirectly admits the fault in the deterministic approach while bypassing
more meaningful and less arbitrary alternatives.
5.3 Probabilistic Approach
Aprobabilisticapproachtoengineeringdesigncanbeasuperioralternativetoadeterministic
approach. Insteadofconsideringonevalueforeachinputinanengineeringdesigncalculation,
a probabilistic approach allows for a distribution of values for each input parameter. A
distribution is used rather than a single value to represent the uncertainty or variability in
the data. With a distribution of inputs, the output will also take the form of a distribution.
This distribution of outputs leads to the greatest strength of the probabilistic analysis, which
is a meaningful result.
Using a probabilistic approach for calculating factors of safety can easily be visualized
in a few different ways. Figure 5.1 shows possible distributions of stress and strength for
an example probabilistic analysis. The probability of failure in the example component or
structure is the area confined in the overlap where the stress exceeds the strength. Figure
5.2 shows a second possible visualization of results from a probabilistic analysis. With the
factor of safety output plotted as a single distribution, the probability of failure is simply
the area under the curve to the left of a factor of safety equal to one. This is a simplified
version of possible results from stochastic analyses, but a more complex analysis will likely
take the same general form.
The probabilistic approach has some inherent advantages over the more widely used
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Figure 5.1: Example probability distributions of stress
and strength
deterministic approach. Two of these advantages are:
• Input parameters represented by single values suggest knowledge of the exact value.
Input parameters represented by distributions show uncertainty or variability in the
data which makes them a more realistic representation.
• Probability of failure is more meaningful than safety factor in many instances. Design-
ing to an acceptable probability of failure is a better engineering practice than setting
an arbitrary factor of safety threshold.
These are two of the more important advantages of the probabilistic method over the
deterministic method, but there are additional, less obvious advantages. There is a smaller
chance of user error when a probabilistic analysis is used. This is inherent to the method,
because the user is not forced to determine a single value for the input parameters. Fun-
damentally accounting for any uncertainty in the calculation allows the user to be more
certain of inputs. Furthermore, the process can be quicker and easier to implement. After
performing a deterministic design calculation, a sensitivity analysis it typically required to
deal with uncertainty. A probabilistic analysis removes the need for a sensitivity analysis
because the uncertainty is handled inherently.
Probabilistic analyses for engineering design have been used in many industries to de-
termine probability of failure [1]. The natural variability of the ground makes geotechnical
design a unique setting where a probabilistic approach should be used more widely. A tran-
sition toward using the probabilistic approach for engineering design of geologic structures
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Figure 5.2: Example output distribution of factor of
safety
is taking place for rock wedge failure [2], slope stability [3], and room-and-pillar failure in
oil shale mining [4], among others.
5.4 Coal Pillar Design
Like many other structural design problems, coal pillar design can be expressed as a factor
of safety. Estimating stress on a coal pillar can be relatively straightforward, but the method
for determining coal pillar strength is not as well established. There are many equations for
coal pillar strength, and any of them can be appropriate in a given set of conditions.
The stress supported by a pillar in a room-and-pillar mine can be assumed to be a func-
tion of the tributary area and the pillar area, shown in Figure 5.3, as well as the overburden
stress. It is assumed that each pillar supports the volume of overburden in the column above
the tributary area of that pillar. For square pillars with a consistent, rectangular pattern,
the equation for pillar stress, σ , becomes:
p
(cid:18)
W +W
(cid:19)2
P E
σ = σ (5.2)
p z
W
E
σ = γz (5.3)
z
Where σ , the the vertical stress, is the product of γ, the unit weight of the overburden,
z
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5.5 Probabilistic Coal Pillar Study
Two mine geometries were assumed to test the probabilistic procedure involved with un-
derground coal pillar design. Both geometries were 6-entry panels with 20-ft entries. One
scenario had 40’ x 40’ pillars, the other had 60’ x 60’ pillars. The results for these designs
were calculated for multiple depths.
A mean value was assigned to each required input parameter and a reasonable standard
deviation for each value was estimated. Each input parameter was assumed to be normally
distributed. Except for the pillar dimensions and the depth of cover, the distribution of all
parameters remained the same for both scenarios.
The compressive strength of coal is notoriously difficult to test in a laboratory. Coal
samples degrade quickly once removed from confinement, and coal exhibits a rather extreme
size effect. The in situ strength of coal is generally accepted to be 900 psi, but this value
has been known to vary. In situ coal strength has been determined to fall between 780 and
1070 psi [7]. Therefore, the mean value for in situ coal strength was assumed to be 900 psi
with a standard deviation of 72.5 psi. This range results in the typical range of in situ coal
strength reported by Mark and Barton to be approximately ±2 standard deviations.
Theroom-and-pillarlayoutwasassumedtoconsistof40-ftsquarepillarson60-ftcenters
for the first scenario and 60-ft square pillars on 80-ft centers for the second scenario. Both of
these geometries result in an entry and crosscut width of 20-ft. The pillar width was given
these mean values with a standard deviation of 0.5-ft. The entry width was assumed to be
the center-to-center spacing minus the pillar width to keep the mine geometry consistent.
The mining height was given an arbitrary mean of 6-ft and standard deviation of 0.25-ft.
All of the input parameters required for this simple study are listed in Table 5.1. The
only parameter changed between the first and second runs is the pillar size. Depth was
varied to compare the probabilities of failure from the probabilistic study to the stability
factors from ARMPS. The stability factors were calculated for the mine geometries under
development loading only.
Monte Carlo simulations were performed for each of the two runs to determine dis-
tributions for the likely factors of safety resulting from these synthetic data sets with the
stress and strength equations discussed above. Random numbers were generated by [8] for
each of the input parameters, with the exception of entry width which is a function of pillar
width, and the factor of safety was determined. Each Monte Carlo simulation consisted of
one million iterations for each of the two runs.
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Table5.1: Listofstatisticalparametersforeach
input value. All distributions were assumed to
be normal.
Parameter Mean St. Dev.
Depth Varied 20 ft
Overburden Unit Weight 165 pcf 6 pcf
Entry Width 20 ft 0.5 ft
Pillar Height 6 ft 0.25 ft
Strength 900 psi 72.5 psi
Pillar Width
Run 1 40 ft 0.5 ft
Run 2 60 ft 0.5 ft
5.6 Results
The results from the Monte Carlo simulations were compared to the stability factors calcu-
lated by ARMPS, and the deterministic safety factor for a variety of depths. The determin-
istic factor of safety results were found by inputting only the distribution means into the
stress and strength equations. For the first scenario, the depth of cover was varied from 400
to 1400-ft. The depth of cover was varied from 400 to 2400-ft for the second scenario.
There is relatively good agreement between all three pillar design methods, as shown in
Figure 5.4. That is, at the depth at which the ARMPS stability factor crosses the suggested
design threshold of 1.5, the deterministic safety factor crosses the suggested design threshold
of 1, and the probabilistic approach passes 50% chance of failure. The minimum stability
factor recommended for a “satisfactory” pillar system is 1.5 for depths of cover greater than
1000-ft [7]. The depth of cover corresponding to a stability factor of 1.5 is approximately
1100-ft. At this same depth, the safety factor resulting from the deterministic method is
approximately one.
The probability of failure at 1100-ft is approximately 0.6, which means 60% of pillars
subjected to this loading scheme are expected to fail. This probability of failure is more
conservative than the other results. The distribution of safety factors is normally distributed
and centered close to one as shown in Figure 5.5. The largest safety factor calculated was
approximately 1.6 and the smallest value was approximately 0.6. This range is due to the
standard deviations assigned to the input parameters.
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Figure 5.4: ARMPS stability factor, deterministic factor of safety, and
the probability of failure for the first scenario (40 ft x 40 ft pillars)
plotted versus depth of cover.
The second Monte Carlo analysis was performed assuming 60’ x 60’ pillars. The depths
for this geometry were varied from 400-2400-ft. The resulting ARMPS stability factors,
deterministic safety factors, and probabilities of failure are plotted versus depth in Figure
5.6.
The synthetic study resulted in more conservative values than ARMPS for the second
scenario. The ARMPS stability factor approaches 1.5 for a depth of 2400-ft. At 2400-ft
deep, the deterministic safety factor is approximately 0.8 and the probability of failure is
0.992.
5.7 Discussion
The resultsfrom the synthetic study andthe results fromthe ARMPSvaried somewhat. The
difference between the results of the two methods increases with increasing depth of cover.
This is most likely because the tributary area method of pillar stress determination was used
for the synthetic study. The tributary area method leads to the most conservative (highest)
estimate of the stress on a pillar. The tributary area has been shown to overestimate the
stress on a pillar by as much as 40% [9].
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Figure 5.5: Factor of safety histogram for the second mine geometry
(40 ft x 40 ft pillars) at a depth of 1100 ft.
Before the probabilistic approach to coal pillar design could become widely applied,
standards would need to be created. Geotechnical engineering involves too much variation
to ever adhere to the six sigma standard. An acceptable probability of failure threshold
would have to be decided upon.
For example, if a probability of failure of 30% were deemed an appropriate design
threshold, then this would correspond to a stability factor of approximately 1.6 for the first
scenario and 1.8 for the second scenario. The probability of failure approach is a more
meaningful standard by which industry-wide design thresholds could be set.
The scope of the probabilistic approach could be increased by performing a similar
calculationforanentirepanelratherthanjustonepillar. ThiscouldbedonewithaGaussian
field representing the distribution of coal strengths, etc. spatially. While the Monte Carlo
for the simple, single-pillar example has a rather quick computation time, a panel-sized
probabilistic method could take a significant amount of time to perform.
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Figure 5.6: ARMPS stability factor, deterministic factor of safety, and
the probability of failure for the first scenario (60 ft x 60 ft pillars)
plotted versus depth of cover.
5.8 Conclusions
Uncertainty quantification is necessary in all engineering practices. This is especially true
when regarding geotechnical engineering. Probabilistic analyses for engineering design are
becoming more prevalent in many fields where a high degree of uncertainty is present, but
remain mostly absent in coal pillar design.
Performing a probabilistic study rather than a deterministic one is a relatively easy
way to quantify the uncertainty in an engineering design. A sensitivity analysis requires
actively varying the inputs a slight degree to determine how the output is affected. This
process can be much more time consuming, more user intensive, and less comprehensive than
a probabilistic analysis like the one performed here.
A probabilistic approach to coal pillar design has potential to be a viable alternative to
traditionaldeterministicmethods. Accountingforvariabilityoruncertaintyintheinputsand
outputs of engineering design calculations provides more meaningful results. Designing to
arbitrary deterministic thresholds indirectly admits the fault in the deterministic approach.
The simple synthetic study performed involved comparing the results of a simple factor
of safety determination to the stability factor calculated by ARMPS. Both the probability
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Works Cited
[1] J Townsend, C Meyers, R Ortega, J Peck, M Reinfurth, and B Weinstock. Review
of the probabilistic failure analysis methodology and other probabilistic approaches for
application in aerospace structural design, volume 3434. National Aeronautics and Space
Administration, Office of Management, Scientific and Technical Information Program,
1993.
[2] H. Park and TR West. Development of a probabilistic approach for rock wedge failure.
Engineering Geology, 59(3):233–251, 2001.
[3] G.Zhou, T.Esaki, Y.Mitani, M.Xie, andJ.Mori. Spatialprobabilisticmodelingofslope
failure using an integrated gis monte carlo simulation approach. Engineering Geology,
68(3):373–386, 2003.
[4] Enno Reinsalu. Stochastic approach to room-and-pillar failure in oil shale mining. In
Proceedings of the Estonian Academy of Sciences, Engineering, volume 6, pages 207–216.
Estonian Academy Publishers, 2000.
[5] ZT Bieniawski. A method revisited: coal pillar strength formula based on field investiga-
tions. In Proceedings of the Workshop on Coal Pillar Mechanics and Design. Pittsburgh,
PA: US Department of the Interior, Bureau of Mines, IC, volume 9315, pages 158–165,
1992.
[6] C. Mark and F.E. Chase. Analysis of retreat mining pillar stability (armps). In
Proceedings-New Technology for Ground Control in Retreat Mining. Pittsburgh, PA: US
Department of Health and Human Services, Public Health Service, Centers for Disease
Control and Prevention, National Institute for Occupational Safety and Health, DHHS
(NIOSH) Publication, pages 17–34, 1997.
[7] Christopher Mark and Timothy M Barton. Pillar design and coal strength. In
Proceedings-New Technology for Ground Control in Retreat Mining. Pittsburgh, PA: US
Department of Health and Human Services, Public Health Service, Centers for Disease
Control and Prevention, National Institute for Occupational Safety and Health, DHHS
(NIOSH) Publication, pages 49–59, 1997.
[8] MATLAB. version 8.0.0.783 (R2012b). The MathWorks Inc., Natick, Massachusetts,
2012.
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Chapter 6
Discussion and Conclusions
6.1 Overview of Study
A two-step, two-scale numerical modeling approach is outlined which can be used as a tool
foranalyzingthestabilityofundergroundcoalmineopenings. Thistwo-scaleapproachstarts
with pillar modeling. Pillars are modeled with sufficient roof and floor material and loaded
to estimate their stress-strain response. These pillar stress-strain curves are then used as
inputs into large, panel-scale models. This two-step approach to numerical modeling allows
for the study of the interaction between small-scale behavior and large-scale behavior in a
computationally efficient manner.
The ground response curve (GRC) is a useful tool for analyzing the stability of under-
ground excavations. The GRC originated in the tunneling industry as an analytical result
from the convergence-confinement method. While the geometries used in underground coal
mining are too complex for analytical solutions like this to be developed, this two-scale
modeling procedure can be used to determine the GRC.
The stress state of pillars in underground coal mine workings is rarely known to great
accuracy. The two-scale approach was implemented with the use of a fictitious material
within the coal seam which was made to respond as the pillars would. The representative
material is used instead of explicitly modeling the pillars so that a far coarser discretization
could be used to speed up processing time.
With better estimates of pillar stress and strength, a probabilistic approach could be
implemented for room-and-pillar coal mine design. This approach has seen widespread use
in other industries because of its utility and ability to handle uncertainty. The process for
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implementing a probabilistic approach to coal mine pillar design is outlined here.
Laboratory testing of samples collected from drilling in the roof was also performed.
This testing was performed to find first estimates of material properties of the roof material
above a room-and-pillar coal mine panel in the Eastern US. Destructive testing included
uniaxial compressive strength testing, Brazil testing, and point-load testing.
6.2 Summary of Results
Laboratory testing was performed on cores collected from two holes drilled into the roof from
the mine workings. The laboratory testing shows that the immediate roof material of this
room-and-pillar coal mine is a strong sandy shale. While the uniaxial compressive strength
seems reasonably similar between the two holes drilled, there are obvious differences in the
strength of laminations present. Preparation of samples from one of the holes was difficult to
perform without damaging the samples. Furthermore, the Brazil testing was mostly fruitless
for samples from that hole because of the weak laminations.
The ground response curve of a room-and-pillar coal mine panel was found by grad-
ual reduction of the internal pressure within the seam. The pressure against the roof and
the convergence of the seam were recorded throughout the process of reducing the internal
pressure. This process of determining the GRC is akin to the original formulation of the
convergence-confinement method. The GRCs obtained are indicative of the panel stability
and the self-supporting capacity of the overburden strata. The modeling results of the GRC
were plotted with the stress-strain response of the pillars in order to assess panel stability.
By using a fictitious material which represents the average response of the pillars within
aroom-and-pillarminepanel, thefullpanelscalewasassessed. Theloadplacedonthepillars
during panel development was estimated. Furthermore, by assuming pillar strength to be
given by the empirical Mark-Bieniawski pillar strength formula, a pillar safety factor was
determined throughout the mined seam.
6.3 Discussion of Results
There were three primary goals set prior to the laboratory analysis:
• Determining acoustic properties of the roof rock.
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• Estimating additional material properties of the roof rock for numerical modeling.
• Concluding whether there is significant variation in the roof rock between the holes.
The acoustic properties were found nondestructively by testing specimens prepared
for uniaxial compressive strength testing. Additional material properties were determined,
mostly from destructive testing and from the literature. While strength variations between
the two holes were found qualitatively, limited statistical analysis could support the claim
with the small sample sizes available.
The ground response curve was estimated for a room-and-pillar panel in FLAC3D with
a method analogous to the convergence-confinement method. The GRC predicts full conver-
gence of the seam at full extraction, as should be expected. The interaction of the ground
response curve and modeled pillar stress-strain curves can be used as a tool to size pillars.
The stress on the pillars in a room-and-pillar panel was estimated using a two-scale
modeling approach. From the stress calculated, a pillar safety factor was also found. These
safety factors agreed well with ARMPS stability factors for the panel. The agreement be-
tween this novel method of pillar stress determination and an industry standard is encour-
aging. Furthermore, the numerical models contain material properties for the studied site,
which increases their reliability.
6.4 Conclusions
Safe design of underground excavations requires an understanding of the response of the rock
mass to the future excavation. In the tunneling industry, the geometry is often sufficiently
simple for this understanding to be reached with analytical solutions. Mining geometries,
however, are far too complex for analytical solutions to be feasible.
The pillar-scale response has a great impact on the panel-scale response, and vice versa.
The interaction between these two length scales is explored here using numerical modeling in
FLAC3D. Rather than analyzing the interaction between these two length scales in a single
simulation, a more computationally efficient approach is outlined.
A two-stage, two-scale numerical modeling approach for assessing room-and-pillar coal
mine stability was introduced. The modeling approach shown here uses a coarse discretiza-
tion in large, panel-scale models which includes fictitious, yet representative material within
the coal seam. This representative material is made to follow the stress-strain response
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of small, pillar-scale models via the implementation of a user-defined constitutive model
developed for this study.
Site-specific design considerations can significantly improve reliability of results, con-
fidence in designs, and tons of coal recovered. One-size-fits-all approaches to underground
coal mine design must be either unsafe for some designs, or wasteful for others. Pillar-sizing,
which is likely the most evident cost-benefit compromise in underground mining, should be
done with site-specific considerations.
6.5 Future Work
This two-scale modeling approach has great growth potential for room-and-pillar coal mines.
These large-scale models can be used to assess stress on pillars, convergence of openings,
subsidence, etc. Conversely, monitoring any of these rock mass responses could help improve
the model inputs.
With the addition of appropriate gob modeling, retreat and gob-side loading can be
studied. Also, more reasonable estimates for subsidence could be found. Finally, associating
thelarge-scalemodelwithrecordedmicroseismicitywouldbeachallengeworthpursuing. By
matching seismicity rate and possibly location with failed states of the model zones, panel
stability assessments would be greatly improved, as would the results of the seismic survey.
6.6 Acknowledgment
This work was supported by NIOSH (contract 200-2011-40313) through the Capacity Build-
ing and Ground Control Research for the Mining Industry initiative.
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room-and-pillar coal mine in the Eastern US. The drilling was performed in order to install
triaxial geophones as part of a passive seismic study of the retreat process. More details
regarding the microseismic survey and a more extensive overview of the geology at this site
can be found here [1].
Approximately eleven feet of sandy shale core was collected from two boreholes for the
testing. The amount of core available for laboratory testing was limited. Considering the
short supply of core available for testing, three modest goals were defined:
• Estimate p- and s-wave velocities to improve the results of the seismic survey.
• Develop reasonable first approximations of material properties for use in numerical
models.
• Determine whether the samples obtained from Holes #1 and #2 are similar enough to
be considered one sample or if they should be considered distinct.
Uniaxial compressive strength and indirect tensile strength testing was performed using
an MTS load cell. The point-load test–a method of indirectly determining the unconfined
compressive strength of a material–was also performed. Because the point-load test requires
little to no sample preparation, it provides a quick and easy means of estimating UCS. Its
ease of use and portability have led to its wide use for mining and civil engineering sites [2].
A.3 Sample Description
Two holes were drilled into the roof rock immediately above a retreating room-and-pillar
coal mine located in the Central Appalachian coal fields of the Eastern US from inside the
mine opening. The locations of the holes relative to the immediate mine panel are shown in
Figure A.1. Approximately 120 inches were drilled for Hole #1, but a total of only 79 inches
of core was collected. Hole #2 was drilled only about 58 inches into the roof, and all of the
core from Hole #2 was collected. The drilling was performed for the purpose of installing
two triaxial geophones as part of a seismic survey, not for the express purpose of laboratory
testing for material properties. The holes were drilled vertically into the roof with a 2.5 inch
diameter bit.
Pictures of the core samples taken from Holes #1 and #2 can be found in Figures
A.2 and A.3, respectively. Upon initial inspection, the two holes appeared to made up of a
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Figure A.1: Contour map showing depth of cover over room-and-pillar
panel 2E. The marked drillhole locations represent the locations of
the two holes drilled into the roof for installation of the seismic array
from which core samples were collected and tested for rock mechanics
properties.
similarrocktype. Coresamplesfrombothholesarelightgrayincolorwithsomelaminations.
Samples from both holes are sandy shale, with the sand content of Hole #1 appearing to
be greater than the sand content of Hole #2. The sand present in the core from Hole #1
is fairly uniformly distributed along the core, while the sand in the core from Hole #2 is
clearly layered between shale. The laminations and sand present in Hole #2 vary greatly
along the core, while Hole #1 seems to be much more consistent.
Of the total collected core length of 79 inches from Hole #1, the total length of core
measuring longer than four inches is 37 inches. More than the 79 inches of the ten feet
of core was reported to be recoverable, but was left underground because material testing
was initially an afterthought and drilling was done primarily for installation of the seismic
network. This ratio of recovered core longer than four inches to the total amount of collected
core results in a rock quality designation (RQD) of 47%. Similarly, 15 inches of core from
Hole #2 was comprised of sections of core greater than four inches in length, resulting in an
RQD of 26%. These results are summarized in Table A.1. The values of RQD obtained for
Holes #1 and #2 correspond to the upper and lower limits of the “poor rock” qualitative
description, respectively, as defined by [3].
After this initial inspection, laboratory tests were performed in an attempt to accom-
plish the goals listed above until no unbroken samples were left. Destructive tests performed
include uniaxial compression test, the indirect uniaxial tensile strength, so-called “Brazil-
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TableA.3: P-andS-wavevelocityes-
timates of the four samples prepared
for UCS testing. Velocities listed are
given in ft/sec (m/s).
Hole Sample S-Wave P-Wave
7620 12400
1 1
(2320) (3790)
7430 12000
1 2
(2260) (3650)
7610 12300
1 3
(2320) (3730)
7920 12000
2 4
(2410) (3650)
A.5 Non-Destructive Testing
One of the primary goals of this laboratory testing was the determination of the acoustic
properties of the roof rock to aid in later seismic analysis. To that end, the speeds of the p-
and s-waves through the cores was estimated. Acoustic testing was performed on the four
samples which were prepared for UCS testing.
To perform the acoustic tests, a Model - 5217A Sonic Viewer was used to generate and
detect a waveform using a piezoelectric transducer and a piezoelectric receiver, respectively.
A pneumatic clamp was also used to hold each sample in place to reduce the measurement
error.
To measure the s-wave velocity, the piezoelectric transducer was placed in contact with
the piezoelectric receiver. The input and output amplitudes and frequencies were adjusted
until a waveform was discernible. The arrival time in µs was recorded for each of the first two
peaks and troughs of the waveform. Each sample was then placed between the piezoelectric
transducer and receiver and the process was repeated. The difference in the arrival times
between corresponding peaks and troughs was then averaged to get an estimate of the s-wave
travel time through each sample. Table A.3 shows the s-wave velocities estimated for the
four samples tested.
The procedure for estimating the p-wave velocity is somewhat simpler. The sample was
placed between a compression-type piezoelectric transducer and receiver and the first arrival
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Figure A.4: Stress-strain curves of the four specimens subjected to UCS testing. (a)
Sample #1; (b) Sample #2; (c) Sample #3; and (d) Sample #4.
• Average modulus–slope of a line secant to the stress-strain curve around the linear
portion.
• Secant modulus–slope of a secant line from the origin to an intersecting point at some
fixed percentage of the ultimate strength.
The most commonly chosen fixed percentage of the ultimate strength is the 50% point
[7].
Out of the four specimens tested for UCS, one of them from Hole #1 failed along a
well defined failure plane. The normal axis of the plane of failure was oriented 60◦ from
the direction of loading. From this failure angle, and knowing that the angle of failure, θ,
is related to the angle of internal friction, φ, by 2θ = 90◦ +φ, the angle of internal friction
can be estimated to be 30◦. Furthermore, cohesion, c, can be calculated from Eq. (A-1). By
setting σ = 0 and σ = 130 MPa, the stress at failure for that sample, cohesion is found to
3 1
be 37.5 MPa.
σ = σ tan2θ+2ctanθ (A-1)
1 3
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Table A.5: Tangent elastic modulus, average
elastic modulus, and secant elastic modulus of
the four samples subjected to UCS testing as
determined from the stress-strain curves ac-
cording to the ISRM suggestions [7]. Moduli
are reported in 106 psi (GPa).
Elastic Modulus
Hole Sample
Tangent Average Secant
3.65 3.57 2.25
1 1
(25.1) (24.6) (15.5)
3.12 3.29 2.20
1 2
(21.5) (22.7) (15.2)
3.36 3.80 2.38
1 3
(23.1) (26.2) (16.4)
3.34 3.54 2.16
2 4
(23.0) (24.4) (14.9)
The cores collected granted only a very small number of specimens with a length great
enough to perform UCS testing. This small sample size for UCS testing does not aid in
the achievement of one of the primary goals–that of determining whether the roof rock
surrounding the two holes could be considered one sample or if they are distinct. In order
to produce a meaningful conclusion toward that goal regarding compressive strength, the
point-load test was performed on a larger sample size.
A.6.2 Brazilian Testing
The Brazilian test was performed on ten specimens from each of the two holes drilled in
accordance with the ISRM suggestions [4]. A double layer of masking tape was applied to
the circumference of each of the samples and they were placed in the apparatus as shown
in Figure A.5. This loading orientation resulted in the load being applied parallel to the
laminations in the cores.
The MTS 810 load cell which was used for the UCS testing was also used for the
Brazilian tests. A constant stroke rate of 1.2 x 10−4 inches per second was applied to each
of the samples. In addition to the peak applied load being recorded, the applied load and
the total displacement of the loading piston were recorded each second during loading. The
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Figure A.6: Raw load vs. displacement curves for Sample #1 from Hole #1 (left) and for
Sample #1 from Hole #2 (right).
The ISRM suggested methods often recommend discarding the highest and lowest strength
value out of a sample before calculating an average. After discarding the maximum and
minimum values, the six remaining median results from Hole #1 have an average of tensile
strength value of 1300 psi (9.0 MPa) with a standard deviation of ±82 psi (±0.56 MPa).
The average of the only two meaningful values obtained from testing Hole #2 is considerably
less at 690 psi (4.7 MPa).
A.6.3 Point-Load Testing
A Roctest Model PIL-7 point load tester was used to perform the point-load test. A load
was applied to each specimen by hand using a hydraulic jack until the sample fractured. The
load was applied axially on all samples tested. Protocols for point-load tests with diametrical
loading of cores are also given by the ISRM [9], but such loading of coal measure rocks is
typically not performed due to a lack of meaningful and consistent results [10].
The load applied by the Roctest point-load tester was increased steadily until failure of
the specimen occurred. Oil pressure was measured electronically at all times during the test
by an electronic gage, and the maximum pressure reached during loading was maintained
and recorded. The applied load at failure can be calculated from the oil pressure and the
effective area of the jack piston, which is published by the manufacturer.
The point-load test was performed on all rock specimens which were not tested for UCS
or tensile strength via the Brazilian test, and which had a length-to-diameter ratio between
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Figure A.7: Distribution of UCS estimates for Holes #1
and #2 as determined from point-load testing with a
K-value of 21.
estimates from Holes #1 and #2 cover approximately the same range–from about 8000 psi
to 22000 psi. The averages, however, are quite different. The average UCS estimate of all
specimens tested from Hole #1 is approximately 16000 psi, while the average UCS estimate
of all specimens tested from Hole #2 is about 12800 psi.
Though the point-load test is used primarily as an indirect method of determining
uniaxial compressive strength, it is also an indirect tensile strength method. As suggested
by the ISRM, the point-load strength index, I , is approximately 0.80 times the uniaxial
s(50)
tensile strength [9]. Using this multiplier, tensile strength was estimated for each of the valid
point-load test samples. A histogram of the resulting estimates is shown in Figure A.8.
A.7 Discussion
There were three primary goals at the outset of this study:
• Determining acoustic properties of the roof rock.
• Estimating additional material properties of the roof rock for numerical modeling.
• Concluding whether there is significant variation in the roof rock from Hole #1 to Hole
#2.
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Figure A.8: Distribution of uniaxial tensile strength
(UTS) estimates for Holes #1 and #2 as determined
from point-load testing.
Acoustic properties were only measured for four samples. Of those four, the average s-
and p-wave velocities were found to be 7640 ft/sec (2510 m/s) and 12200 ft/sec (3990 m/s),
respectively. From these magnitudes, the ratio of s-wave velocity to p-wave velocity, Vs/ Vp, is
estimated at 0.62. Knowledge of the wave velocity magnitudes as well as the velocity ratio
allows for greater accuracy and higher confidence in the locating of seismic events, which
will aid in the passive seismic survey performed at this mine site.
In addition to the acoustic properties, estimates of other material properties of the roof
rock were sought for use as inputs in numerical models. Properties to be used as inputs into
numerical models include density, elastic moduli, UCS and tensile strength, cohesion, and
angle of internal friction. The 95% confidence interval for density of the twenty-four samples
cut and ground was found to be 166.3 ± 3.08 pcf.
ThreemethodswereusedtodetermineYoung’smodulusofthefourspecimenssubjected
to UCS testing, namely: the tangent elastic modulus, the average elastic modulus, and the
secant elastic modulus. Other methods for estimating a Young’s modulus for rock have been
suggested. A majority of them would be expected to result in very similar values to those
obtained here.
The various methods for estimating Young’s modulus has been studied extensively
for differing rock types [6]. The method which showed the greatest consistency for rocks
experiencingplastic-elasticstress-straincurveswasfoundtobethe“modifiedsecantmodulus
at 50 percent maximum stress.” This value is defined as the slope of the line from the 50%
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Table A.6: Material properties of the roof
rock as determined from this series of lab-
oratory tests.
Parameter Unit Value
Density kg/ m3 2670
P-wave velocity m/
s
3700
S-wave velocity m/
s
2330
Young’s modulus GPa 23.2
Compressive strength MPa 142
Tensile strength MPa 7.84
Cohesion MPa 37.5
Angle of internal friction ◦ 30
to group them both into a single material, or if they should be considered distinct. Any
statistical basis for claiming that Holes #1 and #2 should be considered distinct samples
and not of the same dataset could only come from the point-load test results. The UCS test
was not performed on enough samples to conclude any difference. The fact that the speci-
mens from Hole #2 crumbled during Brazilian testing, as well as during sample preparation,
indicated that the roof rock around Hole #2 contains weaker laminations, but that evidence
was nonexistent numerically.
The averages of the point load strength indices for the specimens from Holes #1 and #2
are quite different, but hypothesis testing proves inconclusive. The null hypothesis stating
that they contain the same mean cannot be rejected from the data collected. While it is not
backed statistically, it is clear that the two materials behave quite differently. A difference
in material properties was surmised upon initial inspection, and evidence for it was seen
during sample preparation and from the lack of sample integrity during Brazilian testing of
specimens from Hole #2. It is likely that any weakness in the specimens from Hole #2 exists
only due to the laminations which are not as prevalent in Hole #1.
The material properties listed in Table A.6, among others, will be used for numerical
modeling of the roof rock. The entire roof will be modeled as a jointed rock mass where
the intact rock has the properties listed in Table A.6. The material properties of the joints,
however, will reflect the difference in strength between the roof rock around Holes #1 and
#2.
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Poor sample preparation can often contribute to error in the final strength estimates.
According to the ISRM, substandard preparation of samples can result in premature failure,
and a low estimate of strength [5]. While the samples prepared for this study did not meet
the tolerances suggested by the ISRM, the strength estimates found in this study are well
above published averages.
A.8 Conclusions
A series of lab tests was performed on core collected from the roof rock above a retreating
room-and-pillar coal mine in the Eastern US. The drilling was performed in order to install
triaxial geophones as part of a passive seismic study of the retreat process. Approximately
eleven feet of sandy shale core was collected for the testing.
Three goals motivated the laboratory testing: estimating the p- and s-wave velocities of
the roof rock in order to aid in event location for the passive seismic study; determining first
estimates of other material properties for use in numerical models; and assessing whether
the roof rock surrounding the two holes can be considered the same material, or if there is
a statistically significant difference between them.
A list of the material properties, including the acoustic properties, is given in Table
A.6. These properties will improve the accuracy of the passive seismic event locating in the
seismic survey and will aid in numerical model generation. While no significant difference
was found between the material properties of the roof rock around Holes #1 and #2, a
difference became evident during sample preparation and performing the Brazilian test. The
difference in integrity between specimens from Hole #1 and Hole #2 is assumed to be due
to the presence of laminations in the core taken from Hole #2, which will be reflected in
numerical models by a reduction in joint strength properties.
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Works Cited
[1] William J Conrad. Microseismic monitoring of a room and pillar retreat coal mine in
southwest virginia. Master’s thesis, Virginia Polytechnic Institute and State University
(Virginia Tech), 2016.
[2] E. Broch and J.A. Franklin. The point-load strength test. International Journal of Rock
Mechanics and Mining Sciences & Geomechanics Abstracts, 9(6):669 – 676, 1972.
[3] DU Deere. Geological considerations. Rock mechanics in engineering practice, pages
1–20, 1968.
[4] ZT Bieniawski and I Hawkes. Suggested methods for determining tensile strength of
rock materials. In International Journal of Rock Mechanics and Mining Sciences &
Geomechanics Abstracts, volume 15, pages 99–103. Elsevier, 1978.
[5] ZT Bieniawski and MJ Bernede. Suggested methods for determining the uniaxial com-
pressive strength and deformability of rock materials: Part 1. suggested method for
determination of the uniaxial compressive strength of rock materials. In International
Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, volume 16
(2), page 137. Elsevier, 1979.
[6] PaulMSanti, JasonEHolschen, andRichardWStephenson. Improvingelasticmodulus
measurements for rock based on geology. Environmental & Engineering Geoscience,
6(4):333–346, 2000.
[7] ZT Bieniawski and MJ Bernede. Suggested methods for determining the uniaxial com-
pressive strength and deformability of rock materials: Part 2. suggested method for
determining deformability of rock material in uniaxial compression. In International
Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, volume 16
(2), pages 138–140. Elsevier, 1979.
[8] Malcolm Mellor and Ivor Hawkes. Measurement of tensile strength by diametral com-
pression of discs and annuli. Engineering Geology, 5(3):173–225, 1971.
[9] JA Franklin. Suggested method for determining point load strength. In International
Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, volume 22
(2), pages 51–60. Elsevier, 1985.
[10] Norman Brook. Comprehensive rock engineering: principles, practice, & projects, vol-
ume 3. Pergamon Press Ltd, 1993.
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Table B.3: All flatness measurements made on the samples
subjected to uniaxial compression strength (UCS) tests after
sample preparation. The absolute magnitudes are meaning-
less. The values listed are measurements in milli-inches made
to determine the degree of variation in end flatness. That is,
the relative magnitudes indicate the degree to which an end
varies in 10−3 inches.
Sample # 1 2 3 4
Hole # 1 1 1 2
End # Diameter # Measurement # Values
1 1 1 34 0 23 20
1 1 2 40 5 21 30
1 1 3 43 7 10 40
1 2 1 45 3 20 20
1 2 2 40 5 20 30
1 2 3 31 5 20 40
1 3 1 50 7 10 32
1 3 2 40 5 20 30
1 3 3 30 0 23 30
2 1 1 25 2 23 28
2 1 2 40 6 21 30
2 1 3 50 6 15 21
2 2 1 38 7 15 20
2 2 2 40 5 20 31
2 2 3 40 0 25 40
2 3 1 47 10 12 26
2 3 2 40 5 22 30
2 3 3 30 0 28 34
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(cid:0) (cid:1)
f σI
λ = (C-9)
δf(cid:63)[(S(cid:0)δg(cid:1)
])
δσ
where f(cid:63) is the failure surface function without its constant term.
The implementation of these equations for the Tresca constitutive model will be illus-
trated in the following section.
C.4 Incremental Tresca Constitutive Model in FLAC3D
The Tresca constitutive model assumes yielding will occur when the shear stress reaches a
critical value, k, as shown:
max[τ ,τ ,τ ] = k (C-10)
1 2 3
or in terms of the normal principal stresses:
(cid:20) (cid:21)
|σ −σ | |σ −σ | |σ −σ |
1 2 2 3 3 1
max , , = k (C-11)
2 2 2
The Tresca constitutive model considers only shear stress and assumes no increase in
shear strength with an increase in confinement–as, for instance, the Mohr-Coulomb criterion
does (in fact, the Mohr-Coulomb can be considered a generalization of the Tresca criterion.
i.e. The Mohr-Coulomb criterion reduces to the Tresca criterion when the angle of internal
friction is assumed to be zero.). In the principal stress space of σ - σ - σ , the Tresca failure
1 2 3
surface plots as a regular hexagonal prism parallel to and centered around the hydrostatic
stress axis where σ = σ = σ , as depicted in Figure C.1. Any state of stress which plots
1 2 3
inside of this regular hexagonal prism is expected to be in the elastic state. States of stress
plotted on the prism represent yielding, and states of stress outside of the prism cannot exist
according to the Tresca criterion.
Since the Tresca yield surface is parallel to and prismatic around the hydrostatic axis, it
ishydrostatic-stressindependent. Itis, therefore, onlynecessarytoconsidertheprojectionof
a stress state onto the deviatoric plane. The normal of the deviatoric plane is the hydrostatic
stress axis. The Tresca criterion is plotted on a deviatoric plane in Figure C.2.
By assigning σ ≤ σ ≤ σ , Eq. (C-11) can be simplified to:
1 2 3
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A SERIES OF STUDIES TO SUPPORT AND IMPROVE DPM SAMPLING IN
UNDERGROUND MINES
Sallie Crawford Gaillard
ACADEMIC ABSTRACT
Diesel particulate matter (DPM) is the solid portion of diesel exhaust, which occurs
primarily in the submicron range. It is complex in nature, occuring in clusters and agglomerated
chains, and with variable composition depending on engine operating conditions, fuel type,
equipment maintenance, etc. DPM is an occupational health hazard that has been associated with
lung cancer risks and other respiratory issues. Underground miners have some of the highest
exposures to DPM, due to work in confined spaces with diesel powered equipment. Large-
opening mines present particular concerns because sufficient ventilation is very challenging. In
such environments, reliable DPM sampling and monitoring is critical to protecting miner health.
Though complex, DPM is made up primarily of elemental (EC) and organic carbon (OC),
which can be summed to obtain total carbon (TC). The Mine Safety and Health Administration
(MSHA) currently limits personal DPM exposures in metal/non-metal mines to 160 µg/m3 TC on
an 8-hour time weighted average. To demonstrate compliance, exposures are monitored by
collecting filter samples, which are sent to an outside lab and analyzed using the NIOSH 5040
Standard Method. To support real-time results, and thus more timely decision making, the Airtec
handheld DPM monitor was developed. It measures EC, which is generally well correlated with
TC, using a laser absorption technique as DPM accumulates on a filter sample. Though intended
as a personal monitor, the Airtec has application as an engineering tool. A field study is reported
here which demonstrated the usefulness of the Airtec in tracking temporal and spatial trends in
DPM. An approach to sensitizing the monitor to allow “spot checking” was also demonstrated.
Since DPM in mine environments generally occurs with other airborne particulates,
namely dust generated during the mining process, DPM sampling must be done with
consideration for analytical interferences. A common approach to dealing with mineral dust
interferences is to use size selectors in the sampling train to separate DPM from dust; these
devices are generally effective because DPM and dust largely occur in different size ranges. An
impactor-type device (DPMI) is currently the industry standard for DPM sampling, but it is
designed as a consumable device. Particularly for continuous monitoring applications, the sharp
cut cyclone (SCC) has been suggested as a favorable alternative. In another field study reported
here, the effect of aging (i.e., loading as an artifact of sampling) on the DPMI and SCC was
investigated. Results suggest the effective cut size of the DPMI will be reduced much more
rapidly than that of the SCC with aging – though even in a relatively high dust, high DPM
environment, the DPMI performs adequately.
In a third field study, the possibility of attachment between DPM and respirable dust
particles was investigated. Such a phenomenon may have implications for both reliable sampling
and health outcomes. Data collected by transmission electron microscope (TEM) on samples
collected in the study mine showed that DPM-dust attachment does indeed occur. Moreover, the
study results suggest that respirable particulate sampling – as opposed to submicron sampling,
which is currently used – may be favorable for ensuring that oversized DPM is not excluded
from samples. This strategy may require additional sample preparation to minimize dust
interferences, but methods have been previously developed and were demonstrated here.
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A SERIES OF STUDIES TO SUPPORT AND IMPROVE DPM SAMPLING IN
UNDERGROUND MINES
Sallie Crawford Gaillard
GENERAL AUDIENCE ABSTRACT
Diesel particulate matter (DPM) is the solid portion of diesel exhaust, which occurs
primarily in the submicron range (i.e., less than one micron). It generally forms as agglomerated
chains or clusters. The size and shape is dependent on the engine operating conditions, fuel type,
equipment maintenance, etc. DPM is an occupational health hazard that has been associated with
lung cancer risks and other respiratory issues. Underground miners have some of the highest
exposures to DPM, due to work in confined spaces with diesel powered equipment. In such
environments, reliable DPM sampling and monitoring is critical to protecting miner health.
Though complex, DPM is made up primarily of elemental (EC) and organic carbon (OC),
which can be summed to obtain total carbon (TC). Exposure to DPM, as regulated by the Mine
Safety and Health Administration (MSHA) is monitored by collecting filter samples, which are
analyzed using the NIOSH 5040 Standard Method. To support real-time results, and thus more
timely decision making, the Airtec handheld DPM monitor was developed. Though intended as a
personal monitor, the Airtec has application as an engineering tool. A field study is reported here
which demonstrated the usefulness of the Airtec in tracking changes of DPM in specific
locations as well as over time. An approach to sensitizing the monitor to allow “spot checking”
or making very quick assesments in a location was also demonstrated.
DPM in mine environments generally occurs with other airborne particulates, namely
dust generated during the mining process. Sampling must be completed to avoid these
interferences by sampling DPM only. Since DPM and dust typically occur in different size
ranges, size selectors in the sampling train are used to separate DPM from dust. An impactor-
type device (DPMI) is currently the industry standard for DPM sampling, but it is designed as a
one time use item. Particularly for continuous monitoring applications, the sharp cut cyclone
(SCC) has been suggested as a favorable alternative. In another field study reported here, the
effect of aging (i.e., multiple monitorings using the same size selector) on the DPMI and SCC
was investigated. Results suggest the effective cut size of the DPMI will be reduced much more
rapidly than that of the SCC with aging – though even in a relatively high dust, high DPM
environment, the DPMI performs adequately.
In a third field study, the possibility of attachment between DPM and respirable dust
particles was investigated. Such a phenomenon may have implications for both reliable sampling
and health outcomes. Using microscopy, samples collected in the study mine showed that DPM-
dust attachment does indeed occur. Moreover, the study results suggest that respirable particulate
sampling – as opposed to submicron sampling, which is currently used – may be favorable for
ensuring that oversized DPM is not excluded from samples. This strategy may require additional
sample preparation to minmize dust interferences, but methods have been previously developed
and were demonstrated here.
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ACKNOWLEDGEMENTS
There are many people in my life that have helped me get where I am today. A starting
point will be a struggle, but first I would like to thank my parents.
Mom, you have never given up on me even though it was a struggle to just get me
through high school, but look where I am now! You have always seen the potential in me and
always encouraged my direction even though it may have been hard to watch. I know you are
proud of me and that I finally owned up to the potenial you always new I had. Growing up, I
always new you were a force to be reckonded with at home and in your career. I couldn’t tell you
how many times a collegue of yours told me how impressive you are. I thank you for instilling in
me the dedication and passion you have in your own life and career. Dad, I thank you for giving
me the ability to approach tasks in innovative ways. You created a perfect example of “work
smarter, not harder” in me. I get my workhorse attitude from you and I am sure my past and
future employers appreciate that. Thank you for your support and the countless times you sang
me “You are my sunshine”. To my sisters Emily and Julia, thank you for being there whenever I
needed you. I couldn’t have achieved what I have with out such an amazing family support
system.
To my advisor, Dr. Emily Sarver, thank you for supporting me and being an influential
person in my life. Your drive, passion and dedication is for lack of a better term, impressive.
Other influential people that saw my potential and helped me in gaining the experience I have
today are Dr. Robert Mensah-Biney, Dr. Rudolph Olson, Tom Newman, Kirsten Lovan, Alex
Neidermeier and Joseph Jamison. One more thank you to my Holden Hall boys Scott, Will, Ben
and Kent. My time in Blacksburg would have been boring without you all! I will be forever
grateful for these individuals either knowingly or not giving me their time, advice, guidence and
just plain old looking out for me.
My research would also not be complete with out the help of everyone on Dr. Sarvers
research team, those at CDC/NIOSH Office of Mine Safety and Health Research (OMSHR) for
funding my thesis work under contract No. 200-2014-59646. I would especially like to thank Dr.
Emanuele Cauda, Jim Noll and Shawn Vanderslice of OMSHR for their hard work in sample
prep and analysis and answering all my questions! A special thank you to all the mine personnel
who were nothing but helpful and most enjoyable to be around. Certainly made my trips to the
mine memorable! Last but not least, I would like to thank my committee members, Dr. Kray
Luxbaucher and Dr. Cigdem Keles.
Thank you again to all who have been a part of my journey.
iv
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PREFACE
This thesis presents three field studies related to diesel particulate matter (DPM)
sampling and monitoring in underground mines. Each study is reported in a separate chapter. All
were conducted in the same large-opening stone mine, which has partnered with Virginia Tech to
provide access to an active operation for DPM research. This research is being conducted as part
of a larger project funded by CDC/NIOSH (contract No. 200-2014-59646). The work described
in Chapter 1 was performed by the Virginia Tech research team, and this chapter was published
as a peer-reviewed technical paper in Mining Engineering. It is reproduced here with permission
from the publisher (the Society for Mining, Metallurgy and Exploration). The studies reported in
Chapters 2 and 3 were designed and conducted in collaboration with Dr. Emanuele Cauda of
NIOSH’s Office for Mine Safety and Health Research. Dr. Cauda is a co-author on these
chapters.
In Chapter 1, the FLIR Airtec monitor was used to evaluate temporal changes in DPM in
different locations of the mine. The Airtec is a near real-time instrument, which was developed
by NIOSH and later commercialized as personal DPM monitor. Thus, its primary application is
in alerting individuals to their cumulative exposure during a current work shift. However, the
Airtec can also be used as an engineering tool to track DPM in particular locations or related to
particular activities or operational changes. This is demonstrated in Chapter 1 by showing diurnal
to seasonal patterns in DPM in the study mine. A method of sensitizing the Airtec to allow “spot
checking” of DPM (i.e., within minutes) is also presented. Chapter 1 has been published.
In Chapter 2, the effects of aging as an artifact of DPM sampling on size selector devices
is investigated. Size selectors are commonly used for DPM sampling in mines in order separate
relatively large mineral dust particles from the relatively small DPM. Impactor size selectors are
the current industry standard for this purpose, but sharp-cut cyclones have also been suggested.
The former physically traps the oversized dust particles to remove them from the DPM sample
and is therefore susceptible to loading (or “aging”), whereas the latter separates particles by
splitting the sample stream and should be minimally influenced by aging. However, neither
device type has been thoroughly field tested in this regard. The field study presented here tested
these devices side-by-side to determine their performance with gradual aging (versus new/clean
devices), and the influence on effective particle cut size was specifically investigated.
In Chapter 3, the possibility of attachment between DPM and respirable dust in the mine
atmosphere is investigated. Such a phenomenon is of interest with respect to DPM sampling.
Since sampling in mines typically uses a size selector, any DPM that is effectively oversized due
to attachment with relatively large dust particles may be excluded from a sample. Though little
published literature on the topic exists, attached particulates could have important health
implications too. For the field study reported here, samples of particulates in three size ranges
(submicron, respirable, total airborne) were collected in three different locations of the mine to
determine where the DPM effectively occurs. Additionally, samples of airborne particulates were
collected with a small electrostatic precipitator for analysis by electron microscopy, such that
instances of DPM-dust attachment might be observed if this is indeed happening. The
electrostatic precipitator was used in order to preserve the state of particulates as they occurred in
the mine atmosphere (i.e., either attached to one another or not).
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Chapter 1. Area monitoring and spot-checking for diesel particulate matter in
an underground mine
S. Gaillard, E. McCullough, E. Sarver
Virginia Tech, Department of Mining and Minerals Engineering, Blacksburg, VA, 24060, USA
This paper was originally published in Mining Engineering, Vol. 68, No. 12, 2016, pp. 57-62.
Abstract
Diesel particulate matter (DPM) has been regulated by the U.S. Mine Safety and Health
Administration since 2002 in underground metal and nonmetal mines. To demonstrate regulatory
compliance, DPM samples must be collected and later analyzed by the U.S. National Institute for
Occupational Safety and Health (NIOSH) 5040 standard method, but the FLIR Airtec DPM
monitor can serve as a complementary engineering tool. The monitor is a handheld instrument
that offers near-real-time measurements of elemental carbon (EC), which is a primary constituent
of DPM. As part of an ongoing field study, the monitor was used to survey EC in an
underground stone mine. This effort was aimed at determining spatial and temporal DPM
variations in several key locations. The results of prolonged area monitoring—that is, lasting
several hours — revealed that DPM concentrations were diluted substantially as air moved away
from the primary production zone, but that concentrations could vary quite a bit in a single
location from day to day and between seasons. DPM concentrations were generally lower in
winter than in summer, which is consistent with increased natural ventilation airflows during
winter. Using a modified sampling cassette, an attempt was also made to sensitize the Airtec
monitor to allow for “spot-checking” of EC concentrations — that is, measurements made in
several minutes. Preliminary field data showed that the sensitive cassette performed well in terms
of providing accurate data that could be useful for rapid assessment of DPM.
1. Introduction
Diesel particulate matter (DPM) is the solid fraction of the exhaust emissions from a diesel
engine. It largely consists of elemental carbon (EC) and organic carbon (OC) (Birch, 2003). The
World Health Organization International Agency for Research on Cancer classified diesel
exhaust, including DPM, as a carcinogen (World Health Organization, 2012). It is believed to
cause and/or exacerbate respiratory illness upon inhalation, deposition and retention in lung
tissue. Because DPM exists in both the micro- and nanoparticulate ranges, it can bypass typical
autoimmune defense mechanisms that keep larger particles out of the respiratory system
(Ristovski et al., 2012).
Compared with workers in other occupations involving frequent use of diesel-powered
equipment, such as dock workers and truck drivers, underground miners are exposed to relatively
high DPM concentrations because they work in enclosed environments (Noll and Janisko, 2013;
Noll, Janisko and Mischler, 2013). A variety of engineering and administrative controls have
been devised to reduce DPM exposures in mines, and increased airflow is often a key
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component. In largeopening mines, which are most common in the metal and nonmetal sector,
DPM abatement through increased ventilation can be quite challenging because moving and
controlling large air volumes is difficult (Grau et al., 2002; Grau and Krog, 2009). Dynamic
ventilation conditions often result in variable and unpredictable DPM concentrations over space
and time.
The U.S. Mine Safety and Health Administration (MSHA) has regulated DPM exposure in metal
and nonmetal mines since 2002. Its final rule limits personal exposure to total carbon (TC),
which is the sum of EC and OC, to an eight-hour time-weighted average of 160 µg/m3 (U.S.
Mine Safety and Health Administration, 2006). To demonstrate compliance, operators must use
the U.S. National Institute for Occupational Safety and Health (NIOSH) 5040 Method for the
analysis of collected DPM samples (Birch, 2003). However, the handheld Airtec DPM monitor
(FLIR Systems Inc., Nashua, NH) was developed as a way to provide near-real-time
measurements of EC for tracking personal DPM exposures over a work shift (Janisko and Noll,
2010; Noll et al., 2014). The monitor works by capturing DPM on a filter and successively
measuring laser extinction as the dark EC particles accumulate. The laser extinction is directly
correlated to EC, but the monitor is also programmed to display TC as a time-weighted average
(Takiff and Aiken, 2010). For this, an assumed TC to EC ratio of 1.3 is used, as discussed in
Janisko and Noll (2008). Based on comparative analysis with NIOSH 5040 Method results,
NIOSH confirmed the instrument meets or exceeds its accuracy criteria across a range of EC
concentrations expected in mining environments (Noll and Janisko, 2013; Noll, Janisko and
Mischler, 2013).
In addition to monitoring personal DPM exposures, the monitor can be used for area monitoring
(Janisko and Noll, 2010; Takiff and Aiken, 2010; Noll et al, 2005; McCullough, Rojas-Mendoza
and Sarver, 2015). By operating the instrument in a given location for a prolonged period, an
understanding of the temporal variation, such as over a shift or over multiple shifts if monitoring
on consecutive days, in DPM concentrations can be gained. Such monitoring in multiple
locations can further provide valuable information regarding spatial variation in DPM within a
mine (Janisko and Noll, 2010; Noll and Janisko, 2007). In the case that a quick assessment is
needed, for example, as part of an occasional survey across different mine locations, the monitor
might also be used for “spot-checking.” However, this application will require sensitization of
the instrument in most instances, as the desired time horizon for measurement is much shorter
than that for which the monitor was developed — for example, 10 minutes versus 10 hours. To
measure over shorter time periods, the monitor must be able to detect relatively smaller changes
in EC deposition on the filter.
In this paper, the utility of the Airtec for area monitoring is demonstrated based on data collected
in an underground stone mine. Results are presented from prolonged monitoring across multiple
mine locations on multiple days, and in opposite seasons. Additionally, the monitor is discussed
along with resulting spot-checking data.
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2. Site and experimental details
2.1 Study mine and monitoring locations.
All data were collected in an underground stone mine with a diesel fleet consisting of about 40
pieces of equipment, including haul trucks, drills, loaders, auxiliary equipment and light-duty
vehicles. The mine operates five days a week with two shifts per day. It is considered a large-
opening mine, and air velocities are generally very low, less than 0.5 m/s (100 ft/min) in some
locations, as is often observed in such operations (Grau et al., 2002; Grau and Krog, 2009). One
fan is located on the surface forcing fresh air into the mine at a pressure of about 95 kPa (950
mbar), and the main ramp into the mine serves as another air intake, using natural ventilation.
There is also a large auxiliary fan near the production zone and several booster fans, and
ventilation tubing and curtains are further used to direct airflow in priority areas. Air exits the
mine through a single exhaust.
DPM is the only airborne occupational health hazard known to be of real concern in the study
mine. Concentrations of respirable dust, including silica, are quite low, and blast fumes dissipate
overnight between shifts. Six distinct locations were selected for this study based on their
proximity to activities or airways of interest (Table 1.1). Figure 1.1 illustrates the relative
positions of the locations within the mine, with arrows indicating airflow direction.
Figure 1.1 Schematic of relative position of all monitoring locations in the study mine.
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Table 1.1 Description of monitoring locations in the study mine.
Location Description
Near main mine exhaust and underground crusher operation, moderate traffic
1
(production and non-production equipment/vehicles).
2
Immediately upstream of main auxiliary fan.
3
Outside of portable break room, workers drive to this location for breaks.
4
Escape route far downstream from production zones.
5
Near primary production zone.
6
No production, centrally-located, moderate traffic.
2.2 Equipment and data collection.
In late July through mid- August 2015, the Airtec was used for prolonged DPM monitoring, with
EC concentration measured over time, and spotchecking, with rapid assessments of EC
concentration. In December 2015, additional prolonged monitoring was conducted. An
Anemosonic UA6 ultrasonic anemometer (TSI, Shoreview, MN; discontinued) or PMA-2008
vane anemometer (Mine and Process Service, Inc., Kewanee, IL) was used during some spot
checks to determine the air speed near the monitoring equipment.
Three Airtec monitors, each calibrated to the standard flow rate of 1.7 L/min, were used with the
standard cyclone and impactor, which remove large, non-DPM particles (Noll et al., 2005). The
monitor displays data as a five-minute rolling average for either EC or time-weighted average
TC concentration, such that it does not display nonzero values until at least minute 6. The sample
collection rate of each monitor was set to either one data point or five data points per minute,
meaning that a new five-minute average value was displayed every minute or every five minutes,
respectively.
For prolonged area monitoring, the monitors were operated with standard cassettes and sample
filters, 37 mm in diameter, designed to allow continuous DPM monitoring over an entire work
shift, with the main target parameter being time-weighted average TC concentration, which is
consistent with evaluating compliance with personal exposure limits. Due to the limits of the
optical sensor in the Airtec, this means that when operating the Airtec to monitor a fixed location
it may take a relatively long time before enough EC accumulates on the sample filter for the
instrument to begin reading stable values. In order to collect spot-check data with the Airtec, it
therefore needs to be sensitized.
As a possible approach, NIOSH developed a sensitive cassette that effectively reduces the
exposed filter area to a circle about 10 mm in diameter, such that apparent EC collection and thus
laser extinction happen relatively quickly. All spot-check data in the study mine were collected
using the sensitive cassette, and a preliminary experiment was conducted to compare results from
standard and sensitive cassettes.
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3. Results and discussion
3.1 Prolonged area monitoring of EC concentrations.
During the summer and winter of 2015, 11 and 23 prolonged monitoring data sets were
collected, respectively (Fig. 1.2). The tests were started at roughly the same time of day, near the
beginning of a regular work shift, and continued for at least 300 minutes, with data reported only
between 0 and 300 minutes to be consistent between all tests. In locations where multiple
prolonged tests were conducted, each was on a different day. In all cases, the Airtec was
positioned at approximately head height, or 1.8 m (6 ft), and care was taken to monitor about the
same point in each location from day to day, either near the center of the tunnel cross section or
about 0.6 m (2 ft) off the rib in locations with traffic.
Figure 1.2 Prolonged monitoring results from summer and winter. For locations where multiple data sets were
collected in the same season, n values are given and results are shown as an average with error bars
representing the standard deviation.
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Though the data collected for this study are somewhat limited, several key observations can be
made from Fig. 1.2. First, as may be expected, DPM concentrations, using EC as a proxy, appear
to vary both spatially and temporally in the mine. During the summer, locations 1 and 6, which
are both along the main exhaust route from the mine, had higher EC concentrations than location
3, which is along the intake airways but is likely affected by some recirculating airflow that picks
up DPM near production. From the winter monitoring data, it is clear that location 5, just outby
from the main production zone, had the highest DPM concentrations recorded in that season. The
DPM appears to be substantially diluted by the time it reaches locations 6 and 1.
Furthermore, DPM concentrations in the study mine seem to vary with season, which is
consistent with the wellestablished understanding of ventilation in large-opening mines (Grau et
al., 2002; Grau and Krog, 2009). Comparing summer versus winter data in locations 1 and 6, EC
concentrations are clearly lower in the winter, despite no significant known changes in
production or ventilation controls. According to monthly airspeed measurements taken by mine
personnel in the main exhaust tunnel, where the cross section is small enough to perform a
proper traverse, airflows were on the order of 92 m3/s (195,000 cfm) during the summer tests and
109 m3/s (230,000 cfm) during the winter tests.
Finally, Fig. 1.2 also suggests that DPM concentrations can be quite variable within a particular
location in the mine. Some variation is likely due to accumulation of emissions with progression
of the work shift, and this is demonstrated clearly in the winter data from location 5, but
variability between days is also possible.
Figure 1.3 shows three consecutive weeks of prolonged monitoring data from location 1 from the
summer and winter. This location may be expected to have relatively stable DPM concentrations
over a work shift as it is located furthest from the primary emissions in the production zone. In
the summer, EC values generally tended to increase over the workweek and then drop over the
weekend, when there was no production. This may indicate that during summer workweeks
DPM was accumulating in the mine faster than it could be exhausted overnight. In the winter,
however, the trend of rising EC concentrations over the workweek was generally not observed,
though the week 3 data do show an increase from Monday to Wednesday. So, while
accumulation of DPM from one day to the next in a given location may explain some variation in
prolonged monitoring data, there are surely many other factors at play, including dynamic
ventilation conditions. As shown below, air speed measurements made for this study indicated
that flows can change dramatically, even over relatively short time horizons such as days.
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Figure 1.3 Results of prolonged monitoring at location 1 by weekday from summer and winter. In both
seasons, data were collected on multiple days during three consecutive weeks.
3.2 Spot-checking of EC concentrations.
To confirm that the sensitive cassettes produced reliable EC concentration data, a series of basic
tests were conducted briefly in the study mine. First, two Airtecs both using the sensitive
cassettes were compared side by side. Then, the sensitive cassettes were compared against the
standard cassettes. Locations and test times were chosen such that a range of EC concentrations
could be sampled, but concentrations were expected to be stable during sampling due to the
relative distance between the sampling locations and DPM emissions sources, and anecdotal
experience of mine personnel and the research team. In nine side-by-side tests using sensitive
cassettes, the absolute difference between the monitors was 13.4 ± 9.5 percent. However, in two
of the tests with relatively high differences, 31 and 16 percent, the initial optical sensor value of
one Airtec was observed to be very low, only about half that of a typical initial value. This can
happen if the exposed filter area on the sensitive cassette is slightly misaligned with the laser and
optical sensor, and may have influenced the quality of data collected. Excepting those two tests,
the average difference between the monitor was 10.3 ± 7.2 percent. This is well within the range
of possible spatial variability, which has been reported to be up to 20 percent (Vinson, Volkwein
and McWilliams, 2007).
To compare EC values measured with the sensitive versus the standard cassettes, eight
comparison tests were conducted (Fig. 1.4). For seven tests, a single monitor was used to first
collect data on a standard filter, and then it was immediately used to collect data in the same
location on a sensitive filter. The total lag time in these tests between the end of the standard
cassette data and the data plateau for the sensitive cassette was relatively short, only the 2-3
minutes required to change the cassette and then the time required for the sensitive cassette data
to reach plateau, 6-15 minutes. Thus, it is expected that any changes in DPM concentration in the
sampling location were minor and should not substantially affect the sensitive and standard
cassette comparisons. In test 5, two calibrated monitors were run side by side, one with each
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filter type. Because the sensitive cassette uses a smaller filter area than the standard cassette,
Airtec data from the former must be corrected. In Fig. 1.4, all sensitive cassette data had been
corrected by dividing the EC concentrations by 13.3, the standard-to sensitive filter area ratio.
Figure 1.4 EC concentrations measured in eight comparison tests using standard (dashed lines) and sensitive
(solid lines) cassettes. The x-axis represents the relative data collection time for a given cassette, with all data
starting at 1 minute. In test 5, the cassettes were tested simultaneously using two Airtec monitors running side
by side. In all other tests, the cassettes were tested in back-to-back runs using a single monitor, and data from
both runs were overlaid to allow comparison of EC values and time-to-data plateau.
The need to sensitize the Airtec for spot-checking is well illustrated in Fig. 1.4. While the
sensitive cassette data tended to plateau relatively quickly and remain stable, the standard
cassette data took longer to plateau, if at all. By comparing the apparent EC concentrations
where data plateaued, or fluctuations at least dampened, the sensitive and standard cassette data
generally tended to correlate well. In five of the eight comparison tests — tests 1, 2, 3, 5 and 7 —
the observed ratio of the apparent EC concentration from the standard cassette to the uncorrected
value from the sensitive cassette was 13.5 ± 0.5. This is very close to the expected 13.3 value,
suggesting that the sensitive cassettes are indeed performing as intended. In tests 4 and 6, it
appears that the standard cassette data did not have a chance to reach plateau within the test
period, possibly because the EC concentrations in the test area were too low. This highlights a
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primary advantage of using the sensitive cassette for short-term measurements. In test 8, the
initial optical sensor value on the sensitive cassette run was observed to be very low. All spot-
check data shown here had been corrected by the 13.3 factor.
Another important observation from Fig. 1.4 is that, while data from the sensitive cassettes
tended to plateau quickly, the time to the first nonzero values can vary. Based on observations in
additional follow-up tests, not shown, this also seems to be related to the initial optical sensory
value of the Airtec, which can be influenced by the initial condition of the filter when the
instrument begins collecting data. Slightly used filters, such as from a prior spot-check, generally
tended to produce data plateaus more quickly, beginning on minute 6, than new filters, which
took up to 10 minutes or, rarely, more. With this knowledge, only spot-checking data where a
plateau was observed or inferred are reported below.
To demonstrate the utility of spot-check surveying with the Airtec, data were collected at head
height in all six locations in the study mine during the summer of 2015. Air speed measurements
were also recorded during some of the spot-checks (Fig. 1.5). In each location, spot-checks were
performed on multiple days, during the middle of the workshift at least two hours after the shift
began and at least two hours before it ended. Some of the spot-check data shown in Fig. 1.5 are
from tests where the initial optical sensor value was relatively low, but based on our experience
to date, data collected under such conditions are expected to vary by only up to about 30 percent
versus data collected with a typical initial optical sensor value, with no bias between the two
conditions or the specific instruments. Thus, the large variations in reported spot-check data are
believed to be real.
Figure 1.5 Spot-check and air-speed data collected at head height in all mine locations. Air speeds were
measured only twice in location 6 and not measured at all in location 3.
In general, the spot-check surveys confirmed that spatial and temporal DPM variations can be
significant in the study mine. Consistent with observations from prolonged monitoring, locations
1 and 5, near the exhaust and production zone, tended to have relatively high EC concentrations
that were variable from day to day. This was also the case for location 4, along the main air route
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between production and the mine exhaust, and, somewhat surprisingly, location 3. Based on the
single prolonged monitoring data set from that location, it was expected to have relatively low
EC concentration, but spot-checking revealed that the concentration can be fairly high. Because
spot-checking was done mid-shift, it is possible that traffic to and from the break room near
location 3 caused large but temporary fluctuations in DPM. Also somewhat unexpected are the
spot-check results from location 6, which suggest relatively low EC concentrations in contrast to
the prolonged monitoring results. The spot-checking results from location 2, near the auxiliary
fan, were the most variable. This may be related to movement of concentrated DPM pockets by
the fan. While only a limited amount of air speed data was collected during this study, it
illustrates the dynamic ventilation conditions in the study mine.
Spot-check tests were additionally conducted in locations 2, 4 and 5 to compare measured EC
concentrations at head versus cab height, or 4.9 m (16 ft), with 14 comparisons made (Table 1.2).
For these tests, a spot-check was done at head height and another was done immediately
afterwards at cab height at the same point in the tunnel. Generally, little difference is seen
between DPM concentrations within this vertical distance and no real trend in the relative
difference between the measurement heights. In 10 of the tests, the absolute difference was less
than 10 percent, which is the expected average error in side-by-side spot-check measurements as
reported above.
Table 1.2 Results of spot-check tests conducted at head versus cab height.
Spot-checked EC concentration
Difference
Test (μg/m3)
(%)
Head height Cab height
1 240 227 5.4
2 239 239 0.1
3 256 232 9.9
4 83 72 14.5
5 177 173 2.3
6 75 88 -15.9
7 145 148 -2.3
8 214 195 9.4
9 134 189 -34.3
10 192 197 -2.7
11 286 265 7.7
12 117 115 1.9
13 161 199 -21.2
14 176 190 -7.6
4. Conclusions
While the NIOSH 5040 Method is required for demonstrating compliance with DPM exposure
limits in underground metal and nonmetal mines, the FLIR Airtec DPM monitor is a useful
engineering tool that provides the ability to evaluate DPM concentrations in near real time.
Using its standard operating parameters and sampling cassettes, it can be used not only to track
personal exposures but also to conduct area monitoring. In this work, the area-monitoring
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application of the monitor was demonstrated in an underground stone mine. The monitor was
also studied for a spot-checking application to allow rapid EC measurements. Use of a sensitive
cassette, which reduces the exposed filter area, proved to be a simple and effective way to
sensitize the monitor for this purpose. In general, the results from both prolonged area
monitoring and spot-checking indicate that EC, and thus DPM, concentrations can vary
significantly in both space and time within the study mine.
Beyond use in occupational health programs, the Airtec or similar environmental monitoring
technologies may also contribute to the improved understanding of mine ventilation systems,
particularly in large-opening mines, which are challenged when it comes to airflow modeling and
analysis. Such technologies could further provide insights into the fates of airborne particulates
as they travel from their sources.
5. Acknowledgments
The authors thank NIOSH for funding this work under CDC/NIOSH contract number 200-2014
59646 and especially James Noll and Shawn Vanderslice for their guidance. Sincere appreciation
is also extended to all personnel at the study mine who have so willingly cooperated on and
supported this work, and to Lucas Rojas Mendoza for assisting with data collection. Finally,
thanks to Jamie Cohen, Steven Hyde and others at FLIR Systems Inc. for Airtec applications
assistance.
6. References
Birch, M.E., 2003, “Monitoring of diesel particulate exhaust in the workplace,” NIOSH Manual
of Analytical Methods, 4th Edition, U.S. National Institute for Occupational Safety and Health.
Grau, R., and Krog, R., 2009, “Ventilating large opening mines,” Journal of the Mine
Ventilation Society of South Africa, Vol. 62, No. 1, pp. 8-14.
Grau, R., Mucho, T., Robertson, S., Smith, A., and Garcia, F., 2002, “Practical techniques to
improve the air quality in underground stone mines,” Proceedings of the 9th U.S./North
American Mine Ventilation Symposium, pp. 123-129.
Janisko, S., and Noll, J.D., 2008, “Near real time monitoring of diesel particulate matter in
underground mines,” Proceedings of the 12th U.S./North American Mine Ventilation
Symposium, pp. 509-513.
Janisko, S., and Noll, J.D., 2010. “Field evaluation of diesel particulate matter using portable
elemental carbon monitors,” Proceedings of the 13th U.S./North American Mine Ventilation
Symposium, pp. 47-52.
McCullough, E., Rojas-Mendoza, L., and Sarver, E., 2015, “DPM monitoring in underground
metal/nonmetal mines,” Proceedings of the 15th North American Mine Ventilation Symposium,
pp. 325-330.
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Chapter 2. Impact of aging on performance of impactor and sharp-cut
cyclone size selectors for DPM sampling
Sallie Gaillarda, Emily Sarvera*, Emanuele Caudab
a Virginia Tech, Department of Mining and Minerals Engineering, Blacksburg, VA 24060, USA
b CDC/NIOSH Office of Mine Safety and Health Research (OMSHR), Pittsburgh, PA 15236, USA
.
Abstract
Diesel particulate matter (DPM) is an occupational health hazard in underground mines. It
generally occurs in the submicron range, and is often present in the mine atmosphere with
significant concentrations of dust particles that tend to occur in the supramicron range. Since
dust can interfere with analytical methods to measure DPM, it is often removed from a
sample stream using impactor-type size selector (DPMI). Because the DPMI physically
removes oversized particles from the stream, its performance may be gradually reduced with
aging. Sharp cut cyclones (SCCs) represent an alternative size selector for DPM sampling
applications, with a major advantage being that, by design, they should not be susceptible to
rapid aging. This paper presents results of a field study designed to compare the performance
of aged versus new/clean DPMIs and SCCs in an underground mine. DPMI aging resulted in
clogging of the device, and eventually a reduction of its effective particle cut size – though,
when sample flow rate was maintained, DPM sample mass collection was not affected until
significant aging had occurred. Under the conditions present for this study, effects of SCC
aging were observed to be minimal by the end of the study period.
1. Introduction
Sub-micron particles are increasingly recognized as significant respiratory health hazards
(Cantrell & Watts, 1997; Kenny, et al., 2000; Ristovski, et al., 2012). Diesel particulate
matter (DPM) represents a major source of submicron particles in both environmental and
occupational environments (Kittleson, 1998; Abdul-Khalek et al., 1998). Due to their work
around large equipment in confined spaces, underground miners have some of the highest
exposures to DPM (EPA, 2002; Grau et al., 2004). DPM largely consists of solid elemental
carbon (EC), commonly known as “soot”, and organic carbon (OC) that may be sorbed to EC
particles (Kittleson, 1998; Abdul-Khalek et al., 1998). EC and OC can be measured by
thermal-optical methods such as the NIOSH 5040 Standard Method (Birch, 2016), and their
sum is referred to as total carbon (TC). While the complex nature of DPM does not allow for
its direct measurement, both TC and EC have been accepted as suitable surrogates for
monitoring occupational exposures to DPM (Noll et al., 2007 and Birch, 2016).
In the US, personal DPM exposures in underground metal/non-metal mines are regulated on
a TC basis; in 2008, the 8-hour time-weighted average limit was set at 160 µg/m3 TC
(MSHA, 2008). To measure exposures, personal samples are collected using a small air
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pump to draw DPM onto a quartz fiber filter, which is subsequently analyzed using the 5040
Method. To avoid analytical interference from mineral dust, an “impactor” is often placed
just upstream of the filter. This device uses an impaction substrate, which serves as a particle
size selector. It removes larger particles (i.e., mostly mineral dust) from the flow and allows
smaller particles (i.e., mostly DPM) to pass to the filter (Cantrell and Rubow, 1992). Since
the larger particles are physically trapped in the impactor, it gradually becomes loaded and
should eventually be replaced. Effects of this loading or “aging” on sample results have only
been studied in a laboratory setting to date (Cauda et al., 2014).
The SKC jeweled DPM impactor (SKC, Inc., Eighty Four, PA, USA), referred to as the
DPMI herein, is the current industry standard for DPM monitoring (Birch, 2016). At the
required flow rate for compliance sampling (1.7 LPM), the DPMI has a cut size of about 0.8
µm. Particularly in dusty environments, use of a small cyclone upstream of the impactor is
also common practice. The 10-mm Dorr-Oliver (DO) cyclone provides a first cut of very
large particles (i.e., d of about 4.5 µm, and d of about 3 µm at 1.7 LPM), which could
50 90
cause rapid clogging of the impactor or substantial interference with 5040 Method or similar
analysis. Nevertheless, the DPMI is intended as a single use device for collecting DPM
samples for such analysis (SKC, 2003).
In addition to collecting filter samples for subsequent analysis, DPM can be monitored in
near real-time by the handheld Airtec DPM monitor (FLIR Systems, Inc. Nashua, NH). The
Airtec works by drawing in mine air at 1.7 LPM through a DO cyclone and DPMI, then
particles less than 0.8 µm are deposited onto a filter in a cassette located inside the Airtec
housing (Noll et al, 2013; Noll & Janisko, 2013). The instrument continually measures EC
accumulation on that filter using a laser extinction principle whereby changes in laser
absorption are correlated to EC mass in the sampling environment (Takiff and Aiken, 2010).
In this application, FLIR recommends that the DPMI be replaced after three internal cassette
changes (FLIR, 2011).
As an alternative to the consumable DPMI, sharp-cut cyclones (SCCs) have also been
considered for DPM sampling applications (Cauda et al., 2014). The SCC is named for its
sharp separation curve. Unlike traditional cyclones, which exhibit a gradual separation curve,
the SCC is highly efficient – meaning it rejects nearly all particles larger than its “cut size”
and passes nearly all smaller particles (Kenny et al., 2000). SCCs have been successfully
used in ambient air sampling applications and may perform better than impactors in high dust
concentrations (Kenny and Gussman, 2000). For mining applications, controlled laboratory
studies have shown that they can perform comparably to impactors with respect to cut size
and effective separation of mineral dust from DPM (Kenny et al., 2000; Cauda et al., 2014),
although long-term performance of SCCs in mine settings has not been specifically
investigated. Given that the SCC is designed for continual use, perhaps with periodic
cleaning, it seems an obvious choice for some particular applications such as in continuous
DPM monitoring systems (Barrett et al., 2017, Pritchard et al., 2016).
Use of size selectors for particulate sampling is premised on the notion that their performance
does not appreciably change over the time period of use. That is, a necessary assumption is
that as these devices age they function consistently (i.e., maintain the desired cut size) and do
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Figure 2.1 Three sampling trains used in the field study.
Flow rates for the Airtecs and ELF pumps with DPMIs were set to 1.7 LPM, which should
produce a DPMI cut size of about 0.8 µm. The ELF pumps with SCCs were set to 2.2 LPM
in order to produce a similar cut size (Cauda et al., 2014). This assured that EC mass
measurements from all sampling trains could be directly compared (after adjusting for
sampling flow rate). The flow rate of each pump was measured before and after the 5-hour
sampling period using a Defender 510 Primary Air Flow Calibrator (Mesa Laboratories Co.,
Lakewood, CO). It should be noted that the SCC was not tested with the Airtec because this
would have required increasing the flow rate from the standard 1.7 LPM to 2.2 LPM, which
is outside of the recommended operating range.
The study design was such that four units of each sampling train were used simultaneously in
all 12 sampling periods (Table 2.1). For the first sampling period, all size selectors were
new/clean at the beginning of the period, and all had been aged by 5 hours at the end of the
period. In the next sampling period, two of the SCCs from Train 1 were cleaned, and two of
the DPMIs from Trains 2 and 3 were replaced and their corresponding DO cyclones were
cleaned. These devices were designated as “clean.” The other SCCs were not cleaned and the
other DPMIs were not replaced (and corresponding DO cyclones were not cleaned). These
devices were designated as “dirty”, and had been aged for 10 hours at the end of the second
sampling period. The same protocol was followed for all subsequent sampling periods, such
that the dirty devices were never replaced or cleaned – and they had been aged for a total of
60 hours at the end of the sampling campaign. While sets of dirty DPMIs and DOCs
remained paired for the entire sampling campaign, use of specific ELF pumps and Airtecs
with each size selector train (i.e., DPMI/DO cyclone or SCC) was randomized. However, the
same four Airtecs and eight ELF pumps were utilized for the entire study.
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Table 2.1 Schedule for aging (dirty) or replacement/cleaning (clean) of size selectors with study
progression.
SCC or DPMI Total aging time (hr) of size selector for sampling period (beginning – end)
replicate Day 1 Day 2… …Day 12
1 – new/clean 0-5 0-5 0-5
2 – new/clean 0-5 0-5 0-5
3 – dirty 0-5 5-10 55-60
4 – dirty 0-5 5-10 55-60
To clean the SCCs and DO cyclones, they were taken apart and placed in a mild soap
solution. The parts were allowed to sit for about 5 minutes, gently agitated, and then rinsed
and patted dry. To fully dry the parts before reassembling, they were placed under a fume
hood with the fan on at least overnight. In all instances, the DPM collection filters were new
for each sampling unit. For Train 1, new filters were used for every sample (i.e., since the
SCC is separate from the filter cassette). In Train 2 and 3, for clean DPMIs, the entire
cassette was replaced such that the DPMI and filters were new. For dirty DPMIs, new filters
were placed into the original cassette before each sampling period. This was done by
carefully opening the cassette to replace the filters and then resealing them. For Train 3, new
Airtec internal cassettes and filters were used for every sample.
During sample collection, the inlets of all sampling units were positioned side-by-side (i.e.,
with no more than a few inches between them) and oriented in approximately the same
direction to minimize spatial variability in results. All pumps were switched on and off at
approximately the same time (i.e., within a few seconds of one another).
To get an idea of the dust concentrations in the sampling location, an Optical Particle Sizer
(OPS) Model 3330 (TSI Inc., Shoreview, MN) was used to monitor particle number
concentrations during the last six sampling periods (i.e., days 7-12). The OPS counts
particles in 16 size bins between 0.3 and 10 µm. Assuming that virtually all DPM is less than
0.8 µm and that virtually all mineral dust is greater than 0.8 µm, the OPS data can be used to
assess the relative concentrations of these two particle types, which should be split by the
SCC (Table 2.1). Further, at 1.7 LPM, nearly all dust smaller than 3 µm should pass through
the DO cyclone (i.e., d of 3 µm) such that it must be removed by the DPMI; with increasing
90
dust size, fewer and fewer particles should pass through the cyclone (i.e., d of 4.5 µm and
50
d of 6 µm).
10
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Table 2.2 Particle concentrations (#/cc) in the range of 0.3 to 10 µm measured by OPS. Particles less
than 0.8 µm are assumed to be DPM, and those greater than 0.8 µm are assumed to be mineral dust.
Nearly all dust particles less than about 3 µm should be collected in a DPMI when using a DO
cyclone upstream. Virtually all dust should be rejected from the sample stream by a SCC.
Dust (#/cc)
Total Dust
DPM (#/cc)
(~90% collected (~50% collected (#/cc)
Day
by DPMI) by DPMI)
0.3 – 0.809 µm 0.809 – 3.014 µm 3.752 – 4.672 µm 0.809 – 10 µm
Day 7 2760.58 44.49 5.47 53.65
Day 8 2285.77 102.01 15.29 128.24
Day 9 2601.42 74.73 9.28 90.23
Day 10 625.96 71.14 9.37 87.02
Day 11 1231.11 63.79 8.26 77.74
Day 12 1608.45 69.64 7.49 81.86
2.3 Sample analysis
All filter samples collected in Trains 1 and 2 (ELF pumps) were prepared (i.e., by removing a
1.5 cm2 punch sub-sample) and analyzed by the 5040 Method. A Sunset Laboratory Inc. Lab
OC-EC Aerosol Analyzer (Tigard, OR) was used at the diesel research laboratories at
NIOSH’s Office of Mine Safety and Health Research (OMSHR) campus in Pittsburgh, PA.
Since the quantity of interest in this study was EC mass collected, only the results of the
primary filters (i.e., the top filter in the sampling cassette) are reported here. The 5040
analyzer outputs EC results on a mass per filter area basis (µg/cm2). This was converted to an
EC mass per filter value for each sample using the total filter area (i.e., 8.5 cm2), and also an
EC concentration in the sampling environment (µg/m3) using the sampling time and
measured flow rate (i.e., average of pre- and post-sampling flows).
Filter samples collected in Train 3 were analyzed by the Airtec, which has been calibrated to
5040 EC measurements. The instrument’s method of analysis has been described in detail
elsewhere (Noll and Janisko, 2007; Takiff and Aiken, 2010), but essentially it uses the
voltage decay of its optical sensor to determine mass accumulation of EC over a given period
of time. Using its internal algorithm, which assumes a standard flow rate, the Airtec converts
the EC mass to an environmental concentration value that is displayed on the screen.
However, in this study, the Airtec EC mass (and concentration) values were corrected for the
measured flow rates.
2.4 Penetration efficiency of size selectors
Following the sampling campaign, the penetration efficiency of new and aged (5 and 60
hours) DPMIs and SCCs was also determined. This was done in a calm air chamber on the
NIOSH-OMSHR Pittsburgh campus, using a similar strategy as that described by Cauda et
al. (2014). In brief, spherical particles of standard sizes (i.e., 400, 500, 600 and 800 nm;
Nanosphere ™ solutions purchased from Thermo Scientific, Waltham, MA) were sampled
through the size selector devices. Particle concentrations in the air that passed through the
devices were measured, as were concentrations in the chamber itself (i.e., measured using a
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