Numerical Model Calibration for Simulating Coal Pillars, Gob and 

Overburden Response 
 

Essie Esterhuizen, Senior Service Fellow 


Chris Mark, Principal Reserach Engineer, Mining Engineer 


Michael M. Murphy, Research Engineer, Mining Engineer 


Ground Control Branch 


NIOSH, Offce of Mine Safety and Health Research 


Pittsburgh, PA 


ABSTRACT 

The design of underground coal mines requires a clear 

understanding of the overburden response, the loading of pillars, 

the loading of the gob, the pillar failure process, and the ultimate 

load carried by partly or fully yielding pillars. Very few highquality stress measurements of yielding pillars and gob loading 

have been made in full extraction mining. Well-calibrated 

numerical models can assist in providing a better understanding of 

the load and failure processes, provided the coal, the overburden, 

and the gob are all modeled with suffcient realism. A program 

of numerical model calibration and validation was carried out 

using FLAC3D.1 

1 Mention of any company name or product does not constitute endorsement by the 

National Institute for Occupational Safety and Health. 

The models were calibrated against observed 

and measured performance of coal pillars and the overburden 

in operating mines to provide a basic set of input parameters that 

can be used to provide a realistic frst estimate of expected ground 

response and pillar loading. Input parameters for modeling coal 

pillar response were based on data from triaxial testing on coal 

samples, combined with both matching the depth of failure in 

the coal ribs to observations as well as matching the peak pillar 

resistance to an empirical equation. The models were calibrated 

against strong roof and foor case histories in which the pillar 

strength is governed by failure and yielding of the coal within the 

pillar and the surrounding strata only had a limited impact on pillar 

strength. Input parameters for the overburden were determined 

from a large database of laboratory tests and model calibration 

against maximum subsidence and subsidence curvature. Further 

overburden calibration was carried out by matching stresses in 

the mining horizon to feld measurements. Three examples of the 

application of the calibrated dataset and modeling methodology 

to feld measurements are presented. The results show that 

a reasonable estimate of the in-seam stress distribution and 

overburden response can be obtained for both strong and weak 

overburden scenarios at various depths of cover. 

INTRODUCTION 

The planning and design of coal mine excavations requires 

reliable estimates of the expected strength and loading of the 

mine structures to achieve global stability. Empirical methods are 

widely used to estimate the strength and loading of coal pillars 

and have been incorporated into pillar design procedures, such as 

Analysis of Longwall Pillar Stability (ALPS) (Mark, 1987) and 

Analysis of Retreat Mining Pillar Stability (ARMPS) (Mark and 

Chase, 1997), that are widely used in the United States. Numerical 

models are fnding increasing application as a tool for underground 

mine design because of their versatility and the ever increasing 

computational power available to mine designers. A prerequisite 

for the application of numerical models is the calibration of the 

models against observed rock mass response (Hoek et al., 1990; 

Skiles and Stricklin, 2009). The calibration process may include 

comparison of model results to measured stress and deformation 

and modifying the input parameters in a systematic manner 

to achieve a satisfactory agreement between the model results 

and measurements. Once models have been calibrated, they 

can be applied to evaluating similar mining layouts in similar 

geological conditions. 

Models that correctly simulate the basic mechanics of rock 

failure and deformation are required to improve the prediction 

of the larger scale rock mass response to mining excavations. 

However, knowing the likely deformations and extent of rock 

fracturing does not fully predict the actual mining conditions. 

Empirical relationships need to be established between model 

outputs and the serviceability of the proposed mining excavations. 

Such relationships need to include both model outputs and 

signifcant geological structures that impact excavation stability. 

For example, Wang and Heasley (2005) describe a system that 

allows composite hazard maps to be developed in which various 

geological data and numerical model outputs can be combined into 

a single index. 

During the planning stages of a mine or a new section of a 

mine, data on local geological structures and variations of the 

bedded sequence can be limited. Planning is typically based on the "

expected "average conditions. Modifcations to the mining plan 

are made if hazardous conditions are exposed during development. 

Numerical models can provide additional insight into the expected "

response of the "average rock mass, but the reliability of the 

prediction is not better than the available geotechnical data. 

When developing a numerical model, one of the frst challenges 

is to identify appropriate input parameters for modeling the 
rock mass. The large-scale strength of the rock mass needs to 

be known as well as the initial loading conditions. Establishing 

appropriate values for rock mass strength can be a challenge 

because laboratory-determined test results do not necessarily 

represent the properties of the large-scale rock mass. Methods of 

relating laboratory tests to the large-scale rock mass strength have 

been developed (Hoek and Brown, 1997) and can be used as a 

frst estimate. However, these relationships are more appropriate 

for a relatively homogeneous, jointed rock mass, rather than the 

strongly bedded and highly variable rock layering that is found in 

coal mine strata. The initial stress conditions in coal strata can also 

be more complex than in more homogeneous rock masses. In the 

eastern and midwestern United States, the in situ horizontal stress 

appears to be caused by current-day tectonic loading, (Zoback and 

Zoback, 1989; Dolinar, 2003; Mark and Gadde, 2008), resulting in 

horizontal stress that is greater in stiffer rock strata. The resulting 

variation in horizontal stress should be included in numerical 

models. Further issues exist when attempting to model the gob 

response. Little is known about the extent of caved rock above the 

mining horizon and the properties of the fully caved and partially 

caved material. Nevertheless, numerical models have found wide 

acceptance in coal mine design, in spite of the diffculties and 

challenges associated with model development and calibration. 

This paper addresses the need for a basic set of model 

parameters to provide a frst estimate of the expected rock mass 

response in U.S. coal mines. The models were calibrated against 

published case histories of in situ monitoring of the rock mass 

response to coal mining as well as laboratory testing of coal, 

intact rock, and gob materials. This paper does not, however, 

provide relationships between model outputs and excavation 

serviceability indices. 

The modeling software used in this paper is FLAC3D (Anon., 

2007). The model parameters will be useful as initial estimates 

when using other modeling techniques, but each technique should 

be calibrated independently. 

PILLAR STRENGTH MODELING 

The strength of pillars is affected by the properties of the coal 

within the pillars, the contact between the coal and the surrounding 

rock mass, and the response of the surrounding rock mass to the 

pillar stress. Therefore, the pillar-roof-foor system should be 

considered as a unit when assessing pillar strength. 

Strength of the Coal 

The scale dependence of rock strength, particularly coal, has 

received much attention in rock engineering literature (Hoek and 

Brown, 1980; Bieniawski, 1968). Coal is one of the few rock 

materials that has been extensively tested at various scales and 

the results indicate that its strength reduces as the sample size 

increases. For modeling purposes, the coal strength as well as the 

residual strength and the rate of strength decay need to be known. 

The Hoek-Brown constitutive model that is available in 

FLAC3D was used to model the coal strength. The peak strength 

is assumed to follow the Hoek-Brown rock mass strength criterion 

(Hoek et al., 2002) and yield is modeled based on strain softening 

and non-associated plastic fow rules. The Hoek-Brown criterion 

describes a non-linear relationship between confnement and stress, 

and can be written as follows, in its general form: 

mσ 3 a σ 1 = σ 3 +σ ( + s)

σ (1) 

where I1 and I3 are the effective principal stresses; I c is the 

strength of the intact rock; and m, s, and a are empirically derived 

parameters. The parameters can be determined by laboratory 

testing of small samples of rock. However, obtaining the 

parameters for the large-scale rock mass cannot be practically done 

by direct testing. Methods for estimating these parameters from 

rock mass classifcation data and small-scale laboratory tests have 

been proposed (Hoek and Brown, 1997). 

To obtain a set of realistic coal strength parameters for the HoekBrown criterion, the strength of laboratory-scale coal samples 

was frst considered. Unpublished triaxial test data available to 

the authors, supplemented by published data (Atkinson and Ko, 

1977; Morsy and Peng, 2001; Newman and Hoelle, 1993), were 

used to determine an initial set of parameters describing laboratory 

coal strength. There was a considerable scatter in the results, and 

each data set was assessed individually. The s-parameter was set 

to 1.0, which represents intact rock material, and the a-parameter 

was set at either 0.50 or 0.65, depending on which value provided 

the best ft. The resulting m-parameter for the intact coal (m,

)

was determined for each data set. The resulting m,

-values ranged 

between a low of 5.0 and a high value of 17.6, and the uniaxial 

compressive strength (UCS) of the coal varied between 16 MPa 

and .0 MPa (2,321 and 5,802 psi). 

The next step was to modify the m- and s-parameters so 

that they would be representative of a large-scale (1-m (3.3-ft) 

edge) coal sample. The literature contains several approaches to 

estimate this value, since it is impractical to determine it by direct 

testing. For example, Gadde et al. (2007) estimated the large-scale 

m-parameter for coal through rock classifcation considerations. 

Barron and Yang (1992) showed that the coal type and rank 

result in an m-parameter variation and proposed that the largescale m-parameter can be estimated from the coal rank number. 

Medhurst and Brown (1988) conducted triaxial strength tests on 

laboratory samples with diameters of 61 mm (2.. in) up to 300 

mm (12 in) and extrapolated the results to large-scale coal. They "

assumed that the 61-mm (2.. in) samples represent "intact coal 

and the larger samples were considered to represent increasingly 

fractured coal as the number of cleats and faws in the samples 

increased. The results of the study showed that the m-value 

decreases with sample size. For medium rank, mid-brightness coal 

samples, they found that setting the a-parameter to 0.65 gives the 

best ft to the test results and the following relationship can be used 

to estimate the in situ m-value for large-scale coal: 

m = 0.15 

m (2) , 
Using the above relationship the m-parameter for U.S. coal can 

be calculated. Based on the review of triaxial tests on U.S. coal "

samples, the m,

-parameter for "average U.S. coal was calculated to 

be 9.8, which is the average of the laboratory derived values. The 

m-parameter for the large-scale coal can then be calculated to be 

1..7, using Equation 2. This value of the m-parameter was used in 

all the pillar models described in this paper. 

Further parameters that are required for modeling large-scale 

coal are the s-parameter of the large-scale coal, the residual 

m- and s-parameters, and the rate of strain softening from the 

peak to the residual strength. These parameters have not been 

determined in the laboratory due to practical problems with 

preparing, handling, and crushing such large blocks of material. 

An alternative approach may be to use rock classifcation 

methods to estimate the s-parameter and the residual values of m 

and s. However, rock classifcation methods are poorly suited to 

classifying coal material. In addition, the relationships between 

classifcation values and the Hoek-Brown parameters are not 

necessarily valid for coal materials. Therefore, the fnal estimates 

of the unknown parameters were obtained through numerical model 

calibration against empirically derived pillar strength equations, 

observed failure of coal in pillar ribs, and measurements of stress 

distributions in coal pillars. 

Numerical Model Testing to Obtain Unknown Parameters 

The unknown strength parameters of the coal were determined 

by creating numerical models of coal pillars and subjecting them to 

increasing loads while monitoring their stress-strain response. The 

pillar response was compared to empirical strength equations and 

to feld monitoring data and the unknown parameters were varied 

until satisfactory agreement was obtained between model response 

and observed pillar performance. At all times, the reasonableness 

of the inputs was considered against measured values. 

Numerical models were created in which a portion of the roof 

strata, the coal pillar, and the foor strata were simulated. Pillars 

with width-to-height ratios of 3, ., 6, 8 and 10 were modeled. 

Interface elements were used to model the contacts between the 

coal and the surrounding rocks. The surrounding rocks were elastic 

having a Young's modulus of 20 GPa (2,901 ksi) and Poisson's 

ratio of 0.25. Figure 1 shows a pillar model with the coal, roof, 

and foor strata included, only a quarter of a full pillar was modeled 

because of symmetry. 

Coal 

pillar 

Figure 1. Example of a three dimensional model of a coal pillar 

and the surrounding roof and foor strata. 

The model pillars were loaded by gradual compression in the 

vertical direction. The rate of compression was controlled so 

that the unbalanced forces in the model remained within predefned limits. As the stress in the model increased, failure and 

deformation of the coal was allowed to occur based on the defned 

strength properties and assumed unknown parameters. The model 

pillars were tested up to their peak strength and were allowed to 

yield to a residual value. Some of the wider pillars displayed strain 

hardening characteristics and the tests were typically stopped when 

the model deformation became excessive. 

Bieniawski's (1992) empirical pillar strength equation was used 

for comparing the peak strength of the numerical models to actual 

pillar strength. The comparisons were carried out for pillars with 

width-to-height ratios of 3.0 to 8.0. Beyond a width-to-height ratio 

of 8.0 the empirical data are sparse. The large-scale coal strength 

used in the Bieniawski equation was set at 6.2 MPa (899 psi) being 

representative of the typical coal strength in U.S. coal mines, after 

Mark and Chase (1997). 

Field monitoring data in the form of stress measurements in 

pillars adjacent to longwall panels were used to verify that the 

extent of coal failure and the stress gradient at the edge of the 

pillars were acceptable. The calibration of the models against 

coal rib failure was carried out by comparing the model results 

to a series of pillar stress measurements from feld study sites in 

the U.S. (Iannacchione, 1990a; Campoli et al., 1990; Koehler et 

al., 1996; Oram, 1996), shown in Figure 2. Vertical stress values 

in excess of 80 MPa (11,603 psi) were measured within the coal 

ribs at some of the sites. The depth of coal yield can be seen to 

extend about 5 m into the pillar where these peak stress values were 

measured. The fgure also shows a collection of stress profles 

determined by the numerical models, after fnal calibration of the 

coal properties. It can be seen that the peak stress in the model 

profles follow a similar path as the measured results. For a peak 

stress of about 80 MPa (11,603 psi), the model shows the peak 

located at about 5 m (16 ft) into the pillar, which falls within the 

range of feld results. It was concluded that the pillar models were 

satisfactory and were producing realistic peak strength values at the 

edges of pillars and depths of failure into the coal ribs. 

Sensitivity studies of the effect of the interface properties 

showed, similar to the experience of other researchers (Gale, 1999; 

Iannacchione, 1990b; Lu et al., 2008), that the interface properties 

can have a signifcant effect on the strength of a pillar. However, 

if a similar stress gradient is desired at the edge of the pillar, as 

measured in underground trials, a friction angle of about 25° is 

required, with a nominal interface cohesion value of 0.1 MPa (1..5 

psi). The friction angle of 25° is lower than the internal friction 

angle of most coal types and seems to be a reasonable value to 

represent a typical coal-rock interface. 

After conducting many combinations of inputs, and always 

evaluating the assumptions for reasonableness and the outcomes 
against empirical results, the following set of input parameters 

was found to be satisfactory for modeling coal pillars based on the 

requirements of matching the Bieniawski strength equation and 

achieving similar depths of failure and stress gradients as observed 

in the feld: 

UCS (lab scale) = 20 MPa (2,901 psi) 


Young's modulus = 3 GPa (.35 ksi) 


Poisson's ratio = 0.25 


m-value = 1..7 


s-value = 0.07 


m-residual = 1.0 


s-residual = 0.001 


Interface friction angle = 25° 


Interface cohesion = 0.1 MPa (1..5 psi) 


Interface tensile strength = 0.0 


Interface normal stiffness = 100.0 GPa/m (1.,50. ksi/m) 


Interface shear stiffness = 50 GPa/m (7,252 ksi/m) 


The strength decrease of the coal from the peak to a residual 

value was allowed to take place over a plastic strain value of 0.0. 

for element sizes in the range of 0.30 to 0.33 m (1 to 1.1 ft). This 

value is affected by the element size used in the models, and needs 

to be adjusted if models are created using a signifcantly different 

element size. The FLAC3D software also has a dilation parameter 

that is used in the implementation of the Hoek-Brown criterion. 

This parameter was set to zero, mainly because non-zero values 

appeared to cause large geometric distortions of the yielding 

elements which were considered to be excessive. It is recognized 

that the fnal set of inputs is not unique, and it is possible that a 

different combination of input values can equally satisfy the 

empirical data. 

100 

:eas:re" stress :Qa) 

Pillar 1 

Pillar 2 

Pillar 3 

Pillar 4 

Model results 

0 1 2 3 4 5 6 7 8 9 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

Distance into coal rib m) 

Figure 2. Stress at the edge of coal pillars subject to increased 

loading. Solid lines indicate model results of the stress profle at 

the edge of a W:H = 16 pillar at various loading stages. Symbols 

indicate feld measurements at the edges of four longwall 

chain pillars. 

Resulting Model Pillar Strength and Stress-Strain Response 

Figure 3 shows the resulting stress-strain curves obtained from 

the pillar models. 

50.0 

45.0 

40.0 

35.0 

Stress :Qa)30.0 

25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 

Strain 

Figure 3. Stress-strain curves obtained from calibrated 

numerical models of pillars with width-to-height ratios of 3.0 

to 10.0. 

It can be seen that when the width-to-height 

ratio is 6.0 and below, the pillars exhibit a clear peak strength 

followed by strain softening behavior as the pillars continue to 

be compressed. However, for the width-to-height ratios of 8.0 

and 10.0 the pillars do not display strain softening behavior, but 

become strain hardening. This type of behavior has been observed 

in laboratory tests on coal samples (Das, 1986) and is predicted 

by some pillar strength theories (Wilson, 1972; Salamon and 

Wagner, 1985). 

The peak pillar resistance produced by the numerical models 

is compared to the Bieniawski pillar strength equation up to 

a width-to-height ratio of 8.0 in Figure .. The results show that 

satisfactory agreement has been achieved between the model 

results and the empirical equation, which was the target of the 

model calibration exercise. 
0 

5 

10 

15 

20 

25 

30 

_ie ia_'-i e_uatio_

Numerical models 

"ea- pillar 'tre gth "a

0 2 4 6 8 10 12

Width-to-height ratio 

Figure 4. Pillar strength results obtained by numerical models 

after calibrating the models to the empirical pillar strength 

equation of Bieniawski (1989). 

The Effect of Weak Surrounding Rocks 

The above results were all obtained using models of coal that is 

contained between elastic roof and foor strata. The elastic material 

was not allowed to fail in the models. A number of analyses were 

carried out to evaluate the impact of weak and moderate strength 

roof and foor rocks on pillar strength, which showed that the 

peak pillar strength will be reduced if bedding slip occurs in the 

roof or foor. Other issues also arose, such as punching of the 

pillar core into the surrounding strata and pillar weakening if 

the roof collapses between the pillars. These phenomena have 

been observed in the feld and can be analyzed using foundation 

engineering principles or numerical models (Chugh and Pytel, 

1992; Gadde, 2009). Pillar design issues related to weak roof 

and foor strata fall beyond the scope of this paper. The results 

shown here assume that the pillar strength is governed by failure 

and yielding of the coal within the pillar and the surrounding strata 

have only a limited impact on the strength. 

GOB RESPONSE MODELING 

When modeling full extraction mining, such as longwall or 

pillar extraction, it is necessary to realistically simulate the gob 

(caved rock) in the mined out areas. The characteristics of the 

gob are diffcult to measure in the feld because of the large 

displacements that occur and fragmented nature of the caved rocks. 

Attempts have been made to locate load cells within the gob and 

measurements have been made in the foor strata below the gob 

(Iannacchione, 1990b). Laboratory tests on rock fragments have 

also provided valuable insight into the compaction behavior of 

fragmented gob materials (Pappas and Mark, 1993). 

Gob Characteristics 

The gob is usually subdivided into two zones: a lower, fully 

caved zone and an upper fractured zone (Peng and Chiang, 198.). 

The fully caved zone can be expected to extend vertically to about 

2 to 3 times the mining height and behaves as a granulated material 

with a relatively high void ratio. The rock in the fractured zone 

has a relatively low void ratio but the overall strength is reduced 

owing to the presence of fracturing associated with the passage of 

the longwall panel face stress abutment. 

Laboratory tests on coal measure shale and sandstone fragments 

showed that the stress-strain response of confned gob material 

follows an exponential hardening curve (Pappas and Mark, 1993). 

The tests were carried out on rock fragments that resembled a 

fully caved gob, having void ratios in the region of 30% to .0%. 

It was found that the stronger sandstone gob material had a stiffer 

response than the weaker shale material, as one would expect. A 

hyperbolic equation after Salamon (1990) was found to adequately 

represent the gob stress-strain behavior, which can be expressed 

as follows: 

a ×ε

σ = b − ε (3) 

where a and b are empirically derived parameters and E is the 

vertical strain. The b-parameter is related to the void ratio and the 

a-parameter is the gob stress when the strain is equal to b12. For 

shale gob, the laboratory tests (Pappas and Mark, 1993) showed 

that a = 7.65 MPa (1,110 psi) and b = 0...2, and for sandstone gob, 

a = 13.03 MPa (1,890 psi) and b = 0..27. 

Modeling Gob as a Strain Hardening Material 

Gob modeling can follow two approaches. In the frst 

approach, the intent may be to study roof fracturing, caving and 

gob development in response to mining. In this approach, it is 

necessary to explicitly model the gob formation process so that 

variations in geology and loading conditions can be studied. A 

second approach may be modeling of the effect of the gob on 

the surrounding coal mine entries and pillars. In the second 

situation, the gob is implicitly modeled; that is, the effect of the 

gob is modeled accurately so that the load redistribution to the 

surrounding rock and coal is correct and the large-scale overburden 

defection and subsidence is correct. This paper addresses the 

second scenario, in which rock fracture and gob development is not 

explicitly modeled, but the effect of the gob needs to be included in 

a model. 

When using the FLAC3D software, it is possible to simulate 

the effects of the fully-caved gob as a strain-hardening, granulated "

material using "double-yield elements. These elements can model 

the compaction of granulated materials under increased loading 

using a cap-plasticity criterion and have been successfully used to 

model gob compaction and response (Esterhuizen and Barczak, 

2006). Alternatively, when a large-scale model is set up, equivalent 

gob elements can be created by simply following the gob response 

curve without attempting to simulate the complex material behavior 

that forms the response curve (Board and Damjanac, 2003; 

Esterhuizen and Mark, 2009). 

All the model calibrations presented in this paper were done 

using equivalent gob elements that follow the hyperbolic stressstrain curves (Equation 3). The gob response to various depths of 

cover, mining geometries and overburden types was investigated. 
OVERBURDEN RESPONSE MODELING 

The defection and potential subsidence or collapse of the 

overburden has a signifcant impact on the load redistribution 

around coal mine panels. When full extraction mining is carried 

out, the overburden will settle onto the gob and stress will be 

regenerated in the mined area. The amount of stress regeneration 

depends on the gob stiffness as well as the stiffness of the 

overburden. Subsidence is also directly affected by the overburden 

properties and the panel width-to-depth ratio. Strong overburden 

strata can form a stable arch over a mined panel, which can result 

in signifcantly higher stress in the unmined coal while reducing the 

gob stress and magnitude of subsidence. The overburden stiffness 

also determines how stresses will be distributed over the unmined 

coal. Stiff overburden can be expected to transfer stress over a 

greater lateral distance than softer strata. When modeling the 

overburden, the characteristics of the overburden materials must 

be captured as accurately as possible to reproduce the observed 

response. The accuracy of the overburden models can be verifed 

against feld measurements of subsidence and of stress magnitudes 

in the coal surrounding mined panels. 

Modeling Bedded Strata 

The bedded overburden rocks were modeled using the strain 

softening, ubiquitous joint elements available in the FLAC3D 

software. These elements consist of a strain softening Coulomb 

material that represents the rock matrix and planes of weakness 

representing the bedding. The orientation and strength of the 

planes of weakness can be defned separately from the matrix 

properties and can also exhibit strain softening behavior. These 

elements allow a reasonable approximation of the characteristics of 

bedded strata to be made. 

For the purpose of model calibration, a suite of rock strengths 

and bedding types was created, which could be combined to 

model any rock type, from a strong limestone with no bedding 

weaknesses to a low strength shale or claystone with smooth 

bedding planes. The initial properties of the strata were based 

on extensive databases of rock properties available at NIOSH as 

well as published data (Zipf, 2007; Rusnak and Mark, 2000). The 

approach was to simulate the rock matrix without any bedding "

effects or "rock mass effects. The matrix strength of the in-situ 

rocks was determined from the laboratory scale strength using the 

relationship suggested by Hoek and Brown (1980): 

50 0.18 σ = σ 50 ( )

d (.)

where I 50 is the laboratory sample diameter in mm and d is the 

feld-scale sample diameter in mm. Assuming the laboratory 

sample size is nominally 50 mm (2 in), the strength of a 1,000 mm 

(. in) sample will be 0.58 times the laboratory sample size. 

Initial Stress 

The initial stresses in the models were defned to closely match 

the current understanding of stress in the coal measures in the 

United States. The pre-mining vertical stress is gravity driven and 

is determined by the depth of the overburden. The horizontal stress 

is also depth dependent, but there is a tectonic component that is 

caused by the movement of the North American plate (Zoback and 

Zoback, 1989; Dolinar, 2003; Mark and Gadde, 2008). According 

to current understanding, the tectonic component of the horizontal 

stress is higher in stiff strata than in softer strata (Dolinar, 2003). 

In the numerical models, the pre-mining horizontal stress is 

calculated in each layer of rock, depending on its modulus of 

elasticity. The following equations are used, after Mark and Gadde 

(2008), to calculate the maximum and minimum horizontal stress 

components in MPa units: 

σ h1 = 1.2σ v + 2.6 + 0.003E (5) 

σ h2 = 1.2σ v + 0.0015E (6) 

where E is the elastic modulus of the rock and I(v is the vertical 

overburden stress. 

OVERBURDEN AND GOB MODEL CALIBRATION 

Calibration of the models was carried out by simulating total 

extraction mining of panels at various depths of cover and with 

various excavation spans. The model results were compared 

to predicted and measured subsidence profles and empirically 

determined stress distributions from published case studies from 

around the United States. Correct modeling of the subsidence 

profle helps to confrm that the large-scale stiffness and 

deformation properties of the overburden and gob are reasonable. 

During the calibration stage, many combinations of rock strength 

properties and geometric scenarios were tested. Ultimately it 

was found that a single set of overburden material properties and 

gob properties could be used to obtain satisfactory agreement 

between model results and feld observations for modeling the 

large-scale rock mass response and pillar response around full 

extraction panels. 

Overburden Properties 

The rock strength, deformation properties, and bedding strength 

properties suggested for modeling large-scale coal measure rocks in 

the United States are presented in Table 1. These properties can 

be used for panel scale models, where a single element can include 

both intact rock and weak bedding planes. Element sizes in the 

overburden models typically varied between 5 and 10 m (16 and 33 

ft). Figure 5 shows a typical large-scale model that was used in the 

calibration exercises; the models always extended up to the ground 

surface and rock layering was modeled down to approximately 5-m 

(16-ft) bed thicknesses. Model element thickness varied between 

about 5 and 10 m (16 and 33 ft) in the proximity of the coal seam 

and was sometimes larger when modeling thick beds near the 

ground surface. 

The uniaxial compressive strength shown in Table 1 is the 

laboratory-scale strength, which was reduced by the 0.58 factor 

from Equation . to simulate the large-scale strength in the models. 

Strength reduction owing to strain softening was achieved by 

reducing the rock cohesion only; the friction component of the 
strength was not altered. The Poisson's ratio was set at 0.25 and 

tensile strength set to 10% of the large-scale rock compressive 

strength. Bedding tensile strength was set at 10% of the largescale rock tensile strength. The bedding friction angles may seem 

to be relatively low compared to small-scale laboratory test results. 

However, the presence of weak clayey materials, especially in shale 

beds, can have a signifcant impact on the overall shear resistance 

of a strata layer. The presence of moisture in these clayey materials 

can result in excess pore pressure when the rock stress increases 

and in reduced apparent friction angles. Field observations have 

shown that lateral sliding between beds can occur up to about 150 

m (.92 ft) ahead of a longwall face, which can partly be explained 

by the presence of low friction glide planes within the rock (Listak 

et al., 1987). When modeling the large-scale rock mass, it is 

necessary to include the effect of these weak planes in the rock 

mass strength. 

Table1. Representative rock properties. 

Rock type 

Limestone 1 

Laboratory sample In situ rock material In situ bedding planes 

UCS 

(MPa) 

1.0 

Elastic

modulus

(GPa) 

.0 

Friction

angle (deg)

.2 

Cohesion

(MPa)

18.93 

Tensile 

strength 

(MPa) 

8.12 

Dilation

angle

(deg) 

10 

Bedding 

friction 

angle (deg) 

Bedding 

cohesion 

(MPa) 

Bedding

tensile

strength 

(Mpa) 

32 9..7 6.50 

Limestone 2 100 35 .2 15.10 5.8 10 30 7.55 ..6. 

Limestone 3 80 30 .0 13.39 ..6. 10 28 6.70 3.71 

Sandstone 1 120 .0 .2 16.23 6.96 11 30 8.11 5.57 

Sandstone 2 100 .0 .0 13.52 5.8 12 30 6.76 ..6. 

Sandstone 3 80 35 37 12.08 ..6. 13 27 6.0. 0..6 

Sandstone . 60 35 35 9.06 3..8 1. 25 ..53 0.35 

Sandstone 5 .0 30 30 6.70 2.32 15 20 3.35 0.23 

Shale 1 80 25 32 1..78 ..6. 16 10 2.96 0..6 

Shale 2 60 20 30 12.18 3..8 17 7 2... 0.35 

Shale 3 .0 15 25 8.90 2.32 18 7 1.78 0.23 

Shale . 30 10 20 7.30 1.7. 19 7 0.50 0.17 

Shale 5 20 10 20 ..87 1.16 20 5 0.30 0.12 

Shale 6 10 5 20 2.66 0.58 21 5 0.20 0.06 

Shale 7 5 . 20 1.35 0.29 22 5 0.10 0.03 

i ed

pa el'

Figure 5. Example of a numerical model used to evaluate 

gob and overburden response. Layering represents different 

lithologies modeled. Gob is shown in green and unmined coal 

in dark blue. 

Mined

panels

Gob Properties 

The subsidence profle is useful for calibrating the gob 

compaction characteristics. The maximum subsidence over a 

super-critical panel (panel width exceeds 1.2 times the panel depth) 

can be used to verify the gob compaction assumptions. When a 

panel is super-critical, the full overburden weight is carried by 

the gob, and the resulting subsidence is directly related to gob 

compaction characteristics. The SDPS subsidence prediction 

software (Newman et al., 2001) was initially used to create a 

suite of subsidence curves for various super-critical longwall 

geometries and geologies. Final verifcation was done by modeling 

published feld trials and comparing the model results to actual 

subsidence measurements. 

It was found that the gob compaction characteristics depend 

on the type of rock material in the gob. Gob that consists of the 

stronger rock types is less compressible than the weaker gob 

materials. To assist in selecting the appropriate gob parameters, 

an approach similar to that followed by the authors of the SDPS 

software was followed, in which the "gob is characterized " by 

the ratio of the thickness of "strong to "weak rocks in the 

overburden. Weak rocks include shales and claystones that have 

a uniaxial compressive strength of less than about .0 MPa (5,802 

psi), while limestone, sandstones, and siltstones with strengths 

above .0 MPa (5,802 psi) would be classifed as strong rocks. 

Figure 6 shows the stress-strain behavior of the various gob 

materials used in the models. The fgure shows that the laboratory-
determined curves fall within the range of curves used in the 

models. Interestingly, the strong rock gob curve derived from fullscale subsidence is almost identical to the laboratory-determined 

curve for sandstone materials. Table 2 summarizes parameters for 

describing the gob curves using Equation 3 as used in the models. 

Table 2. Parameters for modeling various gob types using 

Equation 3. 

Overburden 

type 

Ratio of 

strong: weak 

rocks 

a

parameter

(MPa) 

b

parameter

Weak 25% 5.9 0... 

Moderate 35% 8.6 0... 

Strong 50% 12.8 0... 

Very strong 65% 25.2 0... 

 

 

 

 25 

30 

35 

15 

10 

5 

Stress (MpaI 20 

0 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 

Strain

Figure 6. Stress-strain curves for gob materials determined 

through model calibration and results of laboratory tests on gob 

materials, after Pappas and Mark (1998). 

Very strong overburden

Strong overburden

Moderate overburden

Weak overburden

Laboratory test sandstone

Laboratory test shale

VERIFICATION OF CALIBRATED MODELS 

After completing the calibration exercises, a number of the 

case histories that were used for calibration were re-evaluated 

using the fnal set of input parameters and modeling technique. 

Three examples are presented here showing a variety of longwall 

mining and pillar extraction scenarios. The frst example shows 

stress and subsidence results for a supercritical longwall panel 

under relatively weak overburden strata, typical of the Northern 

Appalachian coal felds. The second is a sub-critical longwall 

panel under strong strata found in the western United States. The 

third compares monitoring of pillar stress adjacent to a longwall 

with strong overburden strata. 

Supercritical Longwall Panel 

The frst model simulates a longwall in the Pittsburgh seam 

where detailed subsidence measurements have been made 

(Zimmerman and Fritschen, 2007). The depth of cover is 180 m 

(591 ft) and the panel width is 350 m (1,1.8 ft) with a three-entry 

gate road system. The chain pillars were 2.-m (79 ft) wide and the 

mining height was 1.7 m (5.6 ft). 

The chain pillars, the solid abutments, and the gob were modeled 

using the equivalent pillar approach (Esterhuizen and Mark, 2009) 

in which model elements are prescribed to follow the stress-strain 

relationships of the pillars, gob, and abutment edges. The pillars 

were specifed to follow the stress-strain relationships derived from 

numerical models, using the approach described in this paper. The 

gob was modeled as a weak material associated with 25% strong 

overburden, using the parameters listed in Table 2. The overburden 

in this area consists of alternating layers of shale, siltstone, 

sandstone, and limestone. The limestone is typically strong and 

massive with poorly developed bedding planes. The limestone 

was modeled without any weak bedding planes, but vertical joints 

were included. The extraction of the longwall was modeled by 

extracting the coal elements and replacing them with gob elements 

and allowing the overburden to settle onto the gob. The model 

results were evaluated against the measured surface subsidence and 

empirical predictions of the likely extent of the abutment stress and 

the stress distribution in the chain pillars. 

The subsidence results are presented in Figure 7, which 

shows that excellent agreement is achieved between the vertical 

displacements in the model and subsidence measurements. 

350 450 550 650 

Distance (mI 

Field mea'ureme t'

Locatio of lo g_all pa el 

50 

0.2 

250

0.0 

-0.2 

-0.4 

-0.6 

Subsidence (mI -0.8 

-1.0 

-1.2 

-1.4 

Figure 7. Comparison of model subsidence results and feld 

measurements for a supercritical panel in the Pittsburgh 

coal bed. Subsidence measurements after Zimmerman and 

Fritschen (2007). 

7

Model results

This 

confrms that the gob compaction curve is realistic, since the 

maximum subsidence agrees with observations. In addition, the 

curvature of the overburden at the edges of the subsidence trough 

and the location of the subsidence trough relative to the edge of 

the longwall panel are satisfactory. This indicates that the largescale stiffness and deformation of the overburden is modeled with 

suffcient accuracy. 

The stress distribution on the mining horizon, determined from 

the model results and from the Mark's (1987) empirical equation 

is shown in Figure 8. The columns showing the model results are 

12-m (39-ft) wide, representing the width of the elements. The 

results show that the extent of the abutment zone extends about 72 

m (236 ft) away from the edge of the gob, which is the same as 

the value predicted by the empirical equation of Peng and Chiang 

(198.). The empirical curve predicts the average stress on the 

2.-m-wide chain pillar marked 'A' in Figure 8 to be 23.6 MPa 

(3,.22.9 psi) while the model result is 22.7 MPa (3,292.. psi), 

which is a satisfactory outcome. The results for the second chain 
pillar, marked 'B' in Figure 8, differ by a greater amount; mainly 

because the empirical equation does not take into account the fact 

that this pillar is adjacent to the stiffer unmined abutment and 

assumes the pillar carries the full tributary loading. 

 

30.0 

10.0 

20.0 

25.0 

15.0 

Stress :Qa)

5.0 

0.0 

169158

146134123111

-99-88-76-64-52-41

-29-17

6

6

183042546678

90

102114126138150162174 

Distance from e"ge of panel m)

Figure 8. Comparison of empirical and numerical model 

derived stress distribution on the seam level for a 350 m (1,150 ft) 

wide longwall at 180 m (600 ft) depth of cover in the Pittsburgh 

coal bed. 

Gob stress

Chain pillar B

Chain pillar A

Numerical model results

Empirical equation

Solid abutment

The results show that for this test case, the developed input 

parameters for modeling the coal pillar, overburden and gob 

performed very satisfactorily against the measured subsidence and 

expected stress distributions on the coal seam. 

Subsidence Over a Sub-Critical Longwall Panel 

The second example shows numerical model results for a 

longwall in strong overburden in central Utah. The subsidence 

was measured during the mining of a number of longwall panels 

(Allgaier, 1988). The average depth of cover was about .50 m 

(1,.76 ft) and the average mining height was 3 m (10 ft) in the 

Blind Canyon coal bed. The subsidence related to the frst two 

panels, panel 5E and 6E, of a series of four longwall panels was 

selected for analysis. The panel widths were 1.6 and 16. m (.79 

and 538 ft) for the 5E and 6E panels respectively. The panels were 

separated by two rows of small chain pillars that had a widthto-height ratio of 3.2 and are considered to be yield pillars. The 

general geology is described as sandstones in thick beds and 

sandstone interbedded with siltstone. It is estimated that .5% of 

the overburden consists of sandstone. 

Subsidence monitoring revealed vertical displacements of only 

about 60 mm (2.. in) after mining the frst panel as shown in Figure 

9. 

0.00 

-0.20 

-0.40

-0.60 

Measured firstpa_el

Modelfirst pa_el

Measured seco_d pa_el 

Modelseco_d pa_el 

Firstpa_el seco_d pa_el 

S:bsi"ence m) -0.80

-1.00

-1.20

-1.40

-1.60 

0 100 200 300 400 500 600 700 800 900 1000 

Distance (m) 

Figure 9. Comparison of model subsidence results and feld 

measurements for two subcritical panels in a Utah coal mine. 

Subsidence measurements after Allgaier (1988). 

The panel width-to-depth ratio was 0.32, which is highly subcritical; therefore, the subsidence probably only refected the 

elastic defection of the strata. After mining the second panel, a 

subsidence trough developed with a maximum subsidence of just 

over 1.0 m (3.3 ft) that was centered over the frst panel (see Figure 

9). The location of the yield pillars between the two panels was not 

visible in the subsidence curve. The width-to-depth ratio of the two 

panels and the intervening yield pillars was 0.75, which is still subcritical. 

The two longwalls and the overburden geology were modeled 

by simulating the published geologic profle using the calibrated 

set of input parameters for the overburden and gob. Sandstone 

strengths were set at 100 MPa (1.,50. psi) and interbedded 

siltstone and sandstone materials were modeled with strengths 

between 60 MPa (702 psi) and 80 MPa (11,603 psi). The longwall 

extraction was modeled in stages with the coal being removed and 

replaced by strong gob properties, shown in Table 2. Subsidence 

results were obtained after mining of the frst panel and the second 

panel. The results are also presented in Figure 9, which shows 

that for frst-panel mining, the model results are very similar to 

the feld measurements. The displacements are small, refecting 

elastic displacement of the ground surface. Overburden failure and 

shearing along bedding planes was limited to the lower half of the 

model, with the upper rocks being undisturbed in terms of shearing 

or failure. After mining the second panel, the failure progressed up 

to the ground surface and the subsidence increased considerably, to 

a maximum of 1.16 m (3.81 ft), nearly symmetrically located over 

the mined area. The subsidence profle in the model also shows 

no sign of the yield pillars between the two panels, similar to 

the measurements. 

The shape of the subsidence curve is satisfactory from the point 

of view of providing a reasonable agreement with the extent and 

maximum subsidence. More importantly, however, the modeled 

overburden responded correctly by arching over the frst panel, 

resulting in negligible subsidence, and then subsiding to about 

1 m (3.3 ft) when the second panel was extracted. This outcome 

demonstrates that the overburden modeling approach is reasonable, 

and it is able to capture the initial arching of the strata over the frst 

panel, followed by the failure of the arch when the second panel 

was mined. 

Pillar Stress Case Study in Strong Rock 

The third case study presents a comparison of numerical model 

results to in-mine stress measurements in strong overburden strata. 

The stress changes, cable bolt performance, and entry deformations 

were monitored in a yield-abutment pillar system in the Hiawatha 

seam at the Crandall Canyon mine in Utah (Koehler et al., 1996). 

Two longwall panels at depths of cover of 396 m to .57 m (1,299 

to 1,.99 ft) were separated by a 9.1- (30-ft) wide yield pillar and 

a 36.6-m-wide abutment pillar. The longwall panels were overlain 

by strong sandstone and siltstone with occasional thin shale bands. 
The strength of the roof strata generally fall between 69 Mpa 

(10,008 psi) and 138 MPa (20,015 psi), and several less competent 

zones with strengths below 50 MPa (7,252 psi) were reported. 

Monitoring results showed that the peak abutment stress of .5-

50 MPa (6,527-7,252 psi) was located very near the edge of the 

abutment pillar, and there was a rapid drop off over about half the 

abutment pillar width, unlike the gradual decay one would expect 

from the Mark's (1987) empirical equation. 

A numerical model was created that simulated the mining of the 

two panels, again using the equivalent pillar approach to model 

the pillars adjacent to the panels. The gob was modeled using the 

strong rock parameters in Table 2, and the overburden was modeled 

using the higher strength rock types in Table 1, interspersed with 

thin bands of weaker materials. The massive Castlegate sandstone 

in the upper part of the geologic profle was also included in 

the model. 

Figure 10 shows the stress distribution predicted by the model 

and measured underground after the frst longwall had mined past 

the monitoring site by about 260 m (85. ft) and the pillar system 

was subject to side loading from the frst gob. 

 

 

50.0 

45.0 

40.0 

35.0 

30.0 

25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

Field mea'ureme t' 

Numerical model re'ult' 

-10 10 30 46 58 4 3 112 131 150 16 188 20 226 245 264 283 302 322 

Di'ta ce from edge of pa el m 

Stre''

7

Figure 10. Comparison of numerical model results and feld 

measurements of the stress at the edge of a longwall panel in the 

Western United States, after Koehler et al. (1996). (Mpa)

Abutment 

pillar

Yield pillar

Overburden stress

It can be seen that 

the measurements show a peak stress of .8 MPa (6,962 psi), which 

drops down very rapidly to less than 20 MPa (2,901 psi) within 

the 36-m (118 ft) wide abutment pillar. The model results show 

a similar pattern of high stress, an average of 3. MPa (.,931 psi) 

in the portion of the pillar nearest the gob, dropping down to 17 

MPa (7,252 psi) away from the gob. The yield pillar in the model 

yielded to a greater degree than the observations. This might be 

explained by the fact that the coal in the model was assumed to 

have a uniaxial compressive strength of 20 MPa (2,901 psi), while 

laboratory tests indicated that the coal at this mine was likely 

to be about 30 MPa (.,351 psi). The model stress results for the 

solid abutment is similar to the measured results. It is interesting 

to note that the model shows a long tail to the stress decay, which 

can explain the fact that forward abutment pressures were identifed 

by the monitoring instruments up to 87 m (285 ft) ahead of the 

longwall face. 

This case study shows that the model parameters can also 

provide satisfactory results for evaluating stress changes in 

longwall panels under stiff overburden. Although no subsidence 

data was available for this case, the model showed a dish shaped 

subsidence bowl forming over the two longwall panels, and the 

expression of the yield-abutment pillar system was not visible on 

the surface, which indicates that the strata were likely arching over 

the two panels. 

The outcome of the third case study was again very satisfactory, 

showing that the input parameters and modeling approach is able 

to capture the stress distribution in both a weak rock scenario, 

shown in the frst case study, as well as this strong rock scenario. 

The good agreement with measured stresses in the pillars is further 

verifcation that the numerical models are performing satisfactorily. 

CONCLUSIONS 

Modeling the large-scale response of coal measure rocks due 

to mining can be satisfactorily achieved using well-calibrated 

numerical models, provided the main characteristics of the coal 

pillars, the overburden, and the gob are captured in the models. 

This paper demonstrates how the FLAC3D software was used to 

obtain a base set of input parameters that can be used to evaluate 

the stress and deformation associated with mining in a variety of 

geological conditions, ranging from super-critical panels in weak 

overburden to sub-critical panels in strong rocks. 

The calibration process described had the objective to obtain 

good agreement between model results and pillar strength, surface 

subsidence, and in-seam stress distributions. The models of 

individual pillars were calibrated against strong roof and foor case 

histories in which the pillar strength is governed by failure and 

yielding of the coal within the pillar and the strong surrounding 

strata had a limited impact on pillar strength. Subsidence matching 

assisted in verifying that the large-scale rock mass parameters 

and the gob compaction characteristics are realistic. Further 

calibration was carried out against stress measurements in coal 

pillars and in the unmined coal abutments. Good agreement was 

achieved between model results and actual measurements, which 

demonstrated that the interaction between the pillars and the 

surrounding strata was adequately captured in the models. 

The paper provides a basic set of input data and a modeling 

approach that can be used for numerical modeling investigations 

of various coal mine designs using the FLAC3D software 

package. The models can be expected to provide realistic stress 

and deformation results, but further calibration would be required 

to determine the relationship between model results and actual 

mining conditions. 

The model parameters presented are applicable for the 

FLAC3D software package. The parameters will be useful as 

initial estimates when using other modeling techniques, but each 

technique should be calibrated independently. 

DISCLAIMER 

The fndings and conclusions in this paper have not been 

formally disseminated by the National Institute for Occupational 

Safety and Health and should not be construed to represent any 

agency determination or policy. 
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