IC 9512

INFORMATION CIRCULAR/2009

Proceedings of the International Workshop 

on Numerical Modeling for 

Underground Mine Excavation Design 

Department of Health and Human Services 

Centers for Disease Control and Prevention

National Institute for Occupational Safety and Health
 

Information Circular 9512 

Proceedings of the International Workshop on 

Numerical Modeling for Underground Mine Excavation Design 

Edited by Gabriel S. Esterhuizen, Ph.D., Christopher Mark, Ph.D., P.E., Ted M. Klemetti, 

and Robert J. Tuchman 

DEPARTMENT OF HEALTH AND HUMAN SERVICES 

Centers for Disease Control and Prevention 

National Institute for Occupational Safety and Health
 

Pittsburgh Research Laboratory 

Pittsburgh, PA 

June 2009 
 

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DHHS (NIOSH) Publication No. 2009–141 

June 2009 

SAFER • HEALTHIER • PEOPLETM 
CONTENTS
 

Page

Abstract......................................................................................................................................................... 1 

An efficient approach to numerical simulation of coal mine-related geotechnical issues, 

 by D. P. Adhikary and H. Guo.................................................................................................................. 3 

A review of recent experience in modeling of caving, by M. Board and M. E. Pierce .............................. 19 

Characterization of natural fragmentation using a discrete fracture network approach and implications 

 for current rock mass classification systems, by D. Elmo, S. Rogers, and D. Kennard.......................... 29 

Three-dimensional modeling of large arrays of pillars for coal mine design, by G. S. Esterhuizen 

 and C. Mark ............................................................................................................................................ 37 

Numerical model evaluation of floor-bearing capacity in coal mines, by M. M. Gadde............................ 47 

It is better to be approximately right than precisely wrong: why simple models work in mining 

 geomechanics, by R. E. Hammah and J. H. Curran................................................................................ 55 

An overview of calibrating and using the LaModel program for coal mine design, by K. A. Heasley...... 63 

Deep coal longwall panel design for strong strata: the influence of software choice on results, 

 by M. K. Larson and J. K. Whyatt .......................................................................................................... 75 

Practical application of numerical modeling for the study of sudden floor heave failure mechanisms, 

 by H. Maleki, C. Stewart, R. Stone, and J. Abshire................................................................................ 89 

Advanced numerical solutions for strata control in mining, by A. Studeny and C. Scior ........................ 101 
 

UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT 

ft

GPa 

in

kg/m3

km 

km2

kPa 

L/s 

lb/ft3

m

2

m

3 m

m3/t 

m/sec 

md 

mm 

MPa 

Mt 

Mtpa 

Pa

psi 

tpd 

 foot 

gigapascal 

 inch 

 kilogram per cubic meter 

 kilometer 

 square kilometer 

kilopascal 

 liter per second 

 pound per cubic foot 

 meter 

 square meter 

 cubic meter 

 cubic meter per ton 

 meter per second 

 millidarcy 

 millimeter 

 megapascal 

 million tons 

 million tons per annum 

 pascal 

 pound-force per square inch 

 tons per day 
 

 

 

PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON 

NUMERICAL MODELING FOR UNDERGROUND 

MINE EXCAVATION DESIGN 

Edited by Gabriel S. Esterhuizen, Ph.D.,1

 1

Senior research engineer, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, 

Pittsburgh, PA.

Christopher Mark, Ph.D., P.E.,2

2

Principal research engineer, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, 

Pittsburgh, PA.

Ted M. Klemetti,3 

 3

Research engineer, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, 

Pittsburgh, PA.

and Robert J. Tuchman4 

4

Technical writer-editor, Writer-Editor Services Branch, Division of Creative Services, National Center for Health 

Marketing, Coordinating Center for Health Information and Service, Centers for Disease Control and Prevention, 

Pittsburgh, PA. 

1
 

ABSTRACT 

Numerical models play a significant role in the design of safe underground mining excavations 

and support systems. Advances in the capabilities of numerical modeling software, together with ever 

increasing computational speeds, have made it possible to investigate the very nature of the large-scale 

rock mass and its response to mining excavations. The improved understanding of the rock response 

obtained from modeling enhances our designs, resulting in greater stability and safety of the mining 

excavations. To help advance the state of the art in this field, the National Institute for Occupational 

Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine 

Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 

43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics 

and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers 

address a wide range of issues, including various numerical modeling approaches, rock mass modeling, 

and applications in coal and metal mines. 

 

 

 

AN EFFICIENT APPROACH TO NUMERICAL SIMULATION OF COAL MINE-RELATED
 

GEOTECHNICAL ISSUES 

By D. P. Adhikary, Ph.D.,1

 and H. Guo, Ph.D.1 

1

CSIRO Exploration and Mining, Australia. 

ABSTRACT 

Reliable prediction of mine stability, surface subsidence, mine water inflow, and mine gas emissions is essential not only for improving mine safety and reducing coal 

production costs, but also for assessing and managing the 

environmental impact of mining. 

This paper describes an integrated approach to simulation and prediction of mining-induced surface subsidence, 

mine groundwater inflow, aquifer interference, and mine 

gas emission. It involves a combination of site geological, 

geotechnical, and hydrogeological characterization; study 

of surface subsidence and subsurface rock caving mechanisms; monitoring of pore pressure changes of the surrounding strata, mine water inflows, and mine gas 

emission; and three-dimensional (3-D) numerical modeling. Central to this integrated approach is a 3-D computer 

code called COSFLOW developed by CSIRO Exploration 

and Mining of Australia in collaboration with NEDO and 

JCOAL of Japan to address the coal mine-related issues. 

COSFLOW incorporates unique features (e.g., Cosserat 

continuum formulation) that make it ideal for simulating 

coal mining-related issues and examining the interaction 

between rock fracture, aquifer interference and water flow, 

and gas emission. 

INTRODUCTION 

Mine subsidence is becoming a major issue of 

community concern. Mining-induced subsidence can 

significantly affect mining costs where major surface 

facilities and natural environments need to be protected. 

Longwall mining has been undertaken under important 

surface structures such as river systems, gorges, cliffs, 

power lines, pipelines, communication cables, major roads, 

and bridges. 

Similarly, the ability to accurately predict the behavior 

of water in longwall operations has become a pressing 

issue. While higher-capacity longwall mines are putting 

pressure on dewatering requirements, environmental concerns about loss of water supply overshadow many mines. 

In the future, environmental water issues, associated with 

major aquifers, could affect a mine’s ability to gain mining 

approval. 

As the mines are getting deeper and gassier, prediction 

and management of mine gas-related issues are becoming 

increasingly important. 

Over the last 6 years, CSIRO Exploration and Mining 

has been involved in developing an integrated approach to 

predict the impact of mining on surface subsidence, 

subsurface aquifers, mine water inflow into underground 

coal mines, and mine gas emission. It involves a combination of site geotechnical and hydrogeological characterization, study of surface subsidence and subsurface rock 

caving mechanisms, monitoring of pore pressure changes 

of the surrounding strata, mine water inflows, mine gas 

emission, and 3-D modeling. 

This paper introduces the integrated approach and the 

3-D finite-element code called COSFLOW, which was 

developed to address longwall coal mine-related issues. 

COSFLOW was developed as a result of a major joint 

project between CSIRO (Australia) and NEDO and 

JCOAL (Japan). 

A unique feature of COSFLOW is the incorporation of 

Cosserat continuum theory [Adhikary and Dyskin 1997] in 

its formulation. In the Cosserat model, interlayer interfaces 

(joints, bedding planes) are considered to be smeared 

across the mass, i.e., the effects of interfaces are incorporated implicitly in the choice of stress-strain model 

formulation. An important feature of the Cosserat model is 

that it incorporates bending rigidity of individual layers in 

its formulation, which makes it different (and more efficient in simulating stratified strata) from other conventional implicit models. 

SITE CHARACTERIZATION 

The CSIRO approach to assessing the impact of mining on subsurface aquifers and mine water inflow into 

underground coal mines involves a combination of 3-D 

geological, geotechnical, and hydrogeological site characterization, study of surface subsidence and subsurface rock 

caving mechanisms, monitoring of pore pressure changes 

of the surrounding strata and underground water inflows, 

mine gas emissions, and 3-D numerical modeling. The 

work carried out is described in Guo et al. [2002, 2003a] 

and Adhikary et al. [2004]. This section briefly describes 

the site characterization. 

The 3-D site geotechnical and hydrogeological characterization typically includes: 

(1) Collection of available regional and site-specific 

hydrogeological data; 

3
 
 

 

 

 

 

 

(2) Dedicated drilling program	 with geological and 

geophysical logging for all drillholes; 

(3) In situ stress and strata permeability measurements; 

(4) Laboratory testing of rock and coal strengths; 

(5) Automatic drillhole geotechnical interpretation; 

(6) Two-dimensional (2-D) and 3-D seismic surveys 

(where applicable); 

(7) Field geotechnical and hydrogeological monitoring 

(surface piezometric and extensometer monitoring, 

and underground water inflow (gas emission) 

measurements); and 

(8) In situ 3-D geological, geotechnical, hydrogeological, and gas models. 

CSIRO has been actively involved in such site 

characterization studies, including planning, organization, 

testing, data interpretation, and preparation of a site hydrogeological and geotechnical conceptual models. Figure 1 

shows an example of a modeled stratigraphy from a deep 

mining study at a site in New South Wales, Australia [Guo 

et al. 2003b]. 

Surface

Legend

Mine plan

Sandstone

Sandstone/siltstone

Siltstone

Mudstone

Mudstone/siltstone

Coal

 

Surface 

Mine plan 

Sandstone/siltstone

Mudstone/siltstone

-

-

Legend 

Sandstone 

Siltstone 

Mudstone 

-

Coal

 Figure 1.—Perspective view of 3-D geotechnical model of 

a mine site in New South Wales, Australia, looking from the 

southwest (an area of 5 km by 6 km modeled with depth ranging from 200 to 600 m; colors represent various strata units). 

For the past 5 years, CSIRO has conducted site monitoring, data interpretation, and numerical modeling work at 

Springvale Mine to predict water inflow into its longwall 

panels. Springvale currently mines the 12th longwall 

block, extracting the lower 3.2-m section of the 7-m 

Lidsdale/Lithgow Seam, 360 m below the Newnes Plateau. 

At an average production rate of 2.75 Mtpa, the projected 

mine life is 25 years [Knight and Miller 2005]. 

As part of site hydrogeological characterization at the 

Springvale Mine, CSIRO analyzed the geophysical 

drillhole data. Density, natural gamma, and sonic velocity 

logs were interpreted using the CSIRO/CMTE computer 

program LogTrans to obtain detailed strata classification. 

The interpretation involved the following key steps: 

(1) Detailed analysis of key control cored holes where 

geological logs and core photographs were 

available; 

(2) Statistical characterization of the geophysical signatures of these geological units using LogTrans; 

and 

(3) Automatic computer interpretation of geophysical 

logs of other open holes for geological units using 

the identified geophysical signatures. 

A verification (or training) of LogTrans against the 

existing geological data is the first step in automated strata 

interpretation. A careful verification exercise was conducted using the geological and geophysical data from 

three control drillholes. In the second step, LogTrans was 

used to interpret the remaining drillholes. Figure 2 shows 

LogTrans interpretations of geophysical data from five 

drillholes. 

Figure 2.—LogTrans interpretation of Springvale Mine data, 

to 50 m above the mining seam (SPRxx denotes the Springvale borehole number) (after Guo et al. [2002]). 

As an integral part of the site study, piezometric 

monitoring of the surrounding strata during mining was 

carried out to assess groundwater response to mining. A 

total of 26 piezometers were installed at different horizons 

in 8 boreholes (Figure 3). A typical groundwater pressure 

response is shown in Figure 4. Such a response verifies the 

existence of the aquifer, and the water pressure change 

also provides essential input data to the subsequent 

coupled numerical modeling with COSFLOW. 

4 
1000 

1150 

LEGEND AQ5 SPR32#1 SPR32 

1100 SPR33 AQ4 SPR33#1 

SPR34 SPR31#8
 AQ4 

SPR26
 

AQ4 SPR26#2 

AQ3 

SPR27 AQ3 SPR32#2 SPR33#2 1050 SPR31#7 SPR29 AQ3

SPR35
 

SPR31
 

Elevation head (m) 

Do not 

fit with 

other data SPR33#3 SPR34#1

SPR32#3 AQ2

affected by AQ2 AQ2 

950 Extensively SPR31#6 

mining SPR31#5 SPR32#4 

SPR33#4 

900 AQ1 AQ1 SPR29#1 AQ1 SPR35#1 AQ1 SPR27#1 SPR35#2 

SPR26#1 SPR31#4 SPR34#2 850 SPR31#3 

SPR31#2 

AQ1 SPR31#1 800 

Figure 3.—Aquifer delineation on the basis of piezometer 

data (after Knight and Miller [2005]). 

100 

90 

80 

70 

P1 Water head 

P2 Water head 

P3 water head 

P4 water head 

P5 water head 

P6 water head 

P7 water head 

60 P8 water head

50 

40 

30 

20 

10 

0 

-500 -400 -300 -200 -100 0 100 200 300 400 500 

Relative longwall position (m) 

Figure 4.—Piezometer readings at SPR31; note the drop in piezometric pressures as the longwall face approached the 

borehole location (after Guo et al. [2006]). 

Water head (m) 

The next step in the mining impact assessment is to 

develop a conceptual hydrogeological model with proper

delineation of aquifers and aquitards. On the basis of local 

geology and the piezometric results, CSIRO has developed

a conceptual hydrogeological model (Figure 5) for the

mine (see Knight and Miller [2005]). Five distinctive aquifers (AQ1 to AQ4) separated by low-permeability layers

(aquitards) were identified.

LONGWALL MINING-INDUCED GROUND 

DEFORMATION

 A number of researchers have investigated the

mechanics of strata deformation induced by longwall mining. These studies have recognized four distinctive deformation zones in the overburden rock (Figure 6). Although

5 
terminology is not precise, they can be typically 

described (in order of increasing height above the mining seam) as: 

(1) A caving zone with broken blocks of rock detached from the roof (less than 10 times the 

extraction height, probably about 3–5 times the 

extraction height); 

(2) A disturbed or fractured zone where the rocks have 

sagged downward and consequently suffered 

bending, fracturing, joint opening, and bed 

separation (about 15–40 times the extraction 

height); 

(3) A constrained zone where the strata have sagged 

slightly over the panel without suffering significant 

fracturing or alteration to the original geomechanical properties (variable thickness); and 

(4) A surface zone with tensile fracturing (up to 20 m 

thick). 

AQ1

AQ2

AQ3

AQ4

AQ5

 on

n

 

 

 

???

AQ2

 

 

 

 

Identification of aquifers 

at Mine A	 Hydrogeological model adopted 

in the numerical simulation 

0.0

33.0

50.0

91.0

209.0

286.0

294.0

224.0

364.0

Height above the mining seam (m)

???

???

???

150.0

209.0

0

-50

-100

-150

-200

-250

-300

-350

-400

-450

Head Formation

Middle River Seam

Long Swamp Formati

Lidsdale/Lithgow

Marrangaroo Formatio

Berry Siltstone

Denman Formation

-9.0

Mining seam

0.0 

33.0 

50.0 

91.0 

209.0

286.0 

294.0 

224.0 

364.0 

AQ1 

AQ2 

AQ3 

AQ4 

AQ5 

Height above the mining seam (m) 

??? 

??? 

??? 

150.0 

209.0 

0 

-50 

-100 

-150 

-200 

-250 

-300 

-350 

-400 

-450 

Head Formation 

Middle River Seam 

Long Swam p Form ation 

Lidsdale/Lithgow 

Marrangaroo Formation 

Berry Siltstone 

Denman Formation 

-9.0 

??? 

AQ2 

Mining seam 

In-situ water head = 12m Top 

Needs further measurement 

-20.0 

33.0 

40.0 

224.0 

AQ1 

AQ2 

AQ3 

150.0 

165.0 

0.0 

Very limited information is 

available and needs further 

measurement Banks wall 

Sandstone 

In-situ water head = 58m unit5 

Mt York 

Claystone 

Burra Moko 

unit4 

Needs further measurement Katoomba + 

unit3 

Gap In-situ water head = 98m Sandstone 

unit2 

Irondale Seam unit1 

In-situ water head = 123m Mining seam Seam Needs further measurement Floor 

Base 

Figure 5.—A conceptual hydrogeological model for Springvale Mine (after Knight and Miller [2005]). Caved zone (3t 5t) Fractured zone (15t-40t) Constra ned zone Surface Zone with Tensile fractures (up to 20m) t mnng height Surface Caved Fractured Constrained Zone with

-

– i i

zone(3t-5t) 

zone (15t-40t) 

zone Tensile fractures 

(up to 20m) t –mining height Panel width 

Figure 6.—Deformation zones induced by longwall mining. 

The vertical extent of each of these zones is variable 

and depends on many factors (e.g., longwall width, extraction height, overburden rock properties, local geology, and 

depth of cover). The permeability of rock strata within the 

first two zones can significantly increase and, as a result, 

6 
water from aquifers located within these two zones may be 

drawn into the mining panels. 

COSFLOW FORMULATION 

This section describes some important aspects of the 

3-D finite-element code COSFLOW. Here we provide a 

loosely coupled mechanical and two-phase fluid flow 

formulation, where the mechanical equations and fluid 

flow equations are solved sequentially. Such an approach 

of solving a coupled mechanical and two-phase fluid flow 

problem is widely used in the scientific community 

[Rutqvist et al. 2002]. In such an approach, mechanical 

effects are assumed to occur almost instantaneously when 

compared to diffusion effects. In COSFLOW, sequential 

cycling between fluid flow steps and mechanical steps is 

controlled through a limiting parameter that would switch 

off the fluid flow steps and start the mechanical steps once 

the maximum change in average pore pressure within the 

model exceeds the value set by the limiting parameter. 

A unique feature of COSFLOW is the incorporation of 

Cosserat continuum theory [Cosserat and Cosserat 1909] 

in its formulation. In the Cosserat model, interlayer interfaces (joints, bedding planes) are considered to be smeared 

across the mass, i.e., the effects of interfaces are incorporated implicitly in the choice of stress-strain model 

formulation. An important feature of the Cosserat model is 

that it incorporates bending rigidity of individual layers in 

its formulation, which makes it different from other conventional implicit models. 

The flow of either phase of fluid is controlled by the 

permeability of the porous medium, which remains a 

highly nonlinear function of mining-induced stress and 

resulting fractures. Thus, in order to be able to correctly 

estimate water inflow or gas emission, it is important not 

only to estimate the initial permeability correctly, but also 

to compute its variation during mining. In this code, 

permeability change during mining is computed as a function of the mining-induced strain. 

Mechanical (Cosserat) Model 

Coal measure rocks are essentially stratified in nature. 

Since stratified rock masses exhibit highly anisotropic 

strength and deformation characteristics, it is necessary to 

include effects of stratification into the mathematical formulations describing the load deformation behavior of 

such rock masses. 

There are essentially two different approaches that can 

be adopted in simulating the load deformation behavior of 

stratified rock masses. Firstly, the layered medium can be 

defined in a discontinuum manner (i.e., discrete modeling) 

such that each and every joint and intact layer is discretely 

defined in numerical simulation. However, when closely 

spaced joints occur in large numbers such that the layer 

thickness becomes much smaller than the dimensions of 

the problem region, the discrete modeling of such a 

medium becomes tedious and expensive to perform. The 

only feasible and elective way of incorporating the influence of such a system of joints in the analysis is to 

formulate an equivalent model within the framework of 

continuum mechanics with an appropriate constitutive 

relationship. 

A continuum description of a layered medium can be 

formulated as long as consistency and statistical 

homogeneity in joint properties and spacing can be 

established. Such a continuum model provides a largescale (average) description of the material response to 

loading. The continuum model devised in such a manner is 

often known as a smeared (implicit) joint model in the 

sense that the joints are implicit in the choice of the stressstrain relationship adopted for the equivalent continuum. 

A distinctive advantage of the smeared joint model is that 

in a numerical (e.g., finite-element) solution, the problem 

region can now be discretized with a coarser mesh (i.e., 

subdivided into fewer finite elements) than in the discrete 

models, where the size of the finite elements cannot exceed the layer thickness. Thus, in smeared joint models, 

the size of the elements is dictated solely by computational 

needs rather than by the layer thickness. 

In the models based on the conventional equivalent 

continuum approach, the layered material is replaced with 

a homogeneous anisotropic medium characterized by the 

so-called effective elastic moduli comprising the heterogeneity of the medium. The methods of computing the 

effective characteristics for layered media were first proposed by Lifshitz and Rosenzweig [1946, 1951] for arbitrary anisotropic materials of the layers, then by Salamon 

[1968] for the case of transversely isotropic layers and 

Gerrard [1982] for the orthotropic layers. If sliding 

between the layers can occur during the deformation 

process, the equivalent continuum should be viewed as a 

continuum of elastoplastic type (e.g., Zienkiewicz and 

Pande [1977]; Gerrard and Pande [1985]; Alehossein and 

Carter [1990]). Such equivalent continuum models may 

provide reasonably accurate predictions when joint slips 

are minimal, i.e., the layer bending can be neglected. 

However, when the joint slips are large and the layers can 

bend as they slip against each other, models based on such 

conventional continuum models may considerably overestimate the deformation since the bending rigidity of the 

layers are not incorporated in the model formulation. 

In the case of rock layers with bending stiffness, an 

equivalent continuum model can be formulated successfully on the basis of Cosserat theory [Adhikary and Guo 

2002; Adhikary and Dyskin 1997, 1998]. Adhikary and 

Dyskin [1997] provide a thorough analysis and comparison 

between the conventional equivalent continuum and the 

Cosserat continuum models. 

Whereas the conventional continuum model has 

3 independent degrees of freedom and 6 independent stress 

components in a 3-D case, the Cosserat model for the 

7 
stratified material will have 6 independent degrees of freedom and 10 independent stress components. 

The layer interfaces can exhibit three different modes 

of behavior: (1) elastically connected with the interface 

normal and shear stiffness, (2) plastic with frictional sliding, and (3) disconnected with tensile opening. Similarly, 

the rock layer may either deform elastically or may sustain 

some plastic deformation as well. A description of the full 

elastoplastic Cosserat formulation is provided by Adhikary 

et al. [2002]. For simplicity, a 2-D plane strain Cosserat 

formulation will be presented in this paper. Using the 

Cartesian coordinates (x1,x2) in two dimensions, the 

material point displacement can be defined by a translational vector (u1,u2) and by a rotation Ω3. Here, x3 is 

aligned to the out-of-plane direction and x2 is perpendicular to the layers. 

The general 2-D Cosserat model has four nonsymmetric stress components σ11, σ22, σ21, σ12 and two 

couple stresses m31, m32. When the rock layers are aligned 

in the x1 direction, the moment stress term m32 vanishes. 

The four stresses are conjugate to four deformation measures γ11, γ22, γ21, γ12 defined by: 

∂
u 

γ
 ij =
 j − ε 3ij Ω3 (1)
 ∂xi 

where i and j equal 1 or 2 and ε 3ij is the permutation 

tensor ( ε 312 = −ε 321 = 1 and ε 311 = ε 322 = 0 ). The couple 

stress m31 is conjugate to the respective curvature κ1 

defined by: 

∂Ω

κ 1 = 

3 (2) ∂x1 

The elastic stress strain relationships are described by: 

σ = [ ] De ee (3) 

where 

σ = {σ 11 ,σ 22 ,σ 21 ,σ 12 ,m31} 

(4) e = {γ 11 ,γ 22 ,γ 21,γ 12 ,κ 1}

⎡A11 A12 0 0 0 ⎤ ⎢ ⎥ A ⎢ 22 0 0 0 ⎥

D = ⎢ G11 G12 0 ⎥ (5)
 ⎢ ⎥ ⎢ symm G 22 0 ⎥ ⎢ ⎥ ⎣ B1 ⎦

where 

E A 11 = ν2

() 1 +ν 2

1−ν2 − 2 E (6) 1−ν +

hkn 

1 A 22 = 1 −ν − 2ν2 1 (7) 

+

E() 1 −ν hkn 

ν A12 = A22 (8) 1−ν 

1 1 1 

= +

G11 G hks (9) 

 

G11 = G12 = G21 (10) 

G22 = G11 + G (11) 

Eh2 ⎛ G G− 11 ⎞ B1 = ( 2

) ⎜ ⎟ ⎝ ⎠ (12) 12 1 − ν G G+ 11

and E is the Young’s modulus of the intact layer, ν is the 

Poisson’s ratio, h is the layer thickness, G is the shear

modulus of the intact layer, and kn and ks are the joint 

normal and shear stiffnesses. 

Flow Model 

In COSFLOW, a porous medium is simulated as a 

region having two porosities—one representing a 

continuum porous rock (primary porosity), the other a 

fracture network (secondary porosity). Thus, the flow 

behavior is described mainly by the interaction of the basic 

components, namely, the porous matrix and the surrounding fracture system. The fractures provide rapid hydraulic 

connection but little fluid mass storage, whereas the porous 

matrix represents high storage but low hydraulic connection. The flow model incorporated in COSFLOW is similar 

to the conventional flow model, i.e., the flow in the 

fracture (cleat) system is controlled by the pressure gradient and is described using Darcy’s law, whereas the 

desorption (flow in the matrix) is controlled by the concentration gradient and is described using Fick’s law (e.g., 

King and Ertekin [1989a,b; 1991; 1994; 1995] provide a 

comprehensive list of references and surveys of mathematical models used in the simulation of gas production 

from coal seams). The relationship between gas concentration and pressure is a nonlinear function and is described 

using Langmuir [1916] equations. 

The flow model adopted in this study can be briefly 

described in the following manner. By assuming that the 

flow of fluid (gas/water) obeys Darcy’s law, the continuity 

8 
′

 

 

 

 

 

 

requirement of each fluid phase can be expressed through 

the following sets of equations: 

∂ ⎛ηS m ⎞ ∇ ⋅ qm + Qm + ⎜

⎜ ⎟⎟ = 0 (13) ∂t B ⎝ m ⎠

qm = − krm k (∇Pm − γ m∇d ) (14) Bm μ m 

where ∇ ⋅ is divergence operator; q is volumetric flux or 

flow rate; η is porosity; Q is a source or sink term, which 

for the gas phase represents mass transport between the 

secondary and primary porosity systems; S is fluid saturation; B is the formation volume factor; k is the absolute 

permeability; kr is the elative permeability factor; P is fluid 

pore pressure; γ is fluid unit weight; t is time; μ is viscosity; d is the vertical distance from a given datum; and m 

refers to each of the fluid phases. 

In this formulation, the pore volume is assumed to be 

fully occupied by the combination of the two fluids, i.e.: 

Sw + Snw = 1 (15) 

where w represents the wetting phase and nw represents 

the nonwetting phase. The wetting phase and nonwetting 

phase fluid pressures are assumed to be related as follows: 

P − P = P (16) nw w c 

where Pc is the capillary pressure. 

COSFLOW can simulate either two-phase or singlephase flow. In the case of a single-phase flow, the pore 

volume is allowed to be partially filled by the wetting 

phase fluid, in which case the fluid pore pressure is expressed as: 

Pw = −Pc (17) 

The gas absorbed in the coal seams can enter into the 

coal cleats as free gas and acts as a source term shown in 

Equation 13. This process can be described using an 

approach by Smith and Williams [1984] and Kolesar and 

Ertekin [1986]. In such an approach, the volume of the 

adsorbed gas in the coal matrix can be described by the 

Langmuir adsorption isotherms: 

V PL g VE = PL + Pg (18) 

where VE is the volume of gas that can be adsorbed at 

pressure Pg (also called the equilibrium concentration); 

VL is Langmuir volume, which is the maximum volume of 

gas that can be adsorbed; and PL is the pressure at which 

the volume of the adsorbed gas is half VL. 

The mass transport is described by Equation 19, which 

is derived from Fick’s law: 

Q = 1 (V −VE ) g mat τ (19) 

where Qg is the amount of gas desorbed from the matrix, 

Vmat is the gas volume contained in the matrix, VE is the 

matrix gas equilibrium volume, and τ is the so-called sorption time expressed as 

s 2 

f τ = (20) 8πD 

where D is the micropore diffusion coefficient, and sf is 

coal cleat spacing. This equation includes the proper shape 

factor for cylindrical matrix elements. Schwerer [1984] has 

shown that cylindrical matrix elements are adequate for 

modeling the diffusion process in coals. 

Dynamic Coupling 

The dynamic interaction between mechanical deformation and fluid flow processes can be described through a 

set of coupled nonlinear partial differential equations. The 

presence of a fluid in the mechanical model is considered 

by using the concept of effective stress so that such a 

stress field and the pore-fluid pressure satisfy the following force equilibrium conditions: 

∂σ ij ′ ∂P −α = Fi (21) ∂x ∂x j i 

Here, σ is effective stress, α is the Biot coefficient, 

P is pore pressure, F is body force density, x is a spatial 

coordinate, and i and j indicate the components of the 

vector and tensor variables in Cartesian space. 

The incremental stress changes are related to changes 

in incremental strain and pore pressure either through 

linear (elasticity) stiffness terms prior to yielding or 

through nonlinear (plasticity) stiffness terms after yielding. 

Similarly, change in pore volume is used to compute 

the associated changes in fluid pressures and saturations by 

solving the following sets of equations: 

η S0 η S1 

0 m 1 m = 0 1 (22) Bm Bm 

where 0 and 1 refer to initial and final conditions. 

9 
The flow of either phase of fluid is controlled by the 

permeability of the porous medium, which is either derived 

by field measurements or through theoretical/empirical 

formulations. There are different formulas proposed in the 

literature for estimating the permeability of porous 

medium depending on whether the porous medium is 

intact or contains a network of fractures. The permeability 

of a porous rock remains a highly nonlinear dynamic 

function of mining-induced stress and subsequent fractures. Thus, it is important not only to estimate the initial 

permeability correctly, but also to compute its possible 

variation induced by mining. 

Kozeny and Ber [1927], Hubbert [1940], Krumbein 

and Monk [1943], and De Wiest [1969] attempted to 

establish a relationship between stress and permeability 

through a definition of hydraulic radius, which is a 

function of grain diameter, porosity, grain shape, and packing. As rock masses usually contain natural fractures that 

predominantly control the fluid movements, there is a distinctive advantage in formulating a model on the basis of 

equivalent fracture network. In that framework, fluid flow 

through a single fracture can be expressed using a flowthrough parallel plate analog where a fracture is idealized 

as a planar opening with a constant aperture [Bai and 

Elsworth 1994; Esterhuizen and Karacan 2005]. 

Such an approach to describe the rock mass 

permeability through equivalent fracture idealization is 

well suited for coal measure rocks (i.e., rock masses in a 

coal mining environment). Seedsman [1996] discussed 

hydrogeological aspects of Australian longwalls and 

pointed out that water flow in coal measure rocks in New 

South Wales and Queensland is dominated by defects, 

cleats, joints, bedding, and faults rather than via pores in 

the rock mass. 

For a laminar flow within the fracture network, the 

hydraulic conductivity of a set of parallel fractures with a 

spacing, s, and aperture, a, is given by (e.g., Louis [1969]): 

ρga3 

k = (23) 12sμ 

where ρ is the fluid density, g is the gravitational acceleration, and μ is the dynamic viscosity of the fluid. 

By assuming a fractured rock mass consists of many 

interconnected fractures, it may be further idealized as an 

equivalent porous continuum where the rock mass is represented by an equivalent anisotropic hydraulic conductivity 

matrix defined in terms of mean fracture spacing and mean 

aperture. Here it is assumed that the principal directions of 

this matrix are aligned with the coordinate axes. For a fractured rock with fracture spacing Fsi (i = 1, 2, 3) and fracture apertures Fai (i = 1, 2, 3), the relationships between 

the absolute initial (premining) permeability components 

(k11, k22, and k33) and the fracture parameters can be 

expressed as: 

Fa3 

2 Fa3 

k ini 

11 = + 3

(24) 12Fs2 12Fs3 

ini Fa3 3 

3 Fa1 k 22 = +

12Fs3 12Fs1 (25) 

Fa3 

ini Fa3 

= 1 + 2 k 33 12Fs1 12Fs2 (26) 

This formulation is amenable to easy evaluation of 

modifications to the hydraulic conductivities as a function 

of stress-induced changes in fracture aperture. In this 

study, change in rock mass permeability is formulated on 

the basis of the mine-induced strain [Elsworth 1989; Bai 

and Elsworth 1994; Liu and Elsworth 1997], as follows: 

1 k k ini 

11 = 11 [(1 + β 2 2Δε 3 3 

22 ) + (1 + β 3Δε 33 ) ] (27) 

1 k = ini 3 3

22 k (1 + β Δε ) + (1+ β Δε ) 2 22 [ 1 11 3 33 ] (28) 

1 k = k ini (1 + β Δε ) 3

33 1 11 + ( 33 [ 1 + β Δε )

3

2 2 22 ] (29) 

where Δε ii are the normal strain components and βi are 

expressed as: 

1− Rm β i = 1+ 

⎞

n ⎛ Fa ⎜ i ⎟ (30) ⎜ ⎟ Fs ⎝ i ⎠ i=1,2,3 

Here, Rm is the modulus reduction ratio (ratio of rock 

mass modulus to rock matrix modulus), the term Fai /Fsi 

may be defined as a function of equivalent fracture 

porosity, and n is a constant (in Liu and Elsworth [1997], 

n is assumed to be equal to 1.0). Both Rm and n are considered to be fitting parameters and thus need to be 

calibrated properly against well-documented field data. If 

Rm equals 1.0, then βi equals 1.0, resulting in minimal 

strain-induced permeability changes. When Rm tends to 0.0 

(i.e., the case of highly fractured rock), βi will attain the 

maximum value and thus will induce large changes in 

permeability. 

MINE SUBSIDENCE PREDICTION 

Empirical Methods 

Prediction methods can be classified as empirical 

methods, methods employing influence functions, and 

methods employing theoretical models [Helmut 1983]. The 

empirical methods are derived from statistical analyses of 

previously monitored data and site observation and thus 

10 
 

 

 

 

 

 

are only applicable to the area where the data have been 

analyzed. Nevertheless, because of their simplicity, the 

empirical methods have been widely used. In Australia, 

two empirical methods are widely used to predict subsidence induced by longwall mining. Both methods are 

based on extensive subsidence measurement data and 

observations across a number of coalfields in New South 

Wales. 

The first, the DMR method, was developed by the 

Department of Mineral Resources, New South Wales, 

Australia [Holla and Barclay 2000]. Its first version was 

proposed in 1985 and published in a subsidence handbook 

for the Southern Coalfield. It was then used for longwall 

mining planning in the Southern, Newcastle, and Western 

Coalfields, New South Wales. This method provides several graphs for determining maximum subsidence for 

single and multiple panels. The strain, tilt, and curvature 

can also be determined by using the simple formulas 

provided. 

The second, the Incremental Profile Method, was 

developed by Waddington and Kay [1995]. Its first version 

was proposed as a subsidence prediction method for Appin 

and Tower Collieries in the Southern Coalfield in 1994. It 

was then extended to other collieries of the Southern and 

Newcastle Coalfields. Unlike the DMR method in which 

maximum subsidence parameters are predicted, the Incremental Profile Method predicts the incremental subsidence 

profile for each longwall panel in a series of longwall 

panels. The respective incremental profiles are then added 

to form the cumulative subsidence profile at any stage in 

the development. 

Both empirical methods require geometrical parameters as input such as panel width, pillar width, seam 

height, and mining depth. The effects of any variations in 

overburden geology, strata properties, and stress conditions cannot be assessed using these methods. A recent 

study [Strata Engineering Australia 2003] indicated that 

the geological conditions above the panels could affect the 

subsidence significantly. Only numerical methods are 

likely to be able to predict the effect of overburden geology, strata properties, initial stress, or surface topography 

on subsidence. 

COSFLOW: A Numerical Approach 

Subsidence due to underground coal mining is a 

complex process that involves caving, fracturing, and 

bending of stratified overburden. Such overburden is 

layered and exhibits highly anisotropic strength and 

deformation characteristics. This makes it necessary to 

include effects of stratification into the mathematical 

formulations describing the load deformation behavior. 

The most efficient way to study the load deformation 

behavior of the overburden is to devise an equivalent 

continuum model where the effect of stratification is 

incorporated implicitly in the model formulation, e.g., 

Cosserat model. 

Subsidence Simulation: Appin Colliery 

Appin Colliery is located in the Southern Coalfield of 

the Sydney Basin. The longwall mining method is used to 

extract coal from the Bulli Seam. 

The longwall panels modeled at Appin are 200 m wide 

and the extraction height is 2.3 m in the Bulli Seam, which 

is at a depth of about 500 m. COSFLOW was used to 

simulate the overburden movement caused by mining 

longwall panels 21B to 28A, which were completed from 

1991 to 1996. The monitored subsidence data and 

COSFLOW prediction are shown in the top and bottom of 

Figure 7, respectively. Subsidence, m 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 21B 22B 23 24 25 26 27 28A 

-1.4 

-1000 -500 0 500 1000 1500 2000 2500 3000 3500 

Horizontal distance from LW 21B, m 

 Figure 7.—A comparison of monitored subsidence data 

and COSFLOW prediction (after Guo et al. [2004]). 

A comparison indicates that the 

COSFLOW estimates are generally consistent with the 

monitored data. It can be seen that COSFLOW successfully simulated subsidence development in detail as mining 

progressed from panel 21B to 28A. The results also show 

the effects of chain pillars on the subsidence. 

11 
MINE GROUNDWATER FLOW SIMULATION: 

SPRINGVALE MINE 

Figure 8 shows the plan view of the finite-element 

mesh. The location of pump 2 used for dewatering from 

LW1 to LW405 is also shown.

 

LW940 

LW1 LW16

LW401 

LW20 

LW24 

LW920 

LW930 

9320m 

LW950 LW410 

LW411 

LW412 

LW413 

Pump2 LW405 

A Prediction was made for lower A’ series of panel 

7510m 

 Figure 8.—A plan view of the numerical grid used in the 

simulation. 

 The numerical model 

consists of about 500,000 finite elements and simulated a 

region 7.5 km long in the east-west direction and 9.3 km 

long in the north-south direction, thus covering an area of 

approximately 71 km2

. The permeability and geomechanical values used in the simulation are presented in 

Tables 1 and 2. 

12 

Table 1.—Permeability values used in the simulation 

of water inflow 

Rock unit 

Horizontal 

hydraulic 

conductivity 

(m/sec) × 10–8 

Vertical 

hydraulic 

conductivity 

(m/sec) × 10–8 

Porosity 

Floor 1.0 0.25 0.15 

Mining seam 10.0 10.0 0.10 

Unit 1 2.5 1.0 0.15 

Unit 2 0.05 0.05 0.10

Unit 3 1.0 0.25 0.15

Unit 4 0.1 0.1 0.10 

Unit 5 1.0 0.25 0.15 

Table 2.—Geomechanical parameters used in the numerical simulation of water inflow 

Rock units 

Young’s 

modulus 

(GPa) 

Cohesion 

(MPa) 

Friction angle 

(degrees) 

Tensile strength

(MPa) Remarks 

Base 

Floor 

Mining seam 

Unit 1 

Unit 2 

Unit 3 

Unit 4 

Unit 5 

Top 

18.0 

10.0 

3.5 

10.0 

10.0 

10.0 

10.0 

10.0 

5.0 

8.0 

2.5 

1.3 

3.0 

3.0 

3.0 

3.0 

3.0 

2.0 

35.0 

35.0 

40.0 

35.0 

30.0 

35.0 

30.0 

35.0 

35.0 

3.7 

0.96 

0.5 

1.15 

1.0 

1.15 

1.0 

1.15 

0.77 

No bedding 

No bedding 

No bedding 

0.5-m bed spacing, joint cohesion = 0.5 MPa, 

joint friction angle = 25° 

0.25-m bed spacing, joint cohesion = 0.3 MPa, 

joint friction angle = 25° 

0.5-m bed spacing, joint cohesion = 0.5 MPa, 

joint friction angle = 35° 

0.25-m bed spacing, joint cohesion = 0.3 MPa, 

joint friction angle = 25° 

0.5-m bed spacing, joint cohesion = 0.5 MPa, 

joint friction angle = 25° 

No bedding 

All of the rock units were assumed to dip parallel to 

the mining seam, which dips at 1° to the east and 0.7° to 

the north. The actual overburden sequence has been 

simplified combining lithological layers to represent rock 

characteristics of primary importance to obtain an average 

response and a reasonable fit with measurements (see 

Figure 5). Piezometers installed in the AQ4 horizon 

seemed to be unaffected by the mining underneath; thus, 

for simplicity, AQ4 and AQ5 were not included in the 

numerical simulation. 

Figure 9 shows the numerical predictions of water 

inflow into the lower series of panels (LW6 to LW10). The 

water inflow rate into the mine up to LW6 was much 

smaller, with total flow averaging around 55 L/s. However, 

the measured water inflow rate after mining LW7 onward 

increased substantially, yielding a rate of about 88 L/s after 

mining LW7. In general, COSFLOW can be seen to provide accurate predictions of mine water inflow when 

compared with the mine data. After 3 years, the predicted 

inflow rates are found to be in good agreement with the 

measurements. 
LW406 LW408 LW410

Solid lines COSFLOW predictions

Data points Mine measurements 

Pump2

Total mine water

Flow rates are averaged over 

each longwall retreat duration

 

 

200 

250 

–

–

LW406 LW408 LW410 

Solid lines – COSFLOW predictions 

Data points – Mine measurements 

Pump2 

Total mine water 

Flow rates are averaged over 

each longwall retreat duration 

Flow rate, l/s 

150 

100 

50 

0 

Longwall panels 

Figure 9.—Comparison of numerical prediction with the 

mine measurements (after Guo et al. [2006]). 

 

 

 

Panels up to LW403 are 255 m wide, panels LW404 to 

LW409 are 265 m wide, and panels LW410 onward are 

315 m wide. The noticeable change observed in the water 

inflow rates could be attributed to the change in the width 

of the panel as well as to the so-called multipanel effect. 

Figure 10 shows the distribution of vertical permeability 

changes as predicted by the numerical model. 

Figure 10.—Change in vertical permeability along the 

vertical section A–A′ in Figure 8 (values indicate orders of 

magnitude change). 

13 

It can be 

clearly seen in the figure that pattern of change in vertical 

permeability differs for panels up to LW406 and those 

LW407 onward, indicating a likelihood of increased water 

inflow. 

Figure 11 shows the pore water pressure distribution in 

the coal seam after mining panel LW408 as obtained from 

the numerical simulation.

 Figure 11.—Pore pressure distribution (in pascals) at the 

mining seam after mining LW408; note the position of the 

piezometer, indicated as SPR31 (after Guo et al. [2006]). 

SPR31 

LW408 

LW24

 The location of the piezometer 

installed in borehole SPR31 is marked on the plot. The 

pore water pressure at that location is about 400,000 Pa 

(i.e., water head is about 41 m); the piezometer readings 

fluctuated around 43 m after LW408 was completed. 

METHANE EMISSION SIMULATION: MINE A 

The numerical simulation of methane emissions from 

multiple seams into a longwall panel at an Australian mine 

is presented in this section. The extraction of two adjacent 

panels is modeled. The panels are denoted A and B (see 

Figure 12), where panel A is excavated before panel B. 

The emphasis on gas emission estimates is for panel B; 

panel A is included in the simulation simply to provide 

accurate initial conditions for the mining of panel B. 

Panel B could represent any longwall panel with similar 

predrainage and postdrainage conditions and extraction 

rates in a similar geological regime. The predictions from 

numerical simulations should be equally valid for comparison with measurements obtained from any similar longwall 

panels; thus, the numerical results are compared with mine 

measurements from two longwall panels. 
 

 

Panel B

Panel A

 

 

230 m 40 m 230 m 70 m 1500 m 230 m 40 m 230 m 70 m 1500 m 

Inseam drainage holes @ 40 m spacing

Post - drainage holes @ 100 m spacing

x

x’

2000 m

Inseam drainage holes @ 40 m spacing 

Post - drainage holes @ 100 m spacing 

x 

Panel B 

2000 m 

Panel A 

4000 m 

Figure 12.—Simulation layout of mine A. 

The mining panels are 230 m wide, 2.6 m high, and 

about 390 m deep. A total of 260,000 finite elements were 

used in the simulation. Figure 13 shows the simplified 

geology used in the simulation. The mining seam and two 

other seams were included in the simulation. The geomechanical properties adopted for the numerical simulation for the various rock layers are listed in Tables 3 and 4. 

Table 3.—Geomechanical parameters used in the numerical simulation of gas emission 

Rock units 

Young’s 

modulus 

(GPa) 

Cohesion 

(MPa) 

Friction angle 

(degrees) 

Tensile 

strength 

(MPa) 

Remarks 

Base 

Base 1 

Base 2 

Coal seams 

Unit 1a 

Unit 2 

Unit 3 

Unit 4 

Unit 5 

Top 1 

Top 2 

10.0 

4.0 

3.0 

3.5 

12.0 

8.0 

5.0 

7.0 

6.0 

10.0 

7.0 

4.0 

2.0 

1.15 

1.3 

3.12 

2.3 

1.7 

2.5 

1.6 

3.9 

2.08 

30.0 

30.0 

30.0 

40.0 

35.0 

30.0 

30.0 

35.0 

32.5 

35.0 

35.0 

1.4 

0.7 

0.4 

0.5 

1.2 

0.52 

0.56 

0.96 

0.58 

1.5 

0.8 

No bedding 

0.5-m bed spacing, joint cohesion = 0.8 MPa, 

joint friction angle = 30° 

0.1-m bed spacing, joint cohesion = 0.2 MPa, 

joint friction angle = 20° 

No bedding 

No bedding 

0.25-m bed spacing, joint cohesion = 0.5 MPa, 

joint friction angle = 30° 

0.25-m bed spacing, joint cohesion = 0.05 MPa, 

joint friction angle = 20° 

0.25-m bed spacing, joint cohesion = 2.0 MPa, 

joint friction angle = 20° 

0.25-m bed spacing, joint cohesion = 0.1 MPa, 

joint friction angle = 30° 

0.5-m bed spacing, joint cohesion = 1.0 MPa, 

joint friction angle = 20° 

No bedding 

Table 4.—Flow parameters used in the numerical 

simulation of gas emissions 

Rock permeability in horizontal direction (md) 

Rock permeability in vertical direction (md) 

Coal permeability in horizontal direction (md) − kh 

Coal permeability in vertical direction (md) − kv 

Gas content (m3

/t) 

Langmuir volume (m3

/t) 

Langmuir pressure (MPa) 

Coal sorption time (days) 

Reservoir pressure (MPa) 

30.0 

3.0 

6.0–9.0 

0.6–0.9 

13.5

23.8

1.5 

10 

3.0 

On the basis of coal seam gas pressure, the water table is 

assumed to be 306 m above the mining seam, yielding a 

gas pressure of 3 MPa at the mining seam. 

In this case, the model used measurements of gas production from predrainage boreholes for calibration. The 

simulated mining seam is first predrained, using in-seam 

boreholes (with 96-mm diameter) shown in Figure 12, for 

a simulated time equal to the actual predrainage time. This 

allowed calibration of the input parameters and provided 

initial conditions for the water/gas state before the longwall extraction. 

Following the predrainage simulation, panel A was 

extracted in 10 large steps of 200 m, then 700 m of panel B 

extraction was simulated in steps of 40 m. As the 

simulated extraction progressed, vertical boreholes of 

14 
254 mm in diameter were added to the model on the tailgate (panel A) side of panel B at 100-m spacing, as shown 

in Figure 12. Gas may flow into these boreholes or into the 

longwall panels. These flows are recorded separately for 

comparison with postdrainage measurements and flow into 

the ventilation system, respectively. 

6 0 0 . 0 m 

T o p 1 

3 8 0 . 0 

T o p 2 

2 3 4 2 3 4 . 1 

U n i t 5 

2 2 7 2 2 7 . 1 U p p e r s e a m 2 2 6 . 6 U n i t 5 

U n i t 4 2 2 5 2 2 5 . 3 

U n i t 3 

2 1 3 . 3 U n i t 2 

2 0 8 2 0 8 . 6 U n i t 1 a 2 0 8 2 0 8 . 1 M i n i n g s e a m 

B a s e 2 

2 0 5 2 0 5 . 5 

2 0 3 2 0 3 . 0 

B a s e 1 1 9 7 . 0 L o w e r s e a m 1 9 6 . 5 

B a s e 

0 . 0 

Figure 13.—A geological log used in the simulation of mine A. 

Figure 14 compares numerical predictions and actual 

measurements in the mine. In the figure, methane emission 

into the ventilation air in one of the longwall panels in the 

mine is compared with the COSFLOW prediction for 

panel B.

 

1200 

Mine data Panel A LW310

1000 Mine data Panel a LW310 verage o er 2400m) A (average (a over 2400m v Mine data Panel B a LW311

800 Mine data Panel LW311 (av ov B (averraggee o everr 715 715mm)) 

Numerical Prediction 

600 Numerical Prediction (average) 

Flow rate, (l/s) 

400 

200 

0 

0 100 200 300 400 500 600 700 800 

Longwall retreat, (m) 

Figure 14.—Comparison of numerical results with the mine 

measurements of gas emission into a longwall panel. 

 It can be seen that COSFLOW provides accurate 

predictions of average gas emissions into the longwall 

panel. Many of the fluctuations in measurements seen in 

Figure 14 are probably caused by variations in mining 

extraction rate, interruption to mining and postdrainage 

operations, variability of local geology and gas content, or 

effectiveness of predrainage schemes; none of these factors 

are included in the simulation. In general, COSFLOW can 

be seen to provide accurate predictions of average gas 

productions when compared with the mine data. 

CONCLUSIONS 

Reliable prediction of mining impact on surface 

subsidence, subsurface aquifers, water inflow, and gas 

emission into underground coal mines is essential for 

improving mine safety and reducing coal production costs, 

as well as for assessing the environmental impact of 

mining. 

This paper describes an integrated approach in 

assessing the impact of mining, including a new 3-D 

coupled mechanical two-phase double-porosity finiteelement code called COSFLOW developed by CSIRO 

Exploration and Mining to serve the needs of the mining 

industry. A unique feature of COSFLOW is the incorporation of Cosserat continuum theory in its formulation. 

In the Cosserat model, interlayer interfaces (joints, bedding 

planes) are considered to be smeared across the mass, i.e., 

the effects of interfaces are incorporated implicitly in the 

choice of stress-strain model formulation. An important 

feature of the Cosserat model is that it incorporates 

bending rigidity of individual layers in its formulation, 

which makes it different from other conventional implicit 

models. 

For the past 6 years, CSIRO Exploration and Mining 

has been actively involved in mine site geological, 

geotechnical, and hydrogeological characterization and 

predictive simulation of mine subsidence, mine water 

inflow, and gas emission. In this work, COSFLOW has 

been found to be capable of producing accurate predictions. The example of mining-induced surface subsidence, 

mine groundwater inflow, and mine gas emission predictions presented in this paper shows the remarkable capability of COSFLOW to simulate the mining-induced rock 

deformation, aquifer interference, permeability changes, 

and water/gas flow. 

It is important to note that the predictions made using 

the integrated approach involving field instrumentation, 

field monitoring, and relevant data acquisition, and 

15 
 

 

 

ultimate prediction simulation, can only be as good as the 

geotechnical and hydrogeological input data. Thus, field 

data gathering is a critical task. 

ACKNOWLEDGMENTS 

We would like to express our sincere gratitude to 

NEDO and JCOAL of Japan for providing a significant 

part of the funds during the development of COSFLOW. 

We would also like to thank Springvale Colliery and 

BHPB Illawara Coal for providing us with the mine data. 

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17 

 

 

 

 

 

 

 

A REVIEW OF RECENT EXPERIENCE IN MODELING OF CAVING 

By Mark Board1

1

Itasca Consulting Group, Denver, CO. 

 and M. E. Pierce2 

2

Itasca Consulting Group, Minneapolis, MN. 

INTRODUCTION 

The assessment of the initiation and growth of caving 

in rock masses has become more important as mining in 

hard rock and coal have moved toward higher-production, 

lower-cost methods. In hard rocks, where block, panel, or 

sublevel caving is used, empirical methods, based on rock 

mass characterization, combined with experience are typically used to estimate the hydraulic radius for sustained 

cave growth and the resulting “break” angles and propagation rates of the cave as it grows to the ground surface 

(e.g., Laubscher [2000]). Currently, there are a large 

number of caving projects worldwide in the conceptual 

stages of design, and many of these will be initiated below 

open pits. The economics of the transition between openpit and underground mining often is optimized when 

simultaneous production from the open pit and underground occurs. The shape and timing of the cave propagation, surface breakthrough, and subsidence area are critical 

to planning of infrastructure location, as well as mining 

geometry and timing of transition from open-pit mining to 

underground mining. For this reason, the use of numerical 

models to simulate the undercutting, draw, cave propagation, and surface subsidence processes, combined with 

empirical predictions, is becoming more commonplace. 

There are numerous numerical modeling programs and 

approaches available for performing stress and deformation analysis in geomechanics. The important aspect of 

modeling of caving is not necessarily the numerical program itself, but the methodology for simulating the caving 

process and the estimation of input material models and 

properties. This paper describes an approach for estimating 

rock mass material properties and modeling of caving 

developed as part of the Mass Mining Technology (MMT) 

research project (University of Queensland, Australia) and 

used in simulating cave response at a number of existing 

and planned caving projects. An algorithm to simulate the 

caving process was developed within the macro language 

(FISH) provided with the FLAC3D and 3DEC programs 

(Itasca Consulting Group, Inc.). An example of application 

of this caving algorithm to back analysis of cave growth at 

Palabora Mine in South Africa is presented. 

CONCEPTUAL MODEL OF THE 

CAVING PROCESS 

The caving process involves undercutting of the ore 

body by driving a series of parallel tunnels across the ore 

zone, drilling and blasting the pillars between them on 

retreat, and pulling the swell from draw points on the 

production level below. When the hydraulic radius of the 

undercut has reached a critical dimension, a self-sustained 

cave will develop as long as the broken and bulked ore is 

withdrawn. A conceptual model of the developing cave, 

described by Duplancic and Brady [1999], consists of four 

main behavioral regions (Figure 1): 

PSEUDO-CONTINUOUS DOMAIN 

SEISMOGENIC ZONE 

AIR GAP YIELD ZONE 

CAVED ZONE 

DIRECTION OF ADVANCING UNDERCUT

 Figure 1.—Conceptual model of caving (after Duplancic and 

Brady [1999]). 

1.	 Pseudocontinuous domain: The host rock mass 

around the caving region behaves mainly elastically. Rock mass behavior and properties are 

those of an “undisturbed” rock mass. 

2.	 Seismogenic zone: Microseismic (and sometimes 

seismic) activity occurs in this region mainly 

because of discontinuity damage (discontinuities 

going from peak to residual strength) and the 

initiation of new fractures. 

3.	 Yielded zone: The rock mass in this region surrounding the cave is fractured and has lost some 

or all of its cohesive strength and provides minimal support to the overlying rock mass. Stress 

components within this region are typically low. 

This zone is relatively thin in caves that propagate 

under low-stress conditions (“low” relative to the 

rock mass strength) and may be very thick in 

19
 
caves propagating under high-stress conditions 

(“high” relative to rock mass strength). (This zone 

was originally called the “zone of discontinuous 

deformation” by Duplancic and Brady [1999].) 

4. Caved zone: This region consists of rock blocks 

that have detached from the rock mass and are 

moving toward the draw points in response to 

draw and thus might also be called the mobilized 

zone. The air gap shown in Figure 1 will exist 

only if the overlying yielded zone retains some 

level of cohesion. 

APPROACH TO REPRESENT CAVING IN A 

CONTINUUM-BASED NUMERICAL MODEL 

Two basic modeling approaches have been used for 

simulation of caving: discontinuum-based and continuumbased methods. Theoretically, discontinuum-based approaches are preferable for simulating the caving process 

as one could explicitly account for rock jointing and the 

stress-related breakage of intact rock blocks, as well as 

model the movement of the caved rock by several hundred 

meters. However, the computational requirement to 

perform such a massive analysis is not possible. Therefore,

to make the problem computationally tractable, an algorithm to represent the primary mechanisms of undercutting, draw, and cave propagation within the threedimensional, continuum-based program FLAC3D was 

developed. The flowchart in Figure 2 shows the basic 

features of this algorithm and its implementation using 

rock mass properties derived empirically and using the 

Synthetic Rock Mass (SRM) approach. The steps in implementing the caving algorithm are described below. 

Geotechnical Database 

• Geotechnical logging of oriented core 

• Detailed line mapping 

• Laboratory strength testing 

• In situ stress state 

Rock Mass Constitutive Behavior 

FLAC3D • Strain-dependent material 

Caving Algorithm 

properties Strain-Softening 

• Defined by Empirical or Synthetic Material Model 

Rock Mass Approach 

Mining Parameters 

Excavate Undercut 

Increment 

Adjust material properties in all 

zones based on bulking resulting 

from draw and associated 

yielding, dilation and flow 

• Undercut depth, shape, direction 

• Draw rate (m/day) Stress Equilibrium in 

Rock Mass 

Invoke Draw By QuasiStatic “Pull” on Undercut 

Roof at Prescribed Draw 

Rate and Perform 

Computational Steps 

Figure 2.—Flowchart showing caving simulation within the FLAC3D program.

Geotechnical Database 

The estimation of material properties for caving analysis begins with gathering of an extensive geotechnical 

database. This database is typically gathered from exploration drilling, underground drifting, and open-pit mapping, 

if available. The most important parameters include: 

• Geology 

o Three-dimensional shapes of lithology of the 

major rock units 

o Geometry, continuity, and surface conditions 

of major fault structures and shear zones 

20 
 

 

 

 

 

•	 Geotechnical logging and mapping 

o	 Oriented core, which provides the orientation, 

spacing, and surface condition of joint sets 

o	 Intact rock strength estimate from hammer 

blows or point load measurements 

o	 Occurrence of alteration and microdefects, 

including veinlets, small-scale fracture fabric, 

etc. 

o	 Detailed line or pit cell mapping, including 

measures of fracture orientation, frequency, 

and trace length 

o	 Rock mass characterization parameters such 

as the Geological Strength Index (GSI), Rock 

Mass Rating (RMR), Mining Rock Mass 

Rating (MRMR), and Q′. 

•	 Laboratory testing (uniaxial and triaxial compression and tensile strength testing) 

•	 In situ stress state 

This information is often developed in the form of a geotechnical model in which geotechnical domains with similar rock mass quality and structure are grouped. 

Rock Mass Constitutive Behavior 

to Represent Caving 

Strain-Softening Material Response 

A numerical model that represents the caving process 

must account for the progressive failure and disintegration 

of the rock mass from an intact/jointed to a caved material. 

In this complex process, creation of the cave results in 

(1) deformation and stress redistribution of the rock mass 

above the undercut; (2) failure of the rock mass in advance 

of the cave, with associated progressive reduction in 

strength from peak to residual levels; and (3) dilation, 

bulking, fragmentation, and mobilization of the caved 

material. The failure process is characterized by shearing 

along preexisting joint surfaces and stress-induced fracturing of intact rock blocks. The failure process will necessarily require shear or tensile failure of intact rock bridges 

between joint segments as the rock mass fragments. This 

overall process—loading of the rock mass to its peak 

strength, followed by post-peak reduction in strength to 

some residual level with increasing strain—is often termed 

a “strain-softening” process and is the result of straindependent material properties. 

In the caving model described here, the strainsoftening material is described by the Mohr-Coulomb failure criterion in which the post-peak strength behavior is a 

function of plastic3

 3“Plastic” strain refers to shear strain after peak strength is 

reached. 

 shear-strain-dependent rock mass 

cohesion (c) and angle of friction (φ).4

4

A complete description of the Mohr-Coulomb strain-softening 

material model can be found in the FLAC3D User’s Manual 

(Itasca Consulting Group, Inc.). 

Accumulated 

plastic shear strain (more specifically, the second invariant 

of the deviatoric plastic strain tensor) is a common metric 

for irreversible shear strains in geomaterials and, in a more 

general sense, can be considered as a measure of damage. 

Unfortunately, little is known about the relationship 

between cohesion loss (and friction gain) and plastic shear 

strain, particularly on a rock mass scale, and there are few 

guidelines for selection of values for use in modeling. The 

plastic shear strain required in going from peak strength to 

a fragmented rock mass (termed here the “critical plastic 

strain”) in the periphery of the cave defines the brittleness 

of the rock mass failure and may be related to the GSI of 

the material. This brittleness impacts both the cavability of 

a given unit and the rate at which a cave will propagate in 

height for a given amount of draw. Some generalizations 

may be made regarding these effects. For example, a 

higher-quality rock mass (higher GSI) with greater solid 

rock volume participating in the failure process will often 

act in a more brittle fashion and thus have a lower critical 

strain value. Conversely, a lower-quality rock mass (lower 

GSI) with higher fracture frequency will often act in a 

more ductile fashion and thus have a larger value of the 

critical strain. An estimate of the relationship between the 

critical strain and GSI was determined by back analysis of 

rock mass failure in caves and other openings as a part of 

the MMT project [Lorig 2000] and provides a starting 

point for describing the degree of strain softening to be 

used in simulation of caving. Work is currently under way 

to more rigorously determine the full stress-strain response 

of a jointed rock mass (and thus the critical strain) by using 

the SRM approach, which is described later. 

Empirical Approach to Defining Rock Mass 

Properties 

As stated above, the caving algorithm assumes the 

rock mass strength is represented by a Mohr-Coulomb failure criterion, which is described by the cohesion and angle 

of friction. One methodology for estimating the mean and 

range of rock mass strength parameters is the use of the 

standard Hoek-Brown methodology. Laboratory uniaxial 

and triaxial testing is used to define the mean and distribution of the uniaxial compressive strength (UCS) and 

mi values to determine the intact rock Hoek-Brown 

envelopes. Geotechnical drill core logging or mapping of 

rock face exposures is used to estimate the mean and distribution of the rock mass quality (GSI) for each geotechnical domain. Equivalent Mohr-Coulomb strength 

parameters (c and φ) describing each geotechnical domain 

are determined from a tangent line to the Hoek-Brown 

envelope at a low value of confining stress (normally 

<5 MPa) that reflects the approximate stress conditions 

near the cave back. An alternative approach, described 

below, is the use of the SRM methodology to estimate rock 

mass strength parameters directly. 

21 
 

 

 

 

 

The rock mass modulus is calculated from the empirical relation of Serafim and Pereira [1983] as modified by 

Hoek and Brown [1997]: 

GSI −10 

E 40 rockmass (GPa) = 10 , UCSintact ≥ 100 MPa (1) 

UCS GSI −10 

E int act 40 rockmass (GPa) = 10 , UCSintact < 100 MPa (2) 100 

Impact of Bulking and Dilation 

The bulking and dilation of the rock that accompany 

softening (resulting from creation and opening of new 

fracture surfaces), as well as the corresponding decrease in 

density and modulus, must be accounted for to ensure 

mass conservation (i.e., no mass is created or destroyed 

during the failure process) and realistic representation of 

caved rock within the model. The modulus of the rock 

mass is expected to drop as the rock mass yields, dilates, 

and bulks. Based on a literature review of caved rock and 

rockfill properties, Lorig [2000] suggests that the modulus 

of caved rock at a porosity of 0.3 (a reasonable value for 

the caved rock) is approximately 250 MPa. This porosity is 

equivalent to a bulking factor of 0.43, or 43%. Based on 

these estimates, the modulus of the rock mass is assumed 

to drop linearly from its in situ value to a value of 

250 MPa at a bulking factor of 43% for caved rock. 

The dilation angle of the rock mass is assumed to be 

equal everywhere to 10° based on guidelines provided by 

Hoek and Brown [1997]. In the caving algorithm, the 

bulking within each zone (element) of the FLAC3D model 

is tracked throughout the simulation. Once a zone reaches 

the user-defined maximum bulking factor, its dilation 

angle is set to zero. Finally, the density is set for each zone 

based on lithology. During the simulation of the caving 

process, the zone density is adjusted automatically to 

reflect the volumetric changes that accompany bulking 

according to the following relation: 

ρ d = ρ s /(1 + B) (3) 

where ρ d = dry density of caved rock; 

ρ s = solid density of in situ rock; 

B = bulking factor = n/(1 − n); 

and n = porosity. 

Implementation of the Caving Algorithm 

in FLAC3D 

The caving algorithm is implemented in FLAC3D by 

simulating the undercutting and draw process and the subsequent growth of the yielded and caved zones. 

Essentially, the model represents the process of 

undercutting and draw as closely as possible to how they 

actually occur in the mine. Undercut advance is simulated 

in the model by converting the model zones (elements) that 

represent the undercut to fully fragmented and bulked 

rock. The fragmented and bulked rock are represented 

by setting their properties to those of broken rock (c = 0, 

φ = 42°, E = 250 MPa) and by setting all stress components to zero. The model is computationally cycled to 

allow the surrounding rock mass to equilibrate and arrive 

at a region of yield and redistributed stress around the 

undercut region. To start the simulation of draw, the undercut volume is deleted and the support to the surrounding 

rock mass is replaced with equivalent boundary forces that 

exist after the undercut is replaced by the fragmented, 

bulked rock. Draw of the ore is then simulated by applying 

a small downward velocity to all grid points in the roof of 

the undercut. This velocity is set low enough to ensure 

pseudostatic equilibrium throughout the model (i.e., to 

allow natural gravitational flow of the material and to 

avoid dynamic “pulling” of the overlying material). The 

undercut is advanced and draw simulated in many small 

computational steps at the prescribed draw rate in terms of 

meters per year. 

The mass, m, of material “drawn” from an individual 

undercut zone during a numerical solution increment is 

calculated as follows: 

m = V t A ρ (4) 

where V = average velocity of the zone nodes in the 

undercut roof (m/sec); 

t = elapsed model time; 

A = zone area in plan; 

and ρ = zone density. 

By summing the masses drawn by all the nodes (grid 

points), the total production from the cave within the 

model may be calculated. As the mass is drawn at the 

undercut, the yielded zone will spontaneously form within 

the FLAC3D model (dictated by the stress state and yield 

strength of the rock mass) and may progress upward from 

the undercut. As draw continues, rock within the yielded 

zone will have moved a sufficient distance (typically 

>1 m) to be classified as caved (mobilized) material. The 

extent and growth rate of these two zones (yielded and 

caved) are both functions of the stress state and material 

properties of the rock mass (Figure 3). The hydraulic 

radius at sustained cave growth is a function of the rock 

mass strength and in situ stress state, the shape of the cave 

is affected by the rock mass strength and its anisotropy, 

and “rate” of cave growth (i.e., the height of growth of the 

yielded zone for an increment of draw) is strongly impacted by the post-peak-strength brittleness of the rock 

mass. 

22 
Yield Zone 

Caved (Mobilized)

 Zone 

Undercut

 Figure 3.—FLAC3D simulation of Northparkes E26 Lift II 

cave showing the predicted yielded (cohesion loss) zone 

surrounding the mobilized cave zone [Pierce et al. 2006]. 

 

 

 

The Synthetic Rock Mass (SRM) Approach to 

Defining Rock Mass Constitutive Behavior 

Earlier we described the use of empirical methods for 

defining rock mass material properties for use in the 

caving model. An alternative and more rigorous approach 

to defining material properties and overall constitutive 

response of the rock mass is the SRM method (e.g., Pierce 

et al. [2007]). The SRM approach provides a platform for 

simulating the stress-strain response of large-scale 

“samples” of a rock mass. The basic information typically 

gathered during geotechnical characterization activities 

(laboratory uniaxial and triaxial testing of intact rock, 

direct shear testing of joints, and detailed line mapping of 

the orientation and continuous length of rock fracturing) is 

combined to form a “virtual” or “synthetic” rock mass that 

can be represented within the PFC3D (Itasca Consulting 

Group, Inc.) numerical modeling approach (Figure 4).

+ 

= 

 Figure 4.—A synthetic rock mass “sample” (right) is created by superimposing a stochastically defined discrete fracture 

network (center) onto a PFC3D particle solid (left). 

 The 

PFC3D model can then be used as a “numerical laboratory” to subject the synthetic samples to stress paths of 

interest and study the details of failure mode and overall 

rock mass constitutive behavior. 

The first step in the development of an SRM model is 

to develop an assemblage of bonded spheres in PFC3D 

representing the intact rock (Figure 4). A representative 

network of fractures for a given geotechnical domain or 

lithology is then “mapped” on top of the bonded sphere 

assembly. The representative fracture geometry is referred 

to as a discrete fracture network (DFN). The DFN, developed from statistical analysis of field fracture mapping 

data, is a stochastic representation of the heterogeneous 

nature of the geometry and continuity of rock mass fracturing for a given lithology or geotechnical domain. A 

number of programs are available to produce DFNs of 

disc-shaped fractures from the statistical results of detailed 

line mapping on tunnel or slope bench faces. Examples 

include FRACMAN (Golder Associates, Inc.) and 3FLO 

(Itasca Consultants S.A.S.). The recent development of a 

new smooth-joint contact model within the PFC3D 

[Mas Ivars et al. 2008] makes it possible to realistically 

simulate the shearing behavior of large numbers of nonpersistent joints and the subsequent fracture of intervening 

solid rock bridges. 

The process of exercising an SRM model begins with 

calibrating the interparticle bonds in PFC3D to reproduce 

the intact rock stress-strain response (Figure 5). The 

modulus and peak strength are calibrated against laboratory data for uniaxial and triaxial loading conditions. If the 

“intact” rock blocks in the rock mass are larger than tested 

in the laboratory or have extensive microdefects or veining, then this should be reflected in the rock block strength 

used for calibrating PFC3D. 

Following the intact rock calibration, SRM rock mass 

“specimens” are generated to test the stress-strain characteristics of the jointed rock. One or more DFNs are generated for each lithology at a scale appropriate to represent 

the rock mass scale (e.g., 10-m cube or larger), and the 

structure is mapped onto an array of PFC3D particles. 

These SRM samples may contain upwards of a million 

23 
 

 

particles and tens to hundreds of thousands of fractures. 

The SRM samples may be subject to site-specific stress 

paths or to more standard uniaxial and triaxial compression 

with driving stresses in principal directions (e.g., vertical, 

north-south, and east-west) to determine the impact of 

anisotropy introduced by the joint fabric on rock 

properties. Failure envelopes are fit to the data via the 

same procedures used in the laboratory. Size-strength 

relations can also be used to verify that the scale of the 

SRM results conform to the scale of the problem to be 

analyzed. 

180 

WALL SERVO 

160 

140 

120 

100 

80 

60 

40 

20 Wall Servo 

Fulll Strain 

0 

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 

Y-Axial Strain 

Figure 5.—Uniaxial compression test calibration for intact rock material extracted from an SRM (adapted Y-Axial Stress (MPa)

from Mas Ivars et al. [2008]). 

SRM APPROACH AND CAVING ALGORITHM 

APPLIED TO BACK ANALYSIS OF CAVE 

BEHAVIOR AT PALABORA MINE 

Introduction
 

Open-pit operations at Rio Tinto’s Palabora copper 

mine in South Africa were initiated in 1964 and completed 

in 2000 when the pit reached a depth of approximately 

800 m. Panel caving operations were initiated at the completion of the open pit by undercutting of the ore body at a 

depth approximately 400 m beneath the pit bottom, building to a production rate of 25,000 to 30,000 tpd. In late 

2003, crack development was noted in the base of the pit 

above the cave, which was followed in 2004 by a large 

slope failure on the north and northwest wall of the pit, 

extending to the pit crest (Figure 6). 

24 

Cave 

Undercut Level 

Figure 6.—Slope failure in Palabora pit (left) induced by cave from underground mine (right). 

The extent of this pit 
wall failure was not expected. Back analysis by Brummer 

et al. [2006] attributed the failure mechanism to steeply 

dipping, pervasive joint sets that form wedges that daylight 

into the cave back below, thus undermining the toe of the 

north slope 

Following is a description of an application of the 

SRM approach to define the rock mass constitutive behavior, particularly the carbonatite ore body, and to apply 

these estimates in the FLAC3D caving algorithm for back 

analysis of the cave and pit wall failure. Presumably, if the 

anisotropy of the rock mass material behavior is correctly 

represented by the SRM (with its embedded DFN), the 

cave propagation and slope failure should be represented 

in a reasonably accurate prediction. 

SRM Analysis of the Rock Mass 

The rock mass at Palabora contains four major geotechnical domains for which SRM analyses were 

conducted. Here, the results of the SRM studies for the pri

mary carbonatite ore host are described. The carbonatite is 

a hard, strong rock (UCS ~140 MPa) with relatively 

widely spaced (mean frequency 0.77/m), vertically persistent (trace length mean of 15 m) fracture sets. A DFN for 

the carbonatite was constructed from the statistical distribution of fracturing defined by underground detail line 

mapping as well as open-pit bench mapping (Figure 7). 

­

 Figure 7.—Vertically oriented joint sets in carbonatite from mapping in the underground line mapping (left) and open-pit 

mapping (right) [Mas Ivars et al. 2008]. 

Figure 8 shows an 80-m cube of carbonatite SRM that 

has been subdivided into samples of successively smaller 

dimension.

 Figure 8.—An 80-m cube SRM jointed sample (a) subdivided into a series of samples of various sizes. The variation in UCS with 

sample size (right) shows the size effect on rock mass strength (adapted from Mas Ivars et al. [2008]).

 These samples were then subjected to a series 

of compression tests with primary loading directions in the 

principal (vertical, north-south, east-west) directions. The 

SRM results clearly show size effect and anisotropy of 

25 
 

 

response in moduli and strength (Figures 8 and 9). The 

anisotropy in response is directly related to the vertical 

orientation of the fracture system. 

The strength and modulus anisotropy determined from 

the SRM were taken into account in the FLAC3D continuum model by using a strain-softening, ubiquitous joint 

model in which the stochastic variability of the jointing, 

described by the DFN, is randomly seeded into the 

FLAC3D zones. The properties assigned to the intact rock 

and jointing are derived through the SRM strength testing 

such that the FLAC3D model reproduces the basic uniaxial 

and triaxial response (Figure 9).

 Figure 9.—Stress-strain plots from (a) uniaxial and (b) triaxial compression testing of carbonatite SRM samples from Palabora 

Mine. The SRM is compared to the continuum-based FLAC3D representation of the SRM results via the ubiquitous joint rock mass 

model (UJRM). The results show the significant anisotropy in the strength response [Sainsbury et al. 2008]. 

 Whereas the typical application of the caving algorithm assumes isotropic rock mass 

properties, this particular approach provides for an orientation of weakness resulting from the orientation of the 

dominant jointing. 

Sensitivity studies of the impact of the orientation of 

the anisotropy on generic cave growth and the mobilized 

rock mass for a given undercut area and total draw 

(3.9 Mt) within the FLAC3D caving algorithm were 

conducted [Sainsbury et al. 2008]. As shown in Figure 10, 

for the same amount of total draw, the associated zone of 

deformation (the mobilized zone based on >1 m of movement) is significantly different and affected by the 

assumed orientation of anisotropy. 

 Figure 10.—Sensitivity of cave growth to the primary 

orientation of the fracturing [Sainsbury et al. 2008]. 

A horizontal weakness 

orientation promotes rapid cave growth vertically, while a 

vertical anisotropy results in minimal cave growth— 

in other words, the cave tends to grow at right angles to the 

direction of primary anisotropy. These examples are hypothetical since the anisotropy directions are uniform for 

each element (except for the isotropic case) and thus show 

an exaggerated impact of jointing. However, the point here 

is that, if strong anisotropy in the rock mass structure 

exists, it may significantly impact the direction and rate of 

growth of the cave. 

Application of the Caving Algorithm and SRM to 

Back Analysis of the Palabora Cave 

A back analysis of the caving behavior of Rio Tinto’s 

Palabora Mine was conducted as part of the MMT project 

as a validation exercise of the SRM methodology, and, in 

particular, the methodology for representing material 

anisotropy defined by the SRM testing, and was included 

in the FLAC3D model using the ubiquitous joint constitutive model. The following discussion summarizes the work 

of Sainsbury et al. [2008]. The back analysis was carried 

out by developing a large-scale FLAC3D model of the pit 

and underground and by advancing the undercut and pull 

at the draw rate specified by the actual draw schedule. The 

outputs of the model are the isosurfaces of the mobilized 

zone, the yield zone, and the estimated seismogenic zone. 

The seismogenic zone, which will precede the yield zone,

26 
 

 

is estimated by applying stresses in the FLAC3D elements 

to the following relation [Diederichs 1999], which is based 

on the threshold failure envelope when seismicity is 

initiated: 

σ1 = σ3 + [0.2 to 0.4] * UCSlab (5) 

The results of the analyses are shown in Figures 11 and 

12. Figure 11 shows the isosurfaces of the mobilized and 

yield zones as a function of undercut advance from 2002 to 

2004 (i.e., before and after initiation of the north wall slope 

failure).

 Figure 11.—Isometric view of FLAC3D model output showing progression of mobilized zone (red) and yield zone (blue) as 

undercut is advanced from 2002 to 2004 [Sainsbury et al. 2008].

 As seen in this figure, the predicted yield zone 

isosurface propagates rapidly up-dip and affects the stability of the pit bottom in advance of the caved (mobilized) 

zone. The stress concentration introduced at the pit bottom, 

coupled with the vertical stress relief due to removal of the 

pit material, causes the early interaction of the cave and 

pit. The failure of the pit toe at the north wall, induced by 

interaction with the cave, results in failure up-dip in the 

slope. 

 

 

Actual Seismic
 

Yield Zone
 Record Data
 (Aseismic Zone) 

Actual Seismic 

Record Data 

Yield Zone - Blue 

50-80m 

(after Glazer and Hepworth, 2004) Mobilized Zone - Red Mobilized Zone 

 Figure 12.—Comparison of the location and dimensions of the aseismic and seismogenic zones from acoustic monitoring 

(left, Glazer and Hepworth [2004]) with FLAC3D predictions of the yield zone (right, Sainsbury et al. [2008]). 

Verification of the model’s ability to simulate the vertical advance and shape of the cave was obtained by 

27 
 

 

 

 

comparing the isosurfaces of the yield and seismogenic 

zones to measurements of acoustic emission made by the 

mine-wide microseismic system [Glazer and Hepworth 

2004]. As shown in Figure 12B, the yield zone in the 

FLAC3D model is predicted to be approximately 50–80 m 

in extent beyond the mobilized zone. The yield zone is 

aseismic in nature since the higher-energy acoustic emissions are associated with the high-stress concentrations 

that have been shed in advance of the previously failed 

rock mass. The data gathered from the microseismic system indicate a similar region of yield in advance of the 

cave. The FLAC3D model also shows comparable (to the 

microseismic data) timing to the failure of the crown pillar 

between the pit floor and the shedding of stress concentration and seismicity to the confined region around the pit 

base and sidewalls. 

CONCLUSION 

This paper described a methodology for predicting 

cave growth that was developed over a number of years 

through a mining industry-funded research program—the 

MMT research project. The prediction of caving requires 

knowledge of the strain-softening behavior of the rock 

mass, since the prediction requires representation of the 

process of failure from the in situ rock mass to ultimate 

fragmentation of the ore body. Two methodologies were 

described to estimate strain-dependent strength properties 

of the rock mass for inclusion in a strain-softening, MohrCoulomb constitutive model. The first is the use of empirical relationships for rock mass properties using the GSI 

methodology of Hoek and parameters derived from back 

analysis of numerous caves. The second, more promising 

approach is the use of the SRM technique, in which a 

rigorous methodology is used to combine the material 

response of the basic geologic constituents (intact rock and 

fractures) to define the rock mass constitutive behavior. 

The caving algorithm described has been applied to back 

analysis (and forward analysis) at a significant number of 

caves and shows reasonable correlation to the basic parameters of interest in mining: the shape of the cave, the rate 

of cave growth as a function of draw, and the resultant 

cracking and subsidence regions. 

REFERENCES 

Brummer RK, Li H, Moss A [2006]. The transition 

from open pit to underground mining: an unusual slope 

failure at Palabora. In: Proceedings of the South African 

Institute of Mining and Metallurgy, International Symposium on Rock Slopes in Open Pit Mining and Civil Engineering, pp. 411–420. 

Diederichs MS [1999]. Instability of hard rockmasses: 

the role of tensile damage and relaxation [Dissertation]. 

Waterloo, Ontario, Canada: University of Waterloo. 

Duplancic P, Brady BH [1999]. Characterization of 

caving mechanisms by analysis of seismicity and rock 

stress. In: Proceedings of the Ninth International Congress 

on Rock Mechanics (Paris, France) (2):1049–1053. 

Glazer S, Hepworth N [2004]. Seismic monitoring of 

block cave crown pillar: Palabora Mining Company, RSA. 

In: Proceedings of MassMin 2004 (Santiago Chile, August 

22–25, 2004), pp. 565–569. 

Hoek E, Brown ET [1997]. Practical estimates of rock 

mass strength. Int J Rock Mech Min Sci 34(8):1165–1186. 

Laubscher DH [2000]. Block caving manual. Prepared 

for the International Caving Study. JKMRC and Itasca 

Consulting Group, Brisbane, Australia. 

Lorig L [2000]. Methodology and guidelines for 

numerical modelling of undercut and extraction-level 

behaviour in caving mines. Report to International Caving 

Study (1997–2000). 

Mas Ivars D, Potyondy DO, Pierce M, Cundall PA 

[2008]. The smooth-joint contact model. In: Proceedings 

of the Eighth World Congress on Computational 

Mechanics and Fifth European Congress on Computational 

Methods in Applied Sciences and Engineering (Venice, 

Italy, June 30-July 5, 2008). 

Pierce M, Young RP, Reyes-Montes J, Pettitt W 

[2006]. Six monthly technical reports, caving mechanics, 

subproject 4.2: research and methodology improvement; 

and subproject 4.3: case study application. Itasca Consulting Group report to Mass Mining Technology Project, 

2004–2007, September. 

Pierce M, Cundall P, Potyondy D, Mas Ivars D [2007]. 

A synthetic rock mass model for jointed rock mechanics. 

In: Eberhardt E, Stead D, Morrison T, eds. Rock 

mechanics: Meeting society’s challenges and demands. 

London: Taylor and Francis, pp. 341–349. 

Sainsbury B, Pierce ME, Mas Ivars D [2008]. Analysis 

of caving behaviour using a synthetic rock mass: ubiquitous joint rock mass modelling technique. In: Potvin Y, 

Carter J, Dyskin A, Jeffrey R, eds. Proceedings of the First 

Southern Hemisphere International Rock Mechanics Symposium (SHIRMS 2008) (September 16–19, 2008). Perth, 

Australia: Australian Centre for Geomechanics, Vol. 1, pp. 

243–254. 

Serafim JL, Pereira JP [1983] Considerations on the 

geomechanical classification of Bieniawski. In: Proceedings of the International Symposium on Engineering Geology and Underground Construction (Lisbon, Portugal), 

(1):II.33-II.42. Lisbon, Portugal: Sociedade Portuguesa de 

Geotécnica/Laboratório Nacional de Engenharia Civil. 

28 
 

 

 

 

 

 

CHARACTERIZATION OF NATURAL FRAGMENTATION 

USING A DISCRETE FRACTURE NETWORK APPROACH AND 

IMPLICATIONS FOR CURRENT ROCK MASS CLASSIFICATION SYSTEMS 

By D. Elmo,1

 S. Rogers,1 and D. Kennard1 

1

Golder Associates Ltd., Greater Vancouver Office, 

Burnaby, British Columbia, Canada. 

ABSTRACT 

Design practice in rock engineering relies significantly 

on a consistent characterization of the natural rock fracture 

network. For instance, an accurate representation of natural 

fragmentation is key to establishing representative rock 

mass material strength. The use of a Discrete Fracture 

Network (DFN) approach integrated with a Rock Block 

Analysis is shown to provide a powerful tool for studying 

the distribution of rock blocks as a function of discontinuity persistence, spacing, and orientation. This paper 

presents the results of a study to evaluate the fundamental 

factors influencing natural fragmentation, emphasizing the 

role of discontinuity geometry, orientation, and intensity. 

By providing a quantitative assessment of the in situ block 

size, the proposed approach is shown to have major 

implications for the characterization of the strength of rock 

masses with nonpersistent joints. These preliminary results 

form the basis for the development of an innovative DFNbased rock mass characterization approach, which combines empirically derived rock mass properties with 

orientation-dependent parameters to account for rock mass 

anisotropy. 

INTRODUCTION 

Numerical modeling has played and will continue to 

play an important role in rock engineering design [Hoek 

et al. 1990]. The scope of a model is not to represent rock 

engineering processes in their entirety. Rather, the objective of the analyst is to determine which process needs to 

be considered explicitly and which can be represented in 

an average way. Parametric characterization and its 

association with sample size, representative elemental 

volume, and homogenization/upscaling represent fundamental problems faced in realistic modeling. For this 

reason, any modeling and subsequent rock engineering 

design will, by necessity, include some component of 

subjective judgment. 

Recent advances in the field of data capture and synthesis have allowed the derivation of more accurate threedimensional (3-D) models of naturally jointed rock 

masses, overcoming some of the limitations inherent in an 

infinite ubiquitous joint approach. The true discontinuous 

and inhomogeneous nature of the rock mass should be 

reflected in most modeling conceptualization. Thus, the 

importance of discontinuity persistence cannot be overemphasized if realistic characterization and fracture analysis is to be undertaken [Kalenchuk et al. 2006; Kim et al. 

2007; Elmo et al. 2007, 2008]. It is clear that the volume, 

shape, and stability of rock blocks depend on the characteristics of the natural rock fracture network. In this context, the Discrete Fracture Network (DFN) approach 

represents an ideal numerical tool with which to synthesize 

realistic fracture network models from digitally and conventionally mapped data. 

Whereas numerical simulations provide a potentially 

useful means of overcoming some of the limits of the 

empirical methods, empirical approaches such as rock 

mass characterization and classification systems still represent a fundamental component for many applications in 

both mining and rock engineering practice. Ideally, both 

qualitative and quantitative data should be collected as part 

of the rock mass characterization process, providing the 

necessary parameters for a subsequent classification analysis. Fundamental aspects of rock mass characterization 

include: definition of an accurate geological model, geotechnical data collection, assessment of the role of major 

geological structures, and determination of rock mass 

properties. 

This paper introduces the preliminary concepts of a 

DFN-based rock mass characterization approach, which 

couples empirically derived mechanical properties with 

orientation-dependent parameters to account for rock mass 

anisotropy. This set of properties can then be incorporated 

into a continuum finite-element or finite-difference model. 

The objective is to provide an improved link between 

mapped fracture systems and rock mass strength compared 

to the current practice of using empirical rock mass classifications alone. 

ROCK MASS CHARACTERIZATION METHODS 

AND ROCK MASS PROPERTIES 

One of the key aspects of rock engineering is establishing representative rock mass material strength and deformability characteristics. This section briefly summarizes 

available approaches for deriving the mechanical properties of a jointed rock mass. 

29
 
 

Rock Mass Characterization Methods 

Traditionally, rock mass characterization has been 

achieved using empirical classification methods, including 

the Geological Strength Index (GSI) [Hoek et al. 1995, 

2002], the Rock Mass Rating (RMR) system [Bieniawski 

1989], and the Q-index [Barton et al. 1974]. These classification systems are useful tools that (1) identify significant 

parameters influencing rock mass behavior, (2) derive 

quantitative data for engineering design, and (3) provide a 

quantitative measure to compare geological conditions at 

different sites. In different ways within these classification 

systems, various discontinuity properties such as discontinuity spacing, Rock Quality Designation (RQD), and 

discontinuity roughness are weighted and combined to 

give a value (or range of values) describing the rock mass 

characteristics. Rock mass classification systems such as 

the RMR, the Q-index, or the coupled GSI/Hoek-Brown 

approach are traditionally used to derive properties for 

numerical analysis of rock engineering problems. A summary of RMR, Q, and GSI-based empirical relationships 

for estimating mechanical properties of the rock mass is 

presented in Table 1. 

Table 1.—Empirical relationships for deriving estimates of 

basic rock mass strength and deformability properties 

based on the RMR, GSI, and Q rock mass classification 

systems (modified from Vyazmensky [2008]) 

Numerical Methods 

Numerical modeling methods are increasingly being 

used for deriving rock mass properties through simulated 

rock mass tests. For instance, the Synthetic Rock Mass 

Approach proposed by Pierce et al. [2007] and Cundall 

et al. [2008] involves constructing a synthetic sample of 

the rock mass in two or three dimensions by bonding 

together thousands of circular or spherical particles. DFNbased preinserted joints are introduced by debonding particles along specific joint surfaces and employing a sliding 

joint model. Similarly, by coupling a DFN model with a 

hybrid finite-discrete analysis, Elmo and Stead [2009] 

have demonstrated that the use of a synthetic approach 

could allow engineers to simulate the rock mass response 

to loading by fully accounting for existing jointing conditions while also explicitly accounting for size and shape 

(scale) effects. 

Important factors that play a major role in the 

development of synthetic rock mass properties (independently of the adopted numerical methodology) include the 

following: 

(1) The scale of the synthetic rock mass tests must be 

sufficiently large to capture the representative 

elemental volume for local jointing conditions and, 

in order to accommodate structural anisotropy, 

should be repeated to allow for different 

orientations of σ1 and σ3 relative to the joint 

orientations. 

(2) The stochastic nature of the embedded DFN model 

is such that there are an infinite number of possible 

realizations of the 3-D fracture system based on 

the mapped data. Accordingly, the analysis should 

incorporate a Monte Carlo approach, by running a 

certain number of DFN models and incorporating 

those in the subsequent synthetic rock mass 

modeling. The necessary large computing times 

required to perform such an analysis could limit 

the effectiveness of the Synthetic Rock Mass 

Approach and the associated definition of specific 

formulations of rock mass behavior. 

(3) Most geomechanical models rely on a form of 

calibration process. For lab-scale intact rock 

samples, the calibration process may be a 

straightforward procedure. Instead, calibrating a 

model against the strength of a large-scale and 

naturally fractured rock mass may not be directly 

possible unless considering large-scale physical 

testing. References to large-scale testing can be 

found in the literature, but these are usually 

limited. Some researchers (e.g., Hoek and Brown 

[1980]) have proposed some forms of upscaling 

relationships for estimating the strength of larger 

intact rock samples, but these are typically limited 

30 
 

 

 

 

 

 

 

 

 

to rock specimens with a diameter not greater than 

500 mm. 

THE DFN APPROACH AS A TOOL TO SIMULATE 

MORE REALISTIC GEOLOGICAL MODELS 

Rock discontinuities can be characterized in terms of 

their orientation, intensity, and spatial distribution, in 

addition to their strength and deformability. With the 

exception of fully explicit modeling of an individual 

fracture or simplified fracture sets, the use of a stochastic 

DFN approach provides the best option for creating 

realistic geometric models of fracturing, reflecting the 

heterogeneous nature of a specific fractured rock mass. 

The basis of DFN modeling is the characterization of each 

discontinuity set within a structural domain using statistical distributions to describe variables such as orientation, 

persistence, and spatial location of the discontinuities. The 

DFN approach maximizes the use of discontinuity data 

from mapping of exposed surfaces and boreholes or any 

other source of spatial information. Discontinuity data 

sampled from exposures in variably oriented outcrops 

(two-dimensional) and boreholes (one-dimensional) can be 

used to synthesize a 3-D stochastic discontinuity model 

that shares the statistics of the samples and allows for the 

incorporation of specific (deterministic) discontinuities 

such as larger mappable structures. Observations of 

exposed rock faces, at or near the project site, have the 

advantage of allowing direct measurements of discontinuity orientation, spacing, and persistence and the 

identification of discontinuity sets. Other large-scale geometrical and structural features can be readily observed. 

Increasingly, digital photogrammetry and laser scanning 

techniques (LiDAR) provide an alternative method for 

surface fracture characterization. 

The typical process involved in the generation of a 

DFN model includes the definition of (1) a fracture spatial 

model, (2) fracture orientation distribution, (3) fracture 

terminations, (4) fracture radius distribution, and (5) fracture intensity. Validation of the DFN model is achieved by 

comparing the orientation, intensity, and pattern of the 

simulated fracture traces with those measured in the field 

using a simulated sampling methodology. 

The proprietary code FracMan [Dershowitz et al. 1998; 

Golder Associates 2009] is the platform used in the current 

study for data analysis and synthesis. FracMan allows the 

3-D visualization of blocks defined by intersecting 

discontinuities in the DFN model by employing either an 

implicit cell mapping algorithm or a more conventional 

explicit block search algorithm [Dershowitz and Carvalho 

1996]. Whereas the latter provides an accurate estimate of 

block shape and volume, its use is better suited for the 

kinematic assessment of block stability. The cell mapping 

algorithm is optimized to provide an initial estimate of the 

rock natural fragmentation. As shown in Figure 1, the cell 

mapping algorithm works by initially identifying all of the 

fracture intersections with the specified grid elements. This 

results in a collection of grid faces and connection 

information, which is then used to construct a rock block 

of contiguous grid cells. 

A B

C D

 Figure 1.—Cell mapping algorithm: (A) initial DFN, (B) fractures are mapped to the specified grid, (C) regular blocks are 

formed along the grid cells, and (D) final rock block model. 

MODELING NATURAL FRAGMENTATION USING 

AN INTEGRATED DFN-ROCK BLOCK ANALYSIS 

APPROACH 

It is safe to assume that the number of blocks formed 

and both their volume and relative continuity within the 

geological model are strongly related to the geometry and 

number of intact rock bridges. If joints were assumed to be 

fully persistent, this would erroneously lead to more 

removable blocks than actually existed in situ. With the 

exception of size and geometry of the excavation, which 

are fixed, fracture orientation and length are expressed 

within the DFN model as probability density functions. 

The accuracy of block predictions clearly depends on the 

precision of the initial descriptive parameters, including 

the cell grid size used in the cell mapping algorithm. 

The current study builds on the initial work by Elmo 

et al. [2008]; the principal difference consists in the 

integration of the cell mapping algorithm for fragmentation 

analysis. A series of conceptual discrete-fracture networks 

was generated in FracMan using the parameters listed in 

Table 2. 

The results (Figure 2) clearly show that, for a simple 

fracture network with three joint sets, fracture length has a 

dramatic impact on the block forming potential for a given 

linear intensity P10 assuming the equivalence of all other 

31 
 

 

properties. These results are in agreement with observations by Chan and Goodman [1987] and Hoerger and 

Young [1990]. The analysis shows that there is a decrease 

in the number of rock blocks, independently of fracture 

length, for models with relatively wider spaced fractures 

(i.e., decreasing linear intensity P10). Relatively short 

fractures coupled with a relatively high-intensity P10 can 

still produce a block assemblage characterized by very few 

and widely spaced intact rock bridges. Clearly, this would 

have major implications with respect to rock mass 

strength, the development of primary fragmentation, and 

the mobilization of rock blocks. By interpreting the results 

with respect to block volume and number of blocks 

(calculated as the mean of all sequential stages) 

(Figure 2A), a preliminary attempt has been made to 

characterize the degree of natural fragmentation as a 

function of fracture length and fracture intensity P10 

(Figure 2B). 

(A) 

(B) 

II (4-m-long fractures)

I (1-m-long fractures) 

 Figure 2.—(A) Variation of block volume and number of blocks as a function of fracture intensity P10 with visualization of 

blocky rock masses at points I and II, respectively, and (B) qualitative characterization of the degree of natural fragmentation 

as a function of persistence factor and fracture spacing (modified from Elmo et al. [2008]). 

Table 2.—Parameters used in the conceptual 

DFN-Rock Block Analysis
 

(NOTE: Each DFN model is generated within a 10-m by 10-m 

by 10-m box region.) 

Parameter Set 1 Set 2 Set 3 

Orientation (°) 

Fracture length (m) 

Linear fracture 

(m-1) intensity P10 

000/90 

1, 2, 5, and 

10 

1, 2, 3, and 4 

090/90 

1, 2, 5, and 

10 

1, 2, 3, and 4 

000/00 

1, 2, 5, and 

10 

1, 2, 3, and 4 

For a given fracture length and fracture intensity, the 

current DFN analysis demonstrates that the massive to 

blocky character of a hypothetical rock mass could quantitatively and qualitatively be expressed as a function of 

mean block volume and number of fully formed blocks. In 

Figure 3, the massive to blocky character is defined 

according to the quantitative method to assist in the use of 

the GSI system for rock mass classification proposed by 

Cai et al. [2004]. As discussed by Cundall et al. [2008], 

this method is not scale independent, and the block 

volumes suggested by Cai et al. [2004] should be 

32 
interpreted relative to the scale of a tunnel. To account for 

that, the current DFN-based fragmentation analysis is carried out within a 10-m by 10-m by 10-m region. 

 

I II 

Figure 3.—Rock Block Analysis carried out for a 10-m by 

10-m by 10-m region volume. Quantitative characterization of 

the rock mass natural fragmentation is expressed as a function of mean block volume, number of fully formed blocks, 

and GSI. 

A DFN-BASED ROCK MASS 

CHARACTERIZATION APPROACH
 

The use of numerical modeling to derive synthetic rock 

mass properties is an elegant solution to the problem 

(establishing representative rock mass properties) long 

recognized as one of the main challenges in rock 

mechanics. However, at present it is not practical to perform 3-D large-scale engineering analysis within discontinuum codes that are capable of simulating intact rock 

fracturing. Typically, numerical tests of rock mass 

behavior are used in conjunction with continuum codes. 

Work is currently ongoing to provide an alternative 

modeling route for estimating rock mass properties for 

continuum modeling. Because any process of deriving 

numerically simulated rock mass properties ultimately 

requires the explicit use of a DFN embedded within an 

intact rock matrix, it is proposed to use the DFN model 

itself, coupled with empirically derived rock mass properties, to provide the necessary input parameters for the 

continuum analysis. By superimposing a grid structure to 

the DFN model, the proposed approach takes advantage of 

existing rock mass classification schemes to obtain, for 

each grid cell, an equivalent rock mass rating (Figure 4). 

 Figure 4.—DFN model and grid cell visualization of a sampled parameter (volumetric intensity P32 is shown). Logarithmic 

scale, darker shades define zones with relatively lower volumetric fracture intensity. 

Using the relationships in Table 1 is then possible to derive 

an initial estimate of rock mass properties, including rock 

mass cohesion and friction. Modeling of anisotropic 

behavior would be indirectly undertaken within a continuum code by assigning ubiquitous joint orientations for 

specific zones in the model. Work is ongoing to define a 

sampling procedure for each grid cell in the DFN model to 

define the ubiquitous joint dip, dip direction, and size. 

33 
A PRELIMINARY STUDY ON THE USE OF A 

DFN METHOD TO PROVIDE ESTIMATES OF 

ROCK MASS PROPERTIES
 

It is possible to correlate the results of a combined 

DFN-Rock Block Analysis with existing rock mass classification systems. The scope of the current DFN modeling 

is to further develop these correlations, investigating 

whether inputs to classification schemes can be expressed 

as functions of specific DFN parameters. 

The preliminary analysis considered a DFN model 

generated using the parameters listed in Table 3.

Table 3.—Parameters used for the DFN: fragmentation analysis and correlation with RQD data 

Parameter Set 1 Set 2 Set 3 Set 4 

Subset A: 

 Orientation (°) 

 Mean fracture length1 (m) 

 Linear fracture intensity P10 

203/82 

5 

1, 2, 4, and 8 

119/49 

5 

1, 2, 4, and 8 

327/74 

5 

1, 2, 4, and 8 

277/86 

5

1, 2, 4, and 8 

Subset B: 

 Orientation (°) 

 Mean fracture length1 (m) 

 Linear fracture intensity P10 

203/82 

30 

0.25 

119/49 

30 

0.25 

327/74 

30 

0.25 

277/86 

30

0.25

1

Negative exponential distribution was used. 

 The 

number of joint sets is defined using the Jn parameter 

convention (Q-index), and each set is defined using a 

function that randomly generates numbers within the range 

[0, 360] for dip direction and [0, 90] for dip. The dip and 

dip direction of the random joints are also defined using a 

similar function (Figure 5A). Each DFN model is generated within a 80-m by 80-m by 80-m box region, and three 

simulated boreholes are used to estimate the RQD of the 

rock mass (Figure 5B). 

A
 

B

 Figure 5.—(A) Stereoplot showing the four main joint sets 

and random joints; (B) boreholes used to calculate the RQD 

value for the simulated rock mass. 

The subsequent fragmentation 

analysis is carried out within a 10-m by 10-m by 10-m 

region (assumed pillar region). 

The RQD provides a measure of rock mass quality 

from drill core and is used as an input into geomechanical 

classification schemes, mainly the RMR and the Q system. 

The results (Figure 6A) show that there is an apparent 

correlation between RQD and the DFN volumetric intensity P32. The correlation is independent of orientation (i.e., 

number of joint sets). Notwithstanding the arbitrary choice 

of the input parameters of the current DFN model, there is 

an agreement between simulated results and results 

obtained for a DFN developed from an actual mine site. In 

Figure 6B, the total volume of formed blocks is divided by 

the total volume of the assumed pillar region to define a 

normalized volume index. The results show an apparent 

relationship between RQD and the degree of natural fragmentation of the assumed rock mass. It is argued that RQD 

is direction-dependent, and its value may change significantly with the azimuth and plunge of the simulated boreholes. There is a need to extend the analysis to consider 

different combinations of the assumed initial parameters 

used to generate the DFN models; this analysis is currently 

ongoing. 

34 
 

 

 I II
 

(A)
 

(B)

 Figure 6.—Simulated relationships between RQD and 

(A) volumetric intensity P32 and (B) normalized volume index. 

 

 

 

 

 

 

DISCUSSION AND CONCLUSIONS 

A technique is being developed that would allow 

engineers to employ a DFN-based rock mass characterization approach to derive rock mass properties to be used in 

conjunction with continuum codes. The main advantage of 

the approach is that it relies on quantifiable field rock mass 

descriptors (fracture orientation, length, and intensity) and 

the results of a large number of DFN models can be 

quickly compared to provide an initial estimate of rock 

mass strength, accounting also for scale and anisotropy 

effects. Whereas the initial modeling shows encouraging 

results, research is currently ongoing to further extend and 

validate the proposed methodology by considering different combinations of fracture orientation, length, spacing, 

and termination modes. 

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A synthetic rock mass model for jointed rock. In: Proceedings of the First Canada-U.S. Rock Mechanics Symposium 

(Vancouver, British Columbia, Canada, May 27–31, 

2007), Vol. I, pp. 341–349. 

Serafim JL, Pereira JP [1983]. Consideration of the 

geomechanic classification of Bieniawski. In: Proceedings 

of the International Symposium on Engineering Geology 

and Underground Construction, pp. 1133–1144. 

Vyazmensky A [2008]. Numerical modelling of surface subsidence associated with block caving using a 

finite-element/discrete-element approach [Dissertation]. 

Vancouver, British Columbia, Canada: Simon Fraser 

University. 

36 
 

 

 

 

 

THREE-DIMENSIONAL MODELING OF LARGE ARRAYS OF PILLARS 

FOR COAL MINE DESIGN 

By Gabriel S. Esterhuizen, Ph.D.,1 and Christopher Mark, Ph.D.1 

1

Pittsburgh Research Laboratory, National Institute for 

Occupational Safety and Health, Pittsburgh, PA. 

ABSTRACT 

The stability of the pillar line during retreat pillar 

mining is affected by the mining sequence, the mining 

geometry and the properties of the pillars, the gob, and the 

surrounding strata. Numerical models can assist in 

quantifying the complex interaction between these components as pillars are extracted and the roof caves to form the 

gob. However, modeling the details of the pillar geometry, 

as well as the large-scale surrounding strata, in a single 

three-dimensional model can pose significant challenges in 

terms of computer memory and solution run times. 

This paper describes a modeling technique that allows 

large arrays of pillars to be modeled by making use of 

equivalent elements that capture the stress-strain response 

of the pillars and the immediate roof and floor rocks. The 

stress-strain response is obtained from numerical models 

that have been calibrated against instrumented case 

studies. The pillar response is programmed into relatively 

large equivalent elements in a large-scale threedimensional model, negating the need to model the details 

of the pillars and surrounding excavations. 

An example is presented in which this method is used 

to assess retreat mining in two different geological settings. This modeling technique significantly improves the 

capabilities for evaluating retreat mining pillar stability in 

a variety of geotechnical conditions. 

INTRODUCTION 

Background 

On August 6, 2007, a violent coal bump occurred at 

the Crandall Canyon Mine near Price, UT. Six miners 

working at the time of the incident were presumed trapped. 

Ten days later, three rescuers were killed in a second 

bump. Rescue efforts were suspended, and the original six 

miners remained entrapped and were presumed to have 

been fatally injured. 

The miners at Crandall Canyon had been engaged in 

the process of pillar recovery when the disaster occurred. 

In the United States, pillar recovery accounts for no more 

than 10% of the coal mined underground, yet historically 

it has been associated with more than 25% of all ground 

fall fatalities [Mark et al. 2003]. Maintaining “global 

stability” through proper pillar design is essential to safe 

pillar recovery [Mark and Zelanko 2005]. The Mine Safety 

and Health Administration (MSHA) investigation report 

concluded that the Crandall Canyon disaster occurred 

because the pillars were too small to carry the overburden 

loads [Gates et al. 2008]. 

Current Methods of Design 

Retreat pillar mining presents a complex problem for 

engineering analysis and design. Any analysis is required 

to account for the three-dimensional characteristics of the 

overall panel layout, pillar loading and yield, the stability 

of the rooms, caving of the roof rocks after pillars have 

been extracted, the impact of variable strength strata, and 

variable field stresses. In addition, the surrounding strata 

are layered sedimentary rocks with highly anisotropic 

strength and deformation characteristics. 

Adding to the complexity, pillar recovery is conducted 

in a variety of geologic environments using a range of 

mining methods. In the Western United States, the terrain 

is extremely rugged, the overburden consists largely of 

thick, strong sandstones, and mining is typically conducted 

at depths that can exceed 600 m. In the northern Appalachian coalfields, the topography is rolling, the rocks are 

weaker, and the typical cover depth is less than 300 m. 

Conditions typically fall between these two extremes in the 

central and southern Appalachian coalfields, where most 

pillar recovery operations are located. 

The complexity of the problem led the National Institute for Occupational Safety and Health (NIOSH) to 

develop an empirical method for pillar design called the 

Analysis of Retreat Mining Pillar Stability (ARMPS) 

[Mark and Chase 1997]. The main strength of ARMPS is 

that it relies upon a large database of actual mining case 

histories to suggest the proper stability factors under different circumstances. The original database of 150 retreat 

mining case histories was later updated with nearly 100 

more from mines operating at depths in excess of 225 m 

[Chase et al. 2002]. 

ARMPS has been used extensively to design pillars 

and to evaluate roof control plans in the central Appalachian coalfields for nearly a decade. More recently, 

NIOSH developed the Analysis of Multiple-Seam Stability 

(AMSS) program, which extends ARMPS to multipleseam situations [Mark et al. 2007]. In the wake of the 

Crandall Canyon disaster, MSHA issued a Program Information Bulletin [Stricklin and Skiles 2008] and a Procedure Instruction Letter [Skiles and Stricklin 2008] that 

37
 
 

 

 

 

 

 

 

essentially require that ARMPS be used in all roof control 

plan evaluations to help ensure that pillars are properly 

designed. 

ARMPS uses relatively simple models to estimate the 

strength of the pillars and the magnitudes of the loads 

applied to them [Mark and Chase 1997]. For the pillar 

strength, ARMPS uses the Mark-Bieniawski formula 

[Mark 1987]. Tributary area equations are used to estimate 

the pillar development loads, while the “abutment angle” 

concept is used for the loads transferred to pillars during 

pillar extraction. Analysis of the deep-cover case histories 

in the ARMPS database indicated that the loading model 

may be less accurate for mining geometries that are highly 

“subcritical” (i.e., where the depth is much greater than the 

panel width) or when bridging of strong strata may occur 

in the overburden. In such cases, it seems that ARMPS 

may overestimate the loads applied to the panel pillars 

while underestimating the load carried by the interpanel 

barrier pillars. 

Numerical models have found limited application for 

evaluating retreat pillar mining owing to the excessive 

demands of computing hardware and model run times that 

are required to realistically simulate the complexities of 

the problem. One approach has been to simplify the 

problem through the use of boundary-element methods, 

in which only the coal seam(s) are modeled and the surrounding strata are assumed to be homogeneous. An example of such a program is LaModel [Heasley 1997], which 

uses the thin-plate formulation of the boundary-element 

method [Salamon 1991]. The program was originally 

developed by NIOSH and has found wide application in 

the U.S. coal mining industry. Pillar yield and gob 

compaction are modeled by implementing nonlinear seam 

elements. The thin-plate formulation has been found to 

better simulate observed stress distributions in the coal 

seam and provides a better match to subsidence observations than a simply elastic model [Heasley 1997]. This 

method is powerful, and it is relatively simple to create the 

geometric input data. 

Some of the limitations of the boundary-element 

method stem from the basic assumption that the coal seam 

is surrounded by a homogeneous rock mass consisting of 

thin, elastic plates separated by zero friction laminations. 

This method therefore requires that “average” parameters 

are used for the surrounding rock mass. Since this method 

assumes the rock mass is elastic, failure and stress redistribution in the surrounding rock are not modeled. 

These shortcomings can partly be addressed by judicious 

model calibration against known rock mass response 

[Heasley 2008]. 

Full three-dimensional finite-element and finitedifference methods are available that can model the complexity of geometry, geology, and rock failure associated 

with pillar retreat mining. However, the need to model the 

rock mass response at a scale of single meters in the vicinity of the pillars while also modeling the surrounding rock 

mass and mined areas at a scale of more than 1,000 m 

poses significant challenges in terms of computer 

resources and run times. A method of simplifying the 

model geometry while capturing the essential aspects of 

pillar response was developed by Board and Damjanac 

[2003] for evaluating the potential for pillar collapse in 

trona mines. The approach uses equivalent elements that 

follow the same stress-deformation curve as actual pillars 

and significantly reduces the need for computer resources 

while preserving most of the advantages of full threedimensional models. 

METHOD OF EQUIVALENT PILLAR MODELING 

Approach 

The equivalent pillar modeling method is based on 

replacing a coal pillar, the surrounding rooms, and the 

immediate roof and floor by one or more elements that 

have the same load-deformation response. This allows 

details of the local pillar, roof, and floor response to be 

incorporated into larger elements. Using the larger elements, models can be built to include extensive mined 

areas without sacrificing the effects of local rock mass 

response. A large-scale model can include any number of 

different equivalent elements for different room-and-pillar 

sizes or shapes, allowing typical panel pillars, barriers, and 

main development pillars to be modeled. 

The response of the equivalent elements includes all of 

the phenomena associated with a pillar undergoing 

increasing load, such as floor heave, roof collapse, punch

ing of the pillar into weak surrounding strata, and ultimate 

yield or failure of the pillar (see Figure 1).

­

σ

ε

(a) (b) (c) 

 Figure 1.—Concept of an equivalent element model showing (a) the detailed geology and mining geometry being 

investigated, (b) the resulting stress-strain relationship, and 

(c) the uniform equivalent element that follows the same 

stress-strain relationship. 

 The detail 

required to capture each of these events need not be 

included in the equivalent numerical model, but is implied 

in the load-deformation response of the equivalent pillar 

element. After solving a large-scale model of a particular 

pillar layout, the detailed pillar, roof, or floor response can 

be found by referring back to the original data or model 

that was used to develop the load-deformation response. 

38 
 

The following discussion is based on the implementation of the equivalent pillar method in the FLAC3D finitedifference program [Itasca Consulting Group 2007]. 

FLAC3D has an internal programming language called 

FISH that allows the user to modify the response of 

individual elements in a model. This facility was used 

to specify the response of the equivalent pillar elements. The appendix to this paper contains an example 

of the FISH programming used to define the loaddeformation response of a pillar with a width-to-height 

ratio of 6.0. 

Obtaining Pillar Response Curves 

The response of a pillar and the immediate roof and 

floor strata can be obtained from direct measurement and 

monitoring of pillars in the field. Since appropriate field 

data are relatively scarce and costly to obtain, numerical 

models can be used to obtain reasonable estimates of the 

behavior of pillars under varying geological conditions. 

These models should be calibrated against field observations where possible. 

An example of a FLAC3D numerical model to obtain 

the load-deformation response of a pillar with a width-toheight ratio of 6.0 is shown in Figure 2.

 

 

0 

5 

10 

15 

20 

25 

0 0.005 0.01 

Stress (MPa) 

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 

Strain 

Stress-strain curve of 2m 

high pillar 12m wide 

Stress-strain curve of equivalent 

element 12m high 15m wide 

(A) (B) 

 Figure 2.—FLAC3D model of a single pillar with a width-to-height ratio of 6.0, showing the resulting stress-strain curves obtained 

for the pillar and for the equivalent element. The stress in the equivalent element is lower owing to a larger area of application. 

 The response of 

the model pillar to increasing loading was obtained by 

simulating a downward-moving boundary at the top of the 

model while fixing the lower boundary and constraining 

the sides of the model in the horizontal direction. The 

stress-strain response of the pillar was obtained by recording the average stress at the midheight of the pillar and the 

strain between points located at the top and bottom of 

the pillar. 

The coal was modeled using the strain-softening HoekBrown constitutive model in FLAC3D [Hoek et al. 2002], 

while the laminated nature of the surrounding rocks was 

modeled using the bilinear ubiquitous-joint constitutive 

model. The contact plane between the coal and the surrounding rock was modeled as an explicit interface with a 

friction angle of 25°. Table 1 summarizes the key material 

properties used for the coal and the surrounding rock. 

It was found that the implementation of the Hoek-Brown 

failure criterion in FLAC3D best represents the performance of coal pillars, especially at width-to-height ratios 

greater than 4.0. 

Table 1.—Properties used to obtain the stress-strain 

response of a single pillar 

Property Coal Surrounding 

rock 

Elastic modulus 3 GPa 25 GPa 

Uniaxial compressive strength1 20 MPa 80 MPa 

Hoek-Brown m-parameter 1.47 — 

Hoek-Brown s-parameter 0.07 — 

Hoek-Brown a-parameter 0.65 — 

Friction angle — 32° 

1

Laboratory-scale strength. 

The resulting stress-strain curve for the modeled pillar 

is shown in Figure 2B. It can be seen that the pillar has an 

initial elastic response up to a stress of about 10 MPa, 

followed by strain hardening until the pillar reaches a peak 

strength of 20.4 MPa, followed by strain softening to about 

18 MPa. The model predicts a peak strength similar to that 

predicted by the Mark-Bieniawski equation [Mark 1987], 

which is widely used in the United States, while the post39 
 

 

 

 

 

 

peak strength reduction is similar to field results reported 

by Mark [1987]. 

Figure 2B also shows the stress-strain curve of an 

equivalent element that represents the response of the 

pillar, half of the surrounding entries, and 5 m of the roof 

and floor rocks. The dimensions of the equivalent element 

are 15 m by 15 m wide by 12 m high. The curve was 

obtained by monitoring the average stress across the full 

width of the model at an elevation 5 m below the 

midheight of the pillar and monitoring the strain between 

two points 6 m above and below the midheight of the 

pillar. The equivalent curve therefore captures the overall 

behavior of the pillar and the immediately surrounding 

strata and includes the effects of any local floor heave or 

roof damage. Both the stress and strain values of the 

equivalent element seem to be lower than those measured 

for the pillar because the equivalent element is taller, 

reducing the strain, and wider, reducing the average stress, 

than the original coal pillar. 

Note that changing the interface properties or the 

strength of the roof and floor materials can have a significant effect on the peak and residual pillar strength. The 

stress-strain curve obtained from this analysis can be used 

to define the properties of equivalent pillar elements in 

models representing extensively mined and pillared areas. 

Modeling the Equivalent Pillars 

The key to using equivalent elements in a large-scale 

model lies in modifying the elements that represent the 

coal pillars so that they follow the desired stress-strain 

relationship. We used the Coulomb strain-softening constitutive model in FLAC3D, which can conveniently be 

modified to achieve the desired stress-strain relationships, 

after Damjanac [2008]. It is necessary to modify the element behavior so that horizontal confinement will not be 

generated while it is deformed in the vertical direction, 

because the effect of confinement is already accounted for 

in the pillar stress-strain curve. This can be achieved by 

setting the Poisson’s ratio to zero and resetting the horizontal stress components to zero during model solution. 

Details of the parameter settings and model initiation for 

FLAC3D are presented in the appendix to this paper. 

The equivalent pillar elements used by the authors 

each simulated the response of a pillar and the surrounding 

entries up to the center line of the entries. The stress within 

the equivalent elements will therefore be lower than the 

stress in the pillar, which has a smaller cross-sectional 

area. It is therefore necessary to modify the initial stresses 

in the equivalent elements as follows: 

σ p σ e = (1) 1 − r

where σe is the average stress in the equivalent pillar, σp is 

the average stress in the actual pillar, and r is the extraction ratio. When evaluating the results of an analysis, the 

inverse conversion must be done to obtain the actual pillar 

stresses from the equivalent stress values reported by 

the model. 

Modeling Abutment Edges and Gob 

Crushing of the edges of large abutments or adjoining 

barrier pillars can also be modeled using equivalent elements. A detailed model of a wide abutment and the adjacent opening can be created, and the average stress-strain 

response of the outer segment of the abutment can be 

recorded. Equivalent elements can then be created that 

follow the same stress-strain relationship. Gob can similarly be modeled by creating equivalent elements that 

follow the desired stress-strain response. 

VERIFICATION OF METHOD 

A number of models were created to test the equivalent 

pillar modeling approach against detailed models of full 

pillars. Compression testing of single equivalent pillar elements showed that the stress-strain response followed the 

desired values with an error of less than 1%. 

A second test was conducted in which a panel of six 

entries and five pillars was modeled using both equivalent 

pillar elements and a detailed pillar model. The pillars 

were modeled at 200-m depth and the average vertical 

stress in the pillars was compared. Figure 3 shows the 

results. Again, it can be seen that the equivalent pillar 

method provides satisfactory results. 

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Distance (m)

Stress (MPa)

Equivalent model

Detail model

0.0 

2.0 

4.0 

6.0 

8.0 

10.0 

12.0 

0.0 20.0 40.0 60.0 80.0 100.0 120.0 

Distance (m) 

Stress (MPa) 

Equivalent model 

Detail model 

Pillar Pillar Pillar Abutment

 Figure 3.—Pillar and abutment stresses obtained using 

a detailed model and an equivalent pillar model for a 

panel of six pillars (only three pillars shown because of 

symmetry). 

The difference 

between the average stress in the equivalent pillars and the 

detailed model pillars was less than 2%. 

40 
EXAMPLE APPLICATION 

The example below shows how three-dimensional 

models have been used to investigate the impact of geology and depth on stress distributions around pillar retreat 

panels. The results are compared to predictions of the 

empirically developed ARMPS method. 

Mining Geometry 

Two models were created—the first simulating retreat 

mining at a depth of cover of 200 m, the second at 600 m. 

The geology of the 200-m depth model was selected to 

simulate a typical extraction panel in the northern Appalachian coalfields with relatively weaker and thinner 

bedded strata. The model at 600-m depth was set up to 

simulate pillar extraction in the Western United States, 

where thicker, stiffer strata are present. 

Details of the mining geometry are presented in 

Table 2.

Table 2.—Mining geometry 

Value for Value for 

Parameter 200-m depth 600-m depth 

model model 

Entry and crosscut width 6 m 6 m 

Pillar width 18 m 24 m 

Mining height 2.4 m 2.4 m 

No. of entries in panel 6 5

Width of panel 126 m 126 m 

Length of zone containing pillars 300 m 300 m 

Length of extracted (gob) zone 300 m 300 m 

Barrier width 18 m 60 m 

Width of adjacent panel 126 m 126 m 

 The mining dimensions were selected so that a 

stable layout would be formed in both cases. Two mining 

scenarios were considered for each case. The first scenario 

represented retreat mining in an isolated panel. The second 

scenario assumed that the active mining panel was located 

adjacent to a previously mined panel, separated by a 

barrier pillar. 

Model Setup 

A FLAC3D model was created with horizontal dimensions of 1,100 by 600 m. In the vertical direction, the rock 

mass was modeled from a point 100 m below the coalbed 

up to the ground surface. Figures 4 and 5 show examples 

of the two models, indicating the different degrees of 

layering of the strata. The side boundaries of the models 

were constrained in the horizontal direction and the bottom 

was fixed. The rooms and pillars were modeled using the 

equivalent pillar approach. The equivalent elements were 

12 m high, each representing the 2.4-m-high coal seam and 

9.6 m of the surrounding rocks. The abutment edges were 

also modeled using equivalent elements that represented a 

12-m-wide strip of coal with half an entry mined out of it. 

41 

1,100 m 

700 m 

Coalbed 

Extraction panels 

 Figure 4.—View of a FLAC3D model of retreat mining at a depth of cover of 600 m in the Western United States using equivalent 

pillar elements. Rock layering in the model is shown in shades of gray. 
 

1,100 m 

300 m 

Coalbed 

Equivalent elements representing 

pillars in the extraction panel 

 Figure 5.—View of a FLAC3D model of retreat mining at a depth of cover of 200 m in the northern Appalachian coalfields using 

equivalent pillar elements. Rock layering in the model is shown in shades of gray. 

The overburden was modeled using the strainsoftening ubiquitous-joint model available in FLAC3D. 

This model can simulate both bedding plane shearing and 

intact rock failure, which has been found to be appropriate 

for modeling the anisotropic strength of bedded coal 

measure strata [Zipf 2007; Gale 1999]. The rock strength, 

deformation properties, and bedding strength properties 

used in the models are presented in Table 3.

Table 3.—Representative rock properties 

Rock type 

Uniaxial 

compressive 

strength 

(MPa) 

Elastic 

modulus 

(GPa) 

Rock Bedmatrix ding

friction coheangle sion

(degrees) (MPa) 

Bedding

friction

angle

(degrees) 

Weak shale 20 7.0 20 0.3 5 

Moderatestrength 40 11.0 25 0.5 7 

shale 

Moderatestrength 60 15.0 35 2.0 10 

sandstone 

Strong 

sandstone 100 20.0 40 4.0 12 

Moderatestrength 80 30.0 40 6.0 15 

limestone 

Strong 

limestone 140 40.0 42 12.0 25 

 The compressive strength of the modeled rock was reduced by a factor 

of 0.58 from the values shown in the table to account for 

the strength reduction between laboratory samples and the 

larger-scale in situ rock beds, after Hoek and Brown 

[1980]. The Poisson’s ratio was set at 0.25 and tensile 

strength set to 10% of the in situ rock compressive 

strength. Bedding tensile strength was set at 10% of the 

rock matrix tensile strength. Calibration tests were conducted to ensure that the models provided a reasonable 

estimate of measured surface subsidence and abutment 

stresses. 

The unmined coalbed was modeled as a solid material 

using elements that were 12 m high to match the equivalent pillar elements. It was therefore necessary to modify 

the elastic modulus of the solid coal elements to account 

for the stiffer rock material included in the 12-m section. 

The gob was also modeled using the equivalent element 

approach. It was assumed that complete caving occurred 

everywhere in the mined area to a height of 6 m above the 

floor of the coalbed. The stress-strain behavior of the fully 

caved gob was based on the results of laboratory tests 

[Pappas and Mark 1993]. For these analyses, the results for 

strong sandstone were used to model the gob for the deepcover western example and shale results for the shallowercover eastern example. Vertical stresses were depthdependent, and horizontal stresses were initialized using 

the relationships developed by Mark and Gadde [2008] for 

U.S. coal mines. 

42 
 

After building each model, the vertical stresses within 

the equivalent elements were modified to account for the 

presence of the excavated rooms using Equation 1. The 

model was then allowed to equilibrate with these modified 

stresses. Mining was then modeled in a stepwise manner, 

extracting the equivalent pillar elements and replacing 

them with gob elements until the length of the extracted 

zone reached 300 m. At this stage, the gob zone was 300 m 

long and the zone containing the remaining pillars was also 

300 m long. Owing to symmetry conditions, the effective 

length of these zones was twice the modeled length. The 

model was run to equilibrium at each step, and the results 

of the final step are discussed below. 

RESULTS 

Table 4 compares the results obtained by the FLAC3D 

model using the equivalent element approach with the 

empirically developed ARMPS results within the active 

mining zone (AMZ).

Table 4.—Results obtained by FLAC model and ARMPS empirical method 

Eastern U.S. model Western U.S. model 

Parameter Difference Difference FLAC ARMPS FLAC ARMPS (ARMPS: FLAC) (ARMPS: FLAC) 

Average pillar stress after development (MPa) 8.2 9.1 +11.0% 22.2 24.2 +9.2% 

Average stress in AMZ first panel mining (MPa) 13.3 13.8 +3.8% 26.0 33.2 +28.0% 

Average stress in AMZ second panel mining (MPa) 16.7 15.4 −7.7% 28.9 34.5 +19.0% 

 The AMZ represents a group of 

pillars at the extraction front that are assumed to carry 90% 

of the front abutment load [Mark and Chase 1997]. The 

results presented here are applicable only for the particular 

geometry and geology modeled and should not be considered to be generally valid for other mine geometries or 

geological conditions. 

The results show that at the development stage 

ARMPS predicts pillar stresses that are about 10% higher 

than the FLAC predictions. The main reason for this difference is that ARMPS assumes that the development 

pillars are carrying the full tributary loading, while FLAC 

considers the reduced stiffness of the pillars, allowing 

some of this load to be distributed to other areas. 

The stresses in the AMZ seem to be highly dependent 

on the stiffness ratio of the overlying strata to the pillar 

stiffness. The results show that for the western U.S. model 

with stiffer overburden, ARMPS predicts an average AMZ 

stress that is 28% higher than that calculated by FLAC. 

However, the results for the eastern U.S. case differ by 

only 3.8%. This difference is significant and can partially 

explain why deep-cover retreat mining has been successful 

at relatively low values of the ARMPS stability factor. The 

results also show that the three-dimensional models that 

include details of the geology, relative rock stiffness, pillar 

response, horizontal stress, gob, and rock mass failure can 

provide additional insight into the complex rock response 

resulting from retreat mining. 

CONCLUSIONS 

The method of equivalent pillar modeling allows threedimensional stress analysis of large arrays of pillars to be 

carried out efficiently without losing the essential aspects 

of the interaction between the pillars and the surrounding 

rocks. The method allows models of large areas to be 

created that are manageable in terms of computing requirements. Testing of the technique through comparison to a 

detailed three-dimensional model shows that the equivalent models accurately represent the overall response of the 

rock mass and load distribution among the pillars and surrounding unmined coal. 

An example application has shown that the equivalent 

pillar technique applied to three-dimensional models can 

improve our understanding of the interaction between 

surrounding strata and pillars during retreat mining. The 

impact of variations in geology and geometry can readily 

be assessed. The developed method can therefore contribute to improved design guidelines and greater safety in 

retreat mining. 

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multiple-seam stability. In: Peng SS, Mark C, Finfinger 

GL, Tadolini SC, Khair AW, Heasley KA, Luo Y, eds. 

Proceedings of the 26th International Conference on 

Ground Control in Mining. Morgantown, WV: West Virginia University, pp. 5–18. 

Pappas DM, Mark C [1993]. Behavior of simulated 

longwall gob material. Pittsburgh, PA: U.S. Department of 

the Interior, Bureau of Mines, RI 9458. NTIS No. PB93­

198034. 

Salamon MDG [1991]. Deformation of stratified rock 

masses: a laminated model. J S Afr Inst Min Metall 91(1): 

9–26. 

Skiles ME, Stricklin KG [2008]. Technical support 

assistance in reviewing roof control plans. Arlington, 

VA: Mine Safety and Health Administration, Procedure 

Instruction Letter No. I08-V-02, May 29, 2008. Available at: http://www.msha.gov/regs/complian/pils/2008/ 

pil08-v-2.pdf 

Stricklin KG, Skiles ME [2008]. Precautions for 

the use of the Analysis of Retreat Mining Pillar 

Stability (ARMPS) computer program. Arlington, VA: 

Mine Safety and Health Administration, Program 

Information Bulletin No. P08-08, April 7, 2008. Available at: http://www.msha.gov/regs/complian/PIB/2008/ 

pib08-08.asp 

Zipf RK Jr. [2007]. Numerical modeling procedures 

for practical coal mine design. In: Mark C, Pakalnis R, 

Tuchman RJ, eds. Proceedings of the International Workshop on Rock Mass Classification in Underground Mining. 

Pittsburgh, PA: U.S. Department of Health and Human 

Services, Centers for Disease Control and Prevention, 

National Institute for Occupational Safety and Health, 

DHHS (NIOSH) Publication No. 2007B128, IC 9498, 

pp. 153–162. 

44 
 

APPENDIX.—CREATING EQUIVALENT PILLAR ELEMENTS IN FLAC3D 

Equivalent pillar elements respond to the vertical closure between the roof and floor in the same way that a 

pillar would. In FLAC3D, this can be achieved by using 

the Coulomb strain-softening logic to control the response 

of the equivalent pillar elements. 

When using the strain-softening approach, a number of 

modifications to the element properties must be made so 

that they perform as required. The Poisson’s ratio of the 

elements must be set to zero so that lateral dilation does 

not occur, which can cause additional lateral confinement 

to the equivalent pillar elements. For convenience, the friction angle is also set to zero so that the strength and stressstrain response of the equivalent pillar element can be controlled by varying the cohesion, described below. 

The equivalent elements will respond elastically until 

their strength is exceeded. The evolution of the pillar 

strength after the initial elastic response, through strain 

hardening, strain softening, and ultimate plastic yield, is 

specified by a FLAC3D table, which relates the element 

cohesion to the plastic strain. Since the friction angle is set 

to zero, the cohesion should be one-half the desired 

strength. Table A-1 shows the calculation of the cohesionstrain values used to define the response of an equivalent 

element that simulates the 6.0 width-to-height ratio shown 

in Figure 2. 

Table A-1.—Calculation of plastic strain-cohesion values 

to control equivalent element yielding 

Equivalent 

stress 

(MPa) 

Total 

strain 

Elastic 

strain 

Plastic 

strain Cohesion 

0 0.0000 0.0000 0.0000 0 

6.40 0.0009 0.0009 0.0000 3.20 

10.88 

12.80 

0.0020 

0.0035 

0.0015 

0.0018 

0.0005 

0.0017 

5.44 

6.40 

11.52 0.0067 0.0016 0.0051 5.76 

11.52 0.0160 0.0016 0.0144 5.76 

This table assumes the equivalent pillar 

responds elastically up to 6.4 MPa, then departs from 

elastic behavior up to the peak stress of 12.8 MPa, 

followed by yielding to a residual strength of 11.52 MPa. 

At each point on the stress-strain curve, the elastic component of strain is subtracted so that only the plastic 

component of strain is used when generating the straincohesion pairs. An elastic modulus of 7.2 GPa was used to 

calculate the elastic strains. This value represents the combined modulus of the rock and coal in the equivalent element and can be obtained from the stress-strain curve of 

the equivalent element or approximated by calculation. 

The following text shows how the strain-softening 

properties of the equivalent elements are defined in FLAC, 

followed by the FISH programming to implement the 

equivalent element behavior. In this example, the pillars 

were created with a group name “P1”. The pillars are first 

defined as strain-softening, and the stress-strain relationship for the pillars is provided as a cohesion table. The 

“countpillar” function counts the number of pillars of type 

“P1” in the model and sets up an array to store the memory 

addresses of these pillars. The “parray” function searched 

for the pillars of type “P1” and stores their memory 

addresses in the aforementioned array. It also calculates 

and sets the initial stress in the equivalent pillar elements. 

The “dopillar” function destroys the horizontal stress in the 

equivalent pillar elements during each solution cycle. 

{Assign pillar properties in command mode} 

{Cohesion is one-half desired pillar strength} 

 model ss range group P1

 prop dens=2000 b=bmod s=smod range group P1

 prop fric=0 coh=3.2e6 ctable=10 range group P1

 {Create cohesion table - half of desired strength – 

obtained from Table A-1 above} 

 Table 10 0,3.20e+06 0.0005,5.44e+06 0.0018,6.40e+06 

0.0051,5.76e+06 0.0144,5.76e+06 

{Count the number of pillar elements in group P1} 

def countpillar 

 pnt = zone_head 

 npillar1 = 0

 loop while pnt # null 

 if z_model(pnt) # 'null' 

 if z_group(pnt) = 'P1'

 npillar1 = npillar1 + 1

 endif 

 endif ;not null element 

 pnt = z_next(pnt) 

 endloop 

{Create an array to store pointers to the elements in 

group P1} 

 Parraysize1 = npillar1

 if Parraysize1 = 0 then 

 Parraysize1 = 1 

endif 

end ;countpillar 

countpillar 

45 
 

 

 

 

 

 

 

 

 

 

{Populate the array with pointers to the P1 elements} 

def parray 

if npillar1 > 0 

array pelts1(Parraysize1) 

i=1 

pnt = zone_head 

 loop while pnt # null 

 if z_model(pnt) # 'null'

 if z_group(pnt) = 'P1'
 

pelts1(i) = pnt 

 i = i + 1 

 endif ;belongs to group P1

 endif ;not null element 

 pnt = z_next(pnt) 

endloop 

{Fix initial stress in equivalent pillar elements based on 

extraction} 

percpillar1 = 0.61 

; percpillar is percentage pillars = 1-extraction ratio

 loop iz (1,npillar1) 

 z_szz(pelts1(iz))=z_szz(pelts1(iz)) * percpillar1

 z_extra(pelts1(iz),1) = percpillar1

 endloop 

endif ; if npillar1 

end 

parray 

{Routine to destroy horizontal stress in equivalent 

pillars P1} 

def dopillar 

whilestepping 

if npillar1 > 0 

loop iz (1,npillar1) 

 z_sxx(pelts1(iz))=0.0 

 z_syy(pelts1(iz))=0.0 

 z_sxy(pelts1(iz))=0.0 

 z_sxz(pelts1(iz))=0.0 

 z_syz(pelts1(iz))=0.0 

endloop 

endif 

end 

46 
 

 

 

 

NUMERICAL MODEL EVALUATION OF FLOOR-BEARING CAPACITY IN COAL MINES 

By Murali M. Gadde1
 

1

Peabody Energy, St. Louis, MO. 

47
 

ABSTRACT 

This paper addresses the question of ultimate floorbearing capacity for pillar design in room-and-pillar coal 

mines. It lists some of the idiosyncrasies that limit the 

application of classical bearing capacity analyses that are 

based on closed-form solutions. An approach that uses 

numerical models is described. The models are first validated against a simple case of a strip footing resting on a 

semi-infinite homogeneous weightless soil. Two cases are 

then presented in which calibrated three-dimensional 

models are used to investigate the effect of nonuniform 

distribution of pillar loads and the effect of interaction 

between pillars on floor-bearing capacity. The results show 

that nonuniform pillar loading of the floor is not likely to 

cause a significant change in ultimate bearing capacity of 

the floor, but can explain superficial floor heave that is 

often observed in coal mines. The interaction between 

adjacent pillars can have a significant effect on pillar 

strength if the weak floor has a non-zero friction angle. 

Results show that the strength of the floor adjacent to rib 

pillars experiences greater benefit from interaction compared to rectangular pillars. It is concluded that the design 

of coal mine workings can be adequately conducted by 

using numerical models that simulate the complex pillarfloor interactions. 

INTRODUCTION 

Coal mines in the Illinois basin extract coal using the 

room-and-pillar method. The coalbeds are often underlain 

by weak strata that can fail when the pillar load exceeds 

the bearing capacity, resulting in floor heave and excessive 

closure in the mine workings that can cause surface subsidence. Classical bearing capacity models do not account for 

the idiosyncrasies of a typical coal mine floor stability 

problem, shown in Figure 1, including variations of pillar 

length (L) and width (B), entry width (s), thickness of 

weak floor bed (H), and variations in strata cohesion (c), 

friction angle (φ), and density (γ). B

Weaker bed

Stronger bed

Roof

c1≠0, φ1 ≠0, γ1≠0

c2≠0, φ2 ≠0, γ2≠0

H

A A

B

L

A A 

A typical L

room-and-­

pillar panelar panel 

layout 

Section AA 

s B Entry

Weaker bed 

Entry 

Roof 

c1≠0, φ1 ≠0, γ1≠0 H

s

Stronger bed c2≠0, φ2 ≠0, γ2≠0 

Figure 1.—Features of a typical coal mine floor-bearing 

capacity problem.

 A determination of the 

floor-bearing capacity in a coal mine should consider the 

following: 

• Different geometries of pillars in the plan view 

(square, rectangular, long-continuous, parallelogram, and irregular) 

• Multiple layers of strata with variable thickness 

could exist in the floor within the zone of influence 

of a coal pillar 

• Presence of multiple pillars in close proximity at 

uniform or variable spacing 

• Each layer of rock in the floor is deformable and 

normally has non-zero values of cohesion, friction 

angle, and density 

•	 Some of the floor strata may not be adequately 

described by the Mohr-Coulomb failure criterion 

• Volumetric expansion of the floor strata is possible 

in the postfailure state (dilatation effects may not 

be ignored) 

• Spatial variation of floor properties (both laterally 

and with depth) 

•	 Time-dependent deformation and failure of the 

floor 

•	 Effect of any water accumulation on timedependent pore water pressure changes and accompanying strength degradation 

•	 Nonuniform vertical stress distribution on coal 

pillars 

• Presence of in situ horizontal stresses 
 

 

 

 

 

 

 

 

 

 

Conventional bearing capacity solutions treat the floor 

as an isolated component of the underground opening stability. In reality, however, the floor, coal pillar, and roof 

function together as a system and interact with each other. 

It is often necessary to consider the entire system stability 

rather than any one component’s integrity. In such cases, 

the analytical method should be able to incorporate the 

interaction effects of the different components of the entire 

system. 

When all of the requirements set forth are considered, 

it is impractical to provide a closed-form solution to the 

coal mine bearing capacity problem. There is, however, an 

alternative. With the tremendous advancements made in 

computer hardware and the advent of sophisticated numerical modeling tools over the past 2 decades, it is now possible to incorporate almost every single aspect of the 

bearing capacity problem mentioned above in the analysis. 

Such flexibility and versatility is achieved because numerical models deal with a complex problem by following a 

“parts-to-whole” approach. In a numerical model, the final 

solution to a “big” problem is accomplished by putting 

together solutions to several “small” problems. It is easier 

to incorporate any degree of complexity at the “parts” level 

rather than at the “whole” level as accomplished in a 

closed-form solution. 

Use of numerical modeling to investigate coal mine 

floor stability is not new. Some interesting work was 

done in the past by researchers from several coalproducing countries [Rockaway and Stephenson 1979; 

Chandrashekhar 1990; Bandopadhay 1982; Deb et al. 

2000; Vasundhara 1999; Bhattacharyya and Seneviratne 

1992; Yavuz et al. 2003]. The past studies, however, relied 

heavily on two-dimensional modeling to explain some sitespecific field behavior or were limited to a few parametric 

studies of limited applicability. 

This paper is devoted to applying numerical modeling 

to study two aspects of the floor stability problem: (1) the 

interaction effect of multiple pillars and (2) nonuniform 

distribution of pillar loads on floor-bearing capacity. The 

studies were conducted using the FLAC3D numerical 

modeling code developed by the Itasca Consulting Group, 

Inc. The explicit Lagrangian solution scheme and the 

mixed discretization procedures adopted in FLAC3D using 

the finite-difference approach makes it a powerful tool to 

address nonlinear problems. Further, the explicit scheme 

makes it easier to apply loads and deformations in a 

manner analogous to physical tests. Such a solution 

methodology also provides the model response in a physically comparable manner. FLAC3D provides a programming language called FISH, which facilitates addition of 

functionalities that are not included in the standard features 

of the program and helps automate several aspects of 

modeling. 

MODEL VALIDATION 

The first step in developing a proper numerical modeling methodology is to “calibrate” the process such that 

theoretical solutions are reproduced within a reasonable 

tolerance. This calibration is necessary because the modeling results are sensitive to the mesh size and loading rates 

adopted for the simulation. This particular mesh density and 

the loading rate value, which provides a match with the 

theoretical solutions, can then be used for further studies. 

The simplest bearing capacity problem for which an 

exact closed-form solution exists is that of a strip footing 

resting on a semi-infinite homogeneous weightless soil, 

known as Prandtl’s solution [Terzaghi and Peck 1967]. 

This situation was modeled to verify the modeling 

methodology. For the verification models, the cohesion 

value was arbitrarily chosen as 150 psi and the friction 

angle was varied from 0° to 30° in 5° increments. A constant Poisson’s ratio equal to 0.35 was used in all of the 

models. The soil was assumed to satisfy the MohrCoulomb yield function with perfectly plastic behavior. It 

was also assumed that the soil did not exhibit volume 

change in the postyield state. Although a non-zero density 

value was input for the floor in the models, the computed 

bearing capacity would almost be the same as that of a 

weightless soil because the width of the strip load was only 

12 in. The mesh density and the loading rate were calibrated for the 5° friction angle case and then kept constant 

for much of the research. Of course, it was not possible to 

get an exact match for the mesh density when different 

geometric parameters are varied, but every effort was 

made to keep the discretization as close as possible to the 

one used in the verification models. 

The modeling results indicated that the verification 

models will provide bearing capacity results that match to 

within 3.5% of the theoretical values for a range of material friction angles. The computed and theoretical bearing 

capacity factors (N) are presented in Table 1, which shows 

the results for both a smooth and rough footing.

Table 1.—Comparison of theoretical- and modeling-based 

bearing capacity factor, Nc , for a constant cohesion 

equal to 150 psi
 

Friction 

angle, 

degrees 

Bearing capacity factor, Nc 

Model: smooth Model: rough Theoretical footing footing 

0 5.14 5.15 5.24 

5 6.49 6.49 6.65 

10 8.35 8.31 8.61 

15 10.99 10.99 11.36 

20 14.85 14.89 15.37 

25 20.76 20.80 21.47 

30 30.22 30.23 30.52 

 Clearly, 

the numerical models simulate the bearing capacity 

problem with sufficient accuracy. The validated numerical 

modeling approach, model discretization, and loading rates 

were used to conduct the further studies presented in this 

paper. 

48 
 

 

 

 

 

EVALUATION OF NONUNIFORM PILLAR STRESS
 

DISTRIBUTION 

In all of the traditional bearing capacity theories, the 

vertical load on the footing is assumed to be uniformly 

distributed. However, in underground coal mines, it is 

known that the vertical stress over a pillar is not uniform. 

Although some researchers [Chugh and Pytel 1992] have 

recognized this issue before, no study has ever been done 

on the effect of nonuniform stress distributions on the 

computed bearing capacity. The numerical modeling 

methodology developed here offers an opportunity to study 

this aspect of the bearing capacity problem. 

When a realistic coal mine geometry is considered, in 

addition to the nonuniform stress distribution over the coal 

pillar, some horizontal premining stresses also exist in the 

floor. For the “soft” underclay material, the magnitude of 

the horizontal stresses may not be very high. Nevertheless, 

some non-zero horizontal stresses exist in the floor. To 

account for all of these effects, an actual case of a coal 

mine with weak immediate floor has been chosen. For the 

sake of simplicity, only two-dimensional modeling has 

been conducted here. The geometry near the coal seam 

used in the model is shown in Figure 2. The model contains an 18-ft-wide entry and 52-ft-wide pillar resting on a 

7-ft-thick claystone floor.

 

coal seam

claystone

Coal seam 

Claystone 

 Figure 2.—Part of the modeled geometry to study the 

nonuniform vertical stress distribution effect on bearing 

capacity. 

In the above model, the claystone floor has been 

assumed to behave in a perfectly plastic manner, satisfying 

the Mohr-Coulomb yield criterion. Arbitrarily chosen 

cohesion and friction angle values equal to 300 psi and 

20°, respectively, were assigned to the claystone floor. The 

rest of the model was assigned elastic properties. After the 

initial model was solved to incorporate Poisson’s ratiobased horizontal stresses, the mine opening was created 

and the model was solved again to equilibrium. At this 

stage, the top boundary of the model was fixed in the 

vertical direction and displacement-controlled load was 

imposed on the coal pillar until the floor material completely reached its limit state. The resultant vertical stress 

on the first layer of floor below the pillar was monitored 

continuously as the model was being solved using a FISH 

function. The simulation is shown in Figure 3a, where the 

resultant vertical stress on the floor below the coal pillar is 

plotted against the number of model steps. 

Similarly, to simulate a rigid plate loading on the floor 

in a different model, the entire cover above the coal pillar 

was removed and the displacement loading was applied 

over the top of the coal pillar. This later model was not 

solved for equilibrium before commencing the displacement loading. The vertical stress variation on the floor for 

this loading situation is plotted in Figure 3b. 

The modeling results showed that the limit stress value 

was 828 psi for the nonuniform pillar loading case and 

800 psi for the rigid plate condition for the assumed inputs. 

Therefore, consideration of the realistic vertical stress distribution on the coal pillar did not alter the ultimate bearing capacity by more than about 3%. The slightly higher 

bearing capacity in the nonuniform load case was due to 

the existence of small horizontal stresses in the floor 

compared to the uniform loading case, where no horizontal 

stresses were applied. At the limit state, the extent of 

yielding and the shear strain rate distribution also looked 

similar in both cases. There is, however, one major difference. As shown by the red ellipses in Figure 3a, several 

localized floor failures occurred before reaching the limit 

state. For this case, it was found that when additional loads 

were induced in the coal pillar by the uniform displacement loading, in areas close to the pillar rib where the 

highest vertical stress was acting before, floor failure commenced. As the floor below the rib failed, the vertical 

stress was transferred deeper into the coal pillar, thus 

establishing another stress concentration zone. With further displacement loading, progressively deeper portions of 

the floor reached limit states in a rather abrupt fashion, 

resulting in the stairstepped stress variation shown in Figure 3a. Such stress variation, however, does not seem to 

have altered the ultimate bearing capacity of the floor. 

49 
 

(a) (b) 

 Figure 3.—The variation of resultant vertical stress on floor for (a) nonuniform pillar stress distribution and (b) uniform 

pillar stress distribution. 

It must be reminded here that under a rigid plate or 

when uniform displacement loading is applied to the floor, 

the vertical stress on the floor is nonuniformly distributed. 

Therefore, progressive failure of floor occurs even without 

mining-induced vertical stresses when the loading is 

applied through uniform vertical displacement. However, 

when mining-induced vertical stress acts on the pillar, the 

extent of nonuniformity becomes much larger. Besides, 

applying the uniform vertical displacement at the top of the 

deformable coal pillar reduces the amount of nonuniformity in vertical stress distribution as opposed to a 

rigid plate situation. 

The localized floor failures due to the nonuniform vertical stress explain the practical observation that every 

floor instability seen underground (Figure 4) does not lead 

to surface subsidence.

 Figure 4.—Localized floor instability in an Illinois basin 

coal mine. 

 Under the influence of nonuniform 

vertical pillar stress, areas close to the pillar rib could 

experience localized floor failure, resulting in heave in the 

adjacent mine opening, while the larger portion of the 

pillar itself has stable floor. Detailed in situ investigations 

by Vasundhara et al. [2001] in Australia prove the validity 

of this conclusion. Therefore, from a subsidence prevention point of view, it is the limit state that matters, not the 

localized floor instabilities such as that shown in Figure 4. 

This observation indicates that when collecting data to 

develop design guidelines for surface subsidence prevention, localized underground instabilities should not be 

considered unless there is evidence that the floor failures 

led to surface movements. 

Although very limited study was done, the preliminary 

results given here show that when computing the ultimate 

bearing capacity, the difference between the uniform displacement loading and nonuniform stress distribution is 

negligible. The nature of stress distribution seems to affect 

only the path traversed to reach the limit state, but not the 

limit value itself. Therefore, the results obtained under 

uniform displacement loading could perhaps be used 

without incurring significant errors in the computed 

bearing capacity. 

PILLAR SPACING EFFECT 

In every coal mine, multiple pillars exist in close proximity to each other. Thus, the influence of interference 

effects on floor-bearing capacity cannot be ignored. For 

the sake of brevity, the limits of bearing capacity were 

determined for extreme values for the model inputs. Such a 

study will show the maximum possible influence of the 

presence of multiple pillars on the computed floor-bearing 

capacity for typical Illinois basin coal mine conditions. 

50 
The following extremes for different model inputs will 

include most of the Illinois basin coal mines: 

Pillar 

geometry 

Strip 

pillar 

Square 

pillar 

B/H

s/B

c2 /c1 

φ1, φ2

 40 

0.2 

2 psi 

0° 

4 

0.66 

5 psi 

35° 

For all of the models, symmetry conditions were 

exploited to simulate the effect of the presence of multiple 

pillars. The floor materials were assumed to behave in a 

perfectly plastic manner, satisfying the Mohr-Coulomb 

yield criterion. Each layer of floor by itself was assumed to 

be homogeneous and isotropic. Uniform loading on the 

floor was applied through displacements at the top of the 

floor over the region represented by the pillar. The floor 

contact conditions were assumed to be smooth. Typical 

meshes used for one case each of strip and square pillar are 

shown in Figure 5.

a) b)

 Figure 5.—Typical meshes used for the simulation of 

adjacent pillar effect for (a) strip and (b) square pillars. 

 The model results are presented in 

Tables 2 and 3 for the square and strip footing cases, 

respectively. 

Table 2.—Effect of interference of multiple square footings 

in close proximity 

φ1 φ2 c2 /c1 B/H s/B 

Ratio of model 

strength with and 

without adjacent 

pillars 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

2 

2 

2 

2 

2 

2 

40 

40 

40 

40 

40 

40 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.00 

1.05 

0.98 

1.03 

1.22 

>4.25 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

2 

2 

2 

2 

2 

2 

4 

4 

4 

4 

4 

4 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.00 

1.05 

1.00 

1.05 

1.05 

>3.4 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

5 

5 

5 

5 

5 

5 

40 

40 

40 

40 

40 

40 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.00 

1.03 

0.98 

0.99 

1.31 

>2.6 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

5 

5 

5 

5 

5 

5 

4 

4 

4 

4 

4 

4 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.00 

1.05 

1.00 

1.04 

0.94 

>2 

Table 3.—Effect of interference of multiple strip footings 

in close proximity 

φ1 φ2 c2 /c1 B/H s/B 

Ratio of model 

strength with and 

without adjacent 

pillars 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

2 

2 

2 

2 

2 

2 

40 

40 

40 

40 

40 

40 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.02 

1.18 

1.01 

1.01 

2.60 

>8 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

2 

2 

2 

2 

2 

2 

4 

4 

4 

4 

4 

4 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.19 

1.26 

1.19 

1.26 

2.35 

>6 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

5 

5 

5 

5 

5 

5 

40 

40 

40 

40 

40 

40 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.02 

1.04 

1.01 

1.00 

2.61 

>3.5 

0 

0 

0 

0 

35 

35 

0 

0 

35 

35 

35 

35 

5 

5 

5 

5 

5 

5 

4 

4 

4 

4 

4 

4 

0.66 

0.20 

0.66 

0.20 

0.66 

0.20 

1.19 

1.26 

1.19 

1.26 

1.80 

>3.6 

The influence of multiple pillar interaction is 

assessed by the ratio of model strengths computed with 

and without the presence of multiple pillars. The ratio will 

show the exact extent of the interaction effect and the 

potential error when using traditional bearing capacity 

equations that ignore the effect of adjacent pillars. 

51 
The major conclusions from the models can be summarized as follows: 

• When the friction angle of both floor layers is zero, 

the interaction effect of adjacent pillars is negligible. 

• Irrespective of the B/H value, if the top layer is 

frictionless even when the stronger layer has nonzero friction angle value, there is negligible interaction effect. 

• When the friction angle of the weak floor layer is 

zero and the ratio of B/H is small, there is negligible influence of the adjacent pillar. 

• Interaction of adjacent pillars will influence the 

bearing capacity only if the immediate floor has 

non-zero angle of internal friction. When both 

layers have φ = 35° and s/B = 0.2, the models did 

not reach limit state even after solving for more 

than 500,000 to 1 million model steps. The ratios 

for the strength values in Tables 2 and 3 are based 

on the resultant floor stress obtained when the 

solution was terminated. Therefore, if both the 

layers of floor beds have higher non-zero friction 

values, then such conditions result in virtually 

indestructible floor, and the pillar design may 

depend on the coal strength rather than the floor 

strength. 

• In almost every case studied, the effect of adjacent 

pillars on bearing capacity is higher for strip pillars 

than square pillars. Therefore, rectangular pillars 

will gain more from their neighbors than square 

pillars of the same width. 

The reason for the dramatic increase in the bearing 

capacity with the friction angle in the presence of multiple 

pillars could be seen from the minimum principal stress 

contours and the displacement vectors plotted in Figure 6. 

a) b) pillar area b) pillar area 

Figure 6.—Model results for multiple strip pillars: (a) contours of minimum principal stress (negative numbers 

indicate compression); (b) displacement vectors at the limit state. 

As the vertical load on the pillar increased, the horizontal 

floor movements induced in the adjacent entry were restricted to some extent by the presence of the nearby pillar. 

This restraint to the displacements induced higher confining pressures in the floor, which substantially increased 

the triaxial strength of the floor when the friction angle 

was non-zero. Similarly, for the same amount of confinement, the higher the friction angle, the higher the floor 

triaxial strength. For this reason, when the friction angle of 

the immediate floor was zero, even though the adjacent 

pillar was offering similar restraint, the floor strength did 

not increase a for a non-zero friction angle case. 

It has been noted above that the effect of adjacent 

pillars has more positive effect on the bearing capacity of a 

52 
 

 

 

strip pillar than a square pillar. The reason for this difference can be seen by comparing the minimum principal 

stress and displacement vector plots shown in Figure 6 

with those in Figure 7.

a) b)

Figure 7.—Model results for multiple square pillars: (a) contours of minimum principal stress (negative numbers 

indicate compression); (b) displacement vectors at the limit state. 

 In both figures, the model conditions were exactly the same except for the geometry of the 

pillar. The results show that in the case of a square pillar, 

the amount of floor movement in the entry adjacent to the 

pillar keeps decreasing from the midportion toward the 

intersection. As a result, the horizontal confinement generated in the floor keeps decreasing from the middle of the 

pillar to the intersection area, as seen in Figure 7a. Since 

the overall confinement of the floor below the pillar is 

lower for the square pillar, for the same friction angle 

value, a strip pillar will have higher bearing capacity, as 

shown by the values in Tables 2 and 3. 

CONCLUSIONS 

Based on the discussions presented in this paper and 

the numerical modeling results, the following conclusions 

can be made: 

• When all of the geometric and material property 

aspects of a typical coal mine bearing capacity 

problem are considered, it is impossible to provide 

a closed-form solution for floor strength estimation. 

•	 Limited numerical modeling studies were conducted in the past to study the coal mine floor 

stability problem. The past studies were limited to 

explain some site-specific floor behavior or were 

based on a few parametric studies. 

•	 The nonlinear numerical modeling methodology 

adopted in this paper reproduced theoretical solutions accurately. 

•	 This paper demonstrates the strength of the numerical modeling approach to estimate floor strength 

and to shed some light on the possible errors incurred by using conventional bearing capacity 

theories borrowed from the soil mechanics literature. 

• The modeling exercise showed that nonuniform 

pillar stress distribution may not significantly alter 

the ultimate bearing capacity value compared to 

the rigid plate loading. With nonuniform stresses, 

however, several localized failures occur in the 

stress concentration zones before the entire floor 

below a pillar reaches its limit state. Therefore, 

limited floor heave in underground openings need 

not necessarily imply floor failure below the whole 

pillar. 

• Interaction between adjacent pillars will positively 

impact the floor-bearing capacity only if the 

friction angle of the weak floor material is nonzero. Rectangular pillars will gain more from their 

neighbors than square pillars of the same width. 

The dramatic increase in floor strength with friction is related to the increase in the friction-related 

triaxial strength of the floor material when the 

adjacent pillar restricts the lateral displacement of 

the floor. 

53 
 

 

 

 

It is the author’s opinion that there is no need to 

conduct an exhaustive number of parametric studies to 

develop some “design equations” based on modeling. This 

is due to the widespread availability of advanced modeling 

software tools, which make the task of running a few sitespecific bearing capacity problems a trivial matter. 

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Bandopadhay S [1982]. Analysis of soft floor interaction on underground mining at a western Kentucky mine 

[Thesis]. Carbondale, IL: Southern Illinois University. 

Bhattacharyya AK, Seneviratne SP [1992]. A study of 

floor heave in the mines of the southern coalfields of New 

South Wales by two dimensional finite element modelling. 

In: Proceedings of the 11th International Conference on 

Ground Control in Mining (Wollongong, New South 

Wales, Australia), pp. 457–482. 

Chandrashekhar K [1990]. Effects of weak floor 

interaction on underground room-and-pillar coal mining. 

[Dissertation]. Carbondale, IL: Southern Illinois University. 

Chugh YP, Pytel WM [1992]. Design of partial extraction coal mine layouts for weak floor strata conditions. In: 

Iannacchione AT, Mark C, Repsher RC, Tuchman RJ, 

Simon CC, eds. Proceedings of the Workshop on Coal 

Pillar Mechanics and Design. Pittsburgh, PA: U.S. 

Department of the Interior, Bureau of Mines, IC 9315, 

pp. 32–49. NTIS No. PB92-205509. 

Deb D, Ma J, Chugh YP [2000]. A numerical analysis 

of the effects of weak floor strata on longwall face ground 

control. SME preprint 00-134. Littleton, CO: Society for 

Mining, Metallurgy, and Exploration, Inc. 

Rockaway JD, Stephenson RW [1979]. Investigation 

of the effects of weak floor conditions on the stability of 

coal pillars. U.S. Bureau of Mines contract No. J0155153. 

NTIS No. PB 81-181109. 

Terzaghi K, Peck RB [1967]. Soil mechanics in engineering practice. 2nd ed. New York: John Wiley and Sons. 

Vasundhara LG [1999]. Geomechanical behaviour of 

soft floor strata in underground coal mines [Dissertation]. 

Sydney, Australia: University of New South Wales. 

Vasundhara LG, Byrnes R, Hebblewhite B, Martin S 

[2001]. Long term stability of mine workings in soft floor 

environment: geomechanical investigations at Cooranbong 

Colliery. In: Peng SS, Mark C, Khair AW, eds. Proceedings of the 20th International Conference on Ground 

Control in Mining. Morgantown, WV: West Virginia University, pp. 180–183. 

Yavuz M, Iphar M, Aksoy M, Once G [2003]. Evaluation of floor heaving in galleries by numerical analysis. 

In: Proceedings of the Application of Computers and 

Operations Research in the Minerals Industries. South 

African Institute of Mining and Metallurgy, pp. 185–190. 

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IT IS BETTER TO BE APPROXIMATELY RIGHT THAN PRECISELY WRONG: 

WHY SIMPLE MODELS WORK IN MINING GEOMECHANICS 

By Reginald E. Hammah, Ph.D.,1

 1Rocscience, Inc., Toronto, Ontario, Canada. 

 and John H. Curran, Ph.D., P.Eng.2 

2

University of Toronto, Lassonde Institute, Toronto, 

Ontario, Canada. 

ABSTRACT 

This paper argues that, due to challenges such as great 

uncertainty and presence of ill-posed problems, simple 

models are well suited to mining geomechanics. It builds 

its case by defining what models are, outlining the usefulness of simple models and explaining how they can be 

developed. The paper explains that models are necessarily 

incomplete representations of real-world behavior. The 

strategy it advocates for constructing a simple model 

requires a bottom-up approach—starting with the simplest 

possible model and growing it to capture the essential features of phenomena of interest. The paper calls for engineers to view models for what they really are—tools of the 

trade, not unlike the physical tools of the sculptor. 

INTRODUCTION 

In science and engineering, accuracy is the degree to 

which a measurement or calculated quantity matches its 

“true” value. Precision is a closely related, but different 

concept. It is the degree to which repeated measurements 

or calculations produce same or similar results. It is possible, for example, for a calculation to produce inaccurate 

but precise answers. This would occur if the answers are 

consistently close to each other, but are in reality far from 

being correct. 

The first part of the paper’s title, “It is better to be 

approximately right than precisely wrong,” is a quote that 

has been variously attributed to John Maynard Keynes and 

Warren Buffett. In modeling, it means that although it may 

be possible to calculate something very precisely, the 

result may be meaningless if the underlying model, however elaborate, is incorrect. The result may be precisely 

wrong! In this case, you would be better off with an 

approximate answer from a simpler model that better 

represents the real situation. 

We will argue in this paper that the quote succinctly 

describes the case of mining geomechanics. We believe 

that computer models are fundamentally essential to geomechanics. The paper seeks to emphasize exactly what 

models are, what they can be used for, and how they can 

serve our purposes. 

The paper will describe three broad challenges in mining geomechanics that make it imperative to prefer simple, 

approximate models over more complicated, precise ones. 

These include ill-posed questions and the ubiquitous presence of large uncertainty in mining. 

The paper will discuss why simple models are well 

suited to answering mining geomechanics questions and 

why complicated models must be avoided at the start of 

the modeling process. It will outline what constitutes 

simple models, why they must be used solely as tools, and 

describes a simple strategy for developing such models. 

As part of the effort to justify the use of simple 

models, the paper will examine lessons we can learn from 

a very common pest, the cockroach, which has survived 

for many millennia using seemingly simple models of the 

environment. Parallels will be drawn between a parable 

about a superaccurate map and the application of numerical modeling to the problems of mine geomechanics. 

One of the key issues emphasized in this paper is the 

role of models as tools, not unlike the hammer and chisel 

of the sculptor. Engineers must use modeling the way 

Michelangelo used sculpting tools to express his vision of 

the masterpiece David. 

The paper will illustrate some of the principles advocated through an example in which simple models were 

used to develop a solution to an ore extraction problem. 

WHAT IS A MODEL? 

We will begin by describing what a model is. As in 

science, knowledge and understanding of phenomena in 

engineering are often embodied in the form of models. As 

a result, the creation and modification of models is integral 

to engineering. Engineers use models to predict and control behavior and to develop technologies to satisfy the 

demands of society. 

What then is a model? A model can be defined as a 

representation of a system that allows us to investigate the 

behavior and attributes of the system and, sometimes, to 

predict outcomes of the system under different conditions. 

The representation is usually— 

1.	 A physical model, such as an architect’s model of a 

building; or 

2.	 An abstraction, such as a set of equations or a computer program. 

In this paper, by “model” we mean an abstraction in 

the form of computer software. 

55
 
 

Incompleteness of a Model 

By necessity, models are incomplete representations of 

the real world [Mandelbrot and Hudson 2004; Derman 

2004]. If a model were to include every aspect of the real 

world, it would no longer be a model. This is illustrated by 

the one-paragraph short story entitled On Exactitude in 

Science authored by Argentine writer Jorge Borges [1975]. 

In the story, the cartographers of a fictional empire 

attained such perfection that they created a map “whose 

size was that of the Empire, and which coincided point for 

point with it.” Of course, the map was so impractical 

(it took greater effort to use the map than to actually move 

around the empire) that succeeding generations abandoned 

it to the “Sun and Winters.” 

To create a model, we always make some assumptions 

about the phenomenon we are representing and the 

relationships between the different factors that explain the 

real-world behavior. We strive to include factors that affect 

behavior and exclude those we deem are not essential. As a 

result of our assumptions and exclusion of factors, our 

models are always only approximations, and their results 

are always estimates. It is good practice, therefore, for us 

to develop a feel for how far off these estimates are or can 

be [Poundstone 2005]. We should never take modeling 

results for granted, but always ask probing questions. 

What Can We Accomplish With Models? 

Models allow us to attain many useful ends. These 

include: 

1.	 Development of understanding 

2.	 Proper formulation of questions 

3.	 Reasonable approximation of behavior and provision of meaningful predictions 

4.	 Aid to design of solutions and decision-making 

It will be discussed later that ill-posed questions constitute a big challenge in mining geomechanics. A most 

powerful use of modeling tools is the proper formulation 

of questions. It has been said that a problem well stated is a 

problem half-solved [Hubbard 2007]. Models permit us to 

perform “what if” analysis, which are experiments with 

different inputs, assumptions, and conditions. Answers to 

these questions can often lead to the correct diagnosis of 

problems of key behaviors. 

Through the insights they yield, models also help us to 

reduce uncertainty. Successful modeling does not have to 

eliminate uncertainty. By merely reducing uncertainty, 

especially when its costs are much less than the costs of 

the problem, modeling is often worthwhile. In some cases, 

models can be explicitly used to assess the likelihood of 

events and to help formulate plans for coping with such 

events. 

Models Are Tools 

A “tool” refers to any device used to perform or facilitate work. Just as a handtool might be used to fix a physical object, computer models can be used to accomplish a 

task. They are tools of engineering just as hammers and 

chisels are tools for sculptors. They are tools in the sense 

that they allow us to explore problems in exhaustive detail 

without having to do the lengthy and involved calculations. 

The computer and software do all the drudge work, which 

enables us to analyze and design. 

Through vision and skillful use of the hammer and 

chisel, Michelangelo sculpted the masterpiece David. 

Likewise, our models do not in themselves solve problems. 

We use them to answer questions. 

CHALLENGES OF MINE GEOMECHANICS 

Engineering can be defined as the process of providing 

solutions to the problems of clients as efficiently as possible based on the resources (budget, personnel, time, data, 

etc.) available to them. The third part of this definition is 

about challenges. Although these challenges may not be 

unique to mine geomechanics, they feature strongly in this 

field. We will examine three of the most important categories of challenges to effective mining geomechanics. 

Large Uncertainty 

Mining is carried out in the geological environment, 

which offers one certainty—uncertainty. For our purposes, 

uncertainty [Hubbard 2007] is defined as the— 

•	 Lack of complete certainty, the fact that the “true” 

state or outcome is unknown 

•	 Existence of more than one possibility; or 

•	 Chance of being wrong 

It gives rise directly to risk—the situation in which 

some of the possibilities involve loss, catastrophe, or other 

undesirable outcomes [Hubbard 2007]. 

In the geological environment, the likelihood of 

encountering unanticipated conditions is almost always 

high. The complex behavior of geologic materials and the 

distribution of their properties in space also do not lend 

themselves easily to investigation or measurement. Consequently, rock mechanics modeling has been characterized 

as belonging to the data-limited categories [Starfield and 

Cundall 1988] of Holling’s [1978] classification of modeling problems. 

As has been argued by others [Starfield and Cundall 

1988], we believe that it is dangerous to apply the methods 

of exactitude to mining geomechanics problems. Unfortunately, however, the elegance of elaborate models has so 

fascinated many engineers that answers have been sought 

that fit models rather than conform to reality in an 

uncertain world. 

56 
 

 

Ill-Posed Problems 

Geomechanics problems in mining often come to us as 

questions, ill-posed [Starfield and Cundall 1988] by clients 

who know they have difficulties, but which they cannot 

always articulate. Ill-posed problems often have one or 

more of the following characteristics (adapted from 

[Denker 2003]): 

1.	 Underspecification or the absence of crucial information that somehow must be determined; 

2.	 Unconnected pieces of information that require 

understanding in order to determine what is important and what must be ignored; 

3.	 Inconsistent, conflicting, or contradictory information, as a result of which solutions cannot be 

envisaged, even in principle; 

4.	 Uncertainty as to what solution method or approach must be applied; 

5.	 Ambiguity or the possibility of different answers, 

depending on what assumptions are used; and/or 

6.	 Intractable answers that exist in principle, but 

which we have no reasonable ways of determining 

The first battle in many mining geomechanics situations, therefore, is to understand what the problem is. 

After doing this, we are better placed to provide adequate 

answers. John Tukey, the renowned statistician, once 

wrote: “Far better an approximate answer to the right question, which is often vague, than an exact answer to the 

wrong question, which can always be made more precise 

[Tukey 1962].” 

Limited Resources: Personnel, Budget, Time 

It is not uncommon for mining geomechanics engineers to work with limited resources—small budgets, tight 

deadlines, and insufficient personnel. These constraints 

can be quite severe. Let us take the situation of a rock 

mechanics engineer in a mine as an example. He/she has 

several tasks to fulfill each workday in different parts of 

the operation. This can leave very little time for reflective 

thinking or strategic problem-solving. 

Personnel who are well trained in the use of modeling 

tools and equally well grounded in practical geomechanics 

are scarce. In many firms and companies today, the senior 

engineers who understand well the practical geotechnical 

issues that need to be resolved are often not that comfortable with numerical modeling tools. Even when they are, 

they have only limited time to work with them. As a result, 

they rely on junior engineers for modeling expertise. 

Often, however, the junior engineers, although comfortable 

with software, have not acquired sufficient understanding 

of real-world geotechnical problems and generally require 

clearly defined questions. 

This leads to a situation in which those building the 

models may not be sufficiently aware of the weaknesses or 

assumptions in their models, while those who make the 

decisions may not fully understand what the models are 

doing or how they work (similar to the situation in financial risk modeling described by Rebonato [2007]). We will 

argue later that the best way to rectify this situation is to 

make modeling tools as simple to use as possible. This 

affords senior engineers time and opportunity to also 

“play” with models and more fully use their experience for 

problem-solving and design. 

The Opportunities of Constraints 

It is easy to view the challenges to mine geomechanics 

modeling as negatives. However, they can be looked at 

positively, as opportunities to innovate. Given fewer 

resources, we are forced to make better decisions [Salmon 

2009]. The only question is: What modeling tools are best 

for addressing mining geomechanics problems under our 

constraints? We propose to answer that next. 

SIMPLE MODELS AS USEFUL TOOLS FOR 

MINING GEOMECHANICS 

We have determined that models are powerful tools for 

engineers in the quest to determine the best possible solutions to problems under finite (limited) resources. There 

are costs (time, effort, and money) associated with modeling itself. If we are to be successful, we must keep those 

costs low. 

Let us briefly revisit the parable On Exactitude in 

Science [Borges 1975] for an important lesson on modeling. The cartographers’ point-for-point map, although perfectly accurate, was absolutely impractical. The effort and 

resources required to create and read the map far exceeded 

any utility it offered. The parable teaches that, in the practical world, simple and easy-to-use tools can be much 

more useful than very elaborate ones, which although more 

accurate, may be too costly or impractical to build or use. 

In modeling, simplicity is also referred to sometimes 

as parsimony. The principles of parsimony require that we 

take great care to develop computational algorithms and 

models that use the smallest possible number of parameters in order to explain behavior [Mandelbrot and Hudson 

2004]. They encourage us to avoid unnecessary complexity and pursue the most straightforward approaches. 

Simplicity applies not only to the concepts (essence of 

phenomena) captured by models, but also to how straightforward it is to use modeling tools. Easy-to-use tools free 

engineers from drudgery, enabling them to dedicate brainpower to skeptical probing of what can go wrong. We will 

explore this issue further in a later section. 

Reasons for Simplicity 

As we have discussed, large uncertainties exist in 

mining geomechanics. In addition, questions are commonly ill-posed and must be solved under the tight constraints of time, budget, and human resources. Under these 

conditions, precise answers are not the most useful. Often, 

57 
 

 

 

 

 

 

 

 

 

understanding of behavior and interactions between various factors must take precedence. 

Given these challenges, it is better to omit some details 

of a problem or imperfectly cover those details (keep 

models simple) than to try to cover every conceivable 

aspect, but create an overly complex model. Models that 

yield “good enough” answers and help us to make decisions suffice [Mandelbrot and Hudson 2004]. 

Uncertainty is dealt with through parametric and 

scenario analysis—the assessment of possible ranges of 

behaviors through variation of input properties and consideration of different conditions—or statistical methods. 

These approaches all require development of alternative 

models, accompanied by multiple computations. 

Simple models facilitate the use of such techniques. 

Through the diversity of assumptions and scenarios that 

we can consider, simple models can help us to develop 

designs that are robust to unexpected or unusual 

conditions. The lack of exact numbers should not be 

equated to knowing nothing [Hubbard 2007]. The information they give reduces uncertainty in our understanding 

and helps us improve the quality of the decisions we must 

make. As we have discussed, we can use such models to 

better define ill-posed problems and test our knowledge 

and assumptions. 

There are many other reasons for adhering to the principle of simplicity in the development of mining geomechanics models. Every parameter or input included in a 

model introduces a source of uncertainty since we have to 

assign it a value. Therefore, keeping parameters to a minimum reduces uncertainty in the solution process. 

Simple models and modeling tools are also much 

easier to understand and explain. They make it easier to 

think through problems. When we start out with simple 

models and use increments in our understanding to direct 

further modeling, we are able to identify unnecessary 

details that have insignificant effects on the model system. 

Although it can be argued that simple models are 

flawed (but we should remember so is every other model 

no matter how complicated), they should be judged by 

how much they explain compared to how many input 

parameters they require. Viewed this way, their strengths 

over more sophisticated approaches quickly become evident. They are generally easy to use and manage, and 

much quicker to compute. As a result, they are often of 

great merit due to the time savings they afford. 

What Is a Simple Model? 

Our preceding discussions indicate that the greater the 

number of simplifying assumptions made about the realworld phenomenon we are studying, the simpler the resulting model. We have concluded, therefore, that the ultimate 

goal of modeling is to create parsimonious models— 

models that have great range of explanation using the 

simplest possible concepts and smallest possible number 

of inputs. 

This brings us to a more formal definition of what 

constitutes a simple model. It is the simplest description of 

a complex phenomenon that still captures those features 

we are interested in. It is the model for which any additional gain in explanatory power by including more 

assumptions or parameters is no longer warranted by the 

increase in complexity. The art of modeling then reduces 

to finding the simplest models that do outrageously good 

jobs at describing complex phenomena [Rebonato 2007]. 

It aims to say much with little [Mandelbrot and Hudson 

2004]. 

A Simple Strategy for Building Simple Models 

The definition of what constitute simple models 

alludes to a strategy for building them. The process starts 

with careful reflection on the problem we are trying to 

solve. This exercise helps us to be clear about our purpose. 

We then proceed to build models from the bottom up. 

We begin with radical simplifications. If investigation 

shows that the phenomenon of interest cannot appear at 

this level of simplicity, we add to this model as parsimoniously as possible. The manner in which we enlarge 

our model is guided by the understanding we gain from 

study of the influence of each added assumption (concept) 

or variable. If we determine an addition to be irrelevant to 

our particular task, we eliminate it. 

This process strengthens our fundamental understanding of the phenomenon we are studying. The care and 

detail we exercise in constructing our simple model 

compels us to avoid hand-waving (the failure to rigorously 

address central issues or the glossing over of important 

details). It forces us to strive to fill gaps in our understanding. When a model is built from the bottom up, it is 

deemed to have met its goals the moment it passes the test, 

“Is it fit for its purpose?” 

The Trouble With Complexity and Precision 

When we start with a model that is too complex, we 

can quickly reach the point where understanding is 

replaced by blind faith. A model that starts off complex— 

i.e., has many inputs, assumptions, and aspects—actually 

obscures understanding. When too many details are 

included before the behavior of the model is appreciated, 

interactions among its components will not be clearly 

apparent. Such a model becomes little more than a “black 

box” that mysteriously converts input values to numbers or 

charts. As a result, its outcomes are not readily interpreted 

and are difficult to subject to commonsense tests. Rather 

than clarify, the model confuses. 

Obsessive focus on modeling detail often coincides 

with fascination with precision. Under the considerable 

uncertainties and other constraints of mining geomechanics, obsession with details we cannot get right and 

precision we have no hope of attaining hinder our ability to 

make decisions. Although the ranges of values from simple 

58 
 

 

 

 

 

 

 

models may seem less sharp, they offer the advantage of 

keeping us “honest and humble” about what we are doing, 

namely, estimating. They help us ward off the “hubris of 

spurious precision” [Rebonato 2007]. 

Lessons From Nature 

Studies of living organisms can indicate to us optimal 

strategies for handling large uncertainties and unexpected 

changes in conditions. The length of time a species has 

survived is a good measure of how it has adapted 

under such conditions [Bookstaber and Langsam 1985; 

Bookstaber 2007]. 

The common cockroach is an example of an organism 

that has survived for many millennia because of its strategy for dealing with unanticipated environmental changes 

[Bookstaber and Langsam 1985; Bookstaber 2007]. Scientists have determined that it uses very simple or “coarse” 

rules (models) for deciding what actions to take in 

response to environmental changes. Given a wide set of 

possible inputs about the environment, the cockroach 

ignores most of these details and focuses on a select few. 

At first glance, it seems that such an approach is not 

optimal in the least. However, research has shown that 

although suboptimal for any one environment, “coarse” 

rules are far more efficient over a wide range of different 

environments. This is especially true when some of the 

changes in these environments are unforeseeable. Coarse 

rules are much more likely to anticipate risks and bring 

about necessary adjustments. 

The cockroach’s use of simple models seems to tell us 

that precision and focus on the known comes at the cost of 

reduced ability to address the unknown. When we spend 

less time focusing on detailed investigation, we can spend 

more time thinking and reacting to unknown conditions. 

A NOTE ON EASE OF USE 

From the example above, biology seems to indicate 

that we must run our simple models with different inputs 

and assumptions in order to cope well with our uncertainties and constraints. This requires that models be 

developed and changed or manipulated with relative ease. 

They must be easier and less expensive to manage than the 

real world. 

User-friendly, intuitive software interfaces make this 

possible. Given the challenges of mine geomechanics 

modeling, it can be argued that user-friendly interfaces can 

have far greater impact on the work of engineers than 

sophisticated underlying model concepts. 

The design of a user interface must consider the productivity of users [Curran and Hammah 2006]. It must 

ensure a short, gently sloping learning curve. Practitioners 

are keenly aware that people’s time costs more than computers and software. The real cost of a modeling tool, 

therefore, is not so much purchase price as the user effort 

it demands. 

Intuitive, graphical ways of displaying results are also 

important since they help engineers make sense of model 

results. Visual representation of data is satisfying to most 

users because it helps them to make sense of model results 

in instinctive ways. 

EXAMPLE OF GOLDEN GIANT MINE 

The Golden Giant Mine is a gold operation in the 

Hemlo camp in northern Ontario, Canada. The ore body at 

the mine consists of a main and a lower zone. The main 

ore body, which is tabular, has a strike length of 500 m, an 

average thickness of approximately 20 m, and dips at 

angles between 60° and 70° [McMullan et al. 2004; Curran 

et al. 2003; Hammah et al. 2001]. The lower zone is 

30–80 m below the main zone. The gold-bearing ore is 

located along the contact of a metasedimentary rock formation with felsic metavolcanic rocks. 

Description of the Problem 

Near the main shaft was a pillar that was open above 

and mined out below. It contained 660,000 tonnes of highgrade ore. The original mine plan was to mine all ore at 

depth, abandon the shaft below a certain level, and extract 

the shaft pillar as the final mining block. Analyses indicated, however, that a significant portion of this high-grade 

ore would be lost unless the shaft pillar was mined at the 

same time as the deep ore. 

At the same time, for more than a decade, this pillar 

had been a source of concern, particularly due to its 

proximity to the main production shaft. Preliminary 

modeling had indicated that the pillar and nearby infrastructure were under significant stresses as a result of 

mining throughout the Hemlo camp [Bawden 1995]. There 

were also indications that the stress levels were increasing 

and would adversely impact the shaft stability. 

The task, therefore, was to design an extraction 

sequence for the shaft pillar that would not jeopardize the 

shaft’s integrity. It was evident that the solution would 

have to reduce the stress concentrations around the shaft. 

Constraints and Information From 

Prior Experience 

There were a number of challenges that constrained 

the numerical modeling tool(s) that could be used on the 

project. The overall extents of the mine (stopes, infrastructure, and other excavations) were large and laid out in 

complex, three-dimensional fashion. Due to the tabular ore 

body, the stopes were flat-shaped. The infrastructure excavations, on the other hand, were more regularly shaped. 

In addition, data on stress levels and rock mass properties, 

especially postfailure parameters, were very scant. There 

was, however, evidence of high-stress damage in parts of 

59 
 

 

 

the mine. Lastly, a solution to the problem had to be found 

in short time. 

From prior experience with elastic three-dimensional 

models of the mine, engineers knew that model zones with 

stresses >98 MPa corresponded well with zones of 

observed stress damage. 

Simple Elastic Modeling and the Determination of 

Mining Strategy 

A displacement discontinuity-based boundary-element 

program [Vijayakumar et al. 2000], which readily accommodated the different shapes of excavation, was selected 

as the analysis tool. It could handle the large extents of the 

mine and the complex three-dimensional layout. It also 

afforded the ease of model building and computational 

speeds for developing a solution within the required time. 

On the other hand, however, it required representation of 

the three primary rock mass types—ore body, metasedimentary, and metavolcanic rocks—with only one set 

of elastic properties. 

Despite the simplified assumptions of homogeneous 

material and elastic behavior, the numerical modeling tool 

showed three-dimensional stress flow patterns and stress 

concentrations that matched observations at the mine 

[Hammah et al. 2001]. It helped engineers understand the 

influence that excavation layout had on stress concentrations within the mine. Each single model run took about 

2–3 hours to compute compared with the 20 or more hours 

it took with a more detailed (multimaterial) boundaryelement program. 

Numerical studies with the simplified model helped 

establish that the excavation of a destress slot could reduce 

existing stresses near the main shaft and control stresses 

induced during mining of the shaft pillar. The slot pushed 

high stresses away from the main shaft into non-orebearing rock mass zones. The tool allowed engineers to 

experiment with several alternative slot geometries (location, dimensions, and excavation sequencing) and extraction sequences for the shaft pillar and deeper-lying ore. 

Figure 1 shows a three-dimensional view of the final 

slot geometry and location. The slot was to be 55 m wide 

by 58 m high and parallel to the main ore body, with a dip 

of 60° toward the shaft. 

De-stress slot 

 Figure 1.—Three-dimensional view of destress slot 

geometry and location. The tabular shaded zones 

represent excavated stopes. 

Displacements from the numerical modeling indicated 

that the destress slot would experience closure on the order 

of 1 m. This meant that the slot thickness had to exceed 

1 m [Hammah et al. 2001]. If this condition was not met, 

the walls would make contact and significantly reduce the 

efficiency of the slot. 

This also led to study of the properties (mainly the 

Young’s modulus or stiffness) of the material for backfilling the slot (there was no way a slot of that size could 

be left open). For this investigation, a finite-element program, Phase2

 [Rocscience, Inc. 2009], was used. It could 

accommodate the multiple material properties integral to 

the study. Although this program performed only twodimensional analysis, it was sufficient for this stage of 

design. The modeling outcomes showed that the material 

used to backfill the slot had to have very low stiffness— 

far less than one-fiftieth the stiffness of the host rock. 

Real-World Performance of Destress Slot 

Excavation of the destress slot, according to the 

sequence developed from the numerical modeling 

exercise, began in early 2002 and ended in summer 2003 

[McMullan et al. 2004]. The slot was backfilled with a soft 

paste. Measurement of its performance, which was 

performed through comprehensive instrumentation, has 

shown that it met its goals. 

CONCLUDING REMARKS 

In this paper, we have argued that, in the face of large 

uncertainties, ill-posed questions, and limited resources, 

simple, easy-to-use, modeling tools are most practical for 

mining geomechanics. They facilitate the modeling process. We have also shown that the strategy of building 

models from the bottom up tends to restrict the creation of 

complicated, and potentially meaningless, models. We are 

not advocating simplistic, trivial design and analysis. What 

we are saying is that mining geomechanics is best served 

by using the simplest models that fulfill our purposes. 

60 
 

 

 

 

 

 

 

 

 

We will end with an analogy from the world of 

biology—the growth of a sapling [Salmon 2009]. Given 

enough water and sunshine a sapling will grow. However, 

with careful pruning—removal of low-hanging branches— 

during the early stages of development, the sapling will not 

merely grow but flourish. It will grow faster and become 

taller and stronger. This is because the pruned sapling will 

not waste precious resources on growth that does not serve 

its ultimate purpose. 

The same is true of modeling. When we carefully 

“prune” models and keep them simple, they will help us 

thrive in solving mine geomechanics questions. 

If this paper gives pause for thought any time we must 

solve mining geomechanics problems, it will have fulfilled 

its purpose. 

ACKNOWLEDGMENTS 

The authors would like to thank their colleagues at 

Rocscience, especially Dr. Thamer Yacoub, for sharing 

their insights into the topic of modeling. 

REFERENCES 

Bawden WF [1995]. Hemlo Gold Mines, Inc. 

Golden Giant Mine class one shaft rehabilitation report. 

Technical report submitted to Hemlo Gold Mines, Inc. 

Bookstaber RM [2007]. A demon of our own design: 

markets, hedge funds, and the perils of financial innovation. Hoboken, NJ: John Wiley & Sons, Inc. 

Bookstaber R, Langsam J [1985]. On the optimality of 

coarse behavior rules. J Theor Biol 116:161–193. 

Borges JL [1975]. On exactitude in science (Del 

rigor en la ciencia). In: A universal history of infamy 

(Historia universal de la infamia). London: Penguin 

Books. Translated from Spanish. 

Curran JH, Hammah RE [2006]. Keynote lecture: 

Seven lessons of geomechanics software development. In: 

Yale DP, Holtz SC, Breeds C, Ozbay U, eds. Proceedings 

of the 41st U.S. Rock Mechanics Symposium (Golden, 

CO, June 17–21, 2006). Alexandria, VA: American Rock 

Mechanics Association. 

Curran JH, Hammah RE, Yacoub TE [2003]. Can 

numerical modelling tools assist in mine design? The case 

of Golden Giant mine. ISRM News J 7(3). 

Denker J [2003]. A rant about story problems including ill-posed problems, and the importance of not always 

following instructions. Available at: www.av8n.com/ 

physics/ill-posed.htm 

Derman E [2004]. My life as a quant. Hoboken, NJ: 

John Wiley & Sons. 

Hammah RE, Curran JH, Yacoub TE, Chew J [2001]. 

Design of de-stress slot at the Golden Giant mine. In: Proceedings of DC Rocks, 38th U.S. Rock Mechanics Symposium (Washington, DC, July 7–10, 2001). 

Holling CS [1978]. Adaptive environmental assessment and management. Chichester, U.K.: Wiley. 

Hubbard DW [2007]. How to measure anything. 

Hoboken, NJ: John Wiley & Sons. 

Mandelbrot B, Hudson RL [2004]. The (mis)behavior 

of markets. New York: Basic Books. 

McMullan J, Bawden WF, Mercer R [2004]. Excavation of a shaft destress slot at the Newmont Canada Golden 

Giant mine. In: Proceedings of the Sixth North American 

Rock Mechanics Symposium (Houston, TX, June 5–10, 

2004). 

Poundstone W [2005]. Fortune’s formula. 1st ed. New 

York: Hill and Wang. 

Rebonato R [2007]. Plight of the fortune tellers: 

why we need to manage financial risk differently. Princeton, NJ: Princeton University Press. 

Rocscience, Inc. [2009]. Phase2

 v7.0. Finite element 

analysis for excavations and slopes. [http:// 

www.rocscience.com/products/Phase2.asp]. Date accessed: 

April 2009. 

Salmon F [2009]. Recipe for disaster: the formula that 

killed Wall Street. Wired Mag, Feb. 23. 

Starfield AM, Cundall PA [1988]. Towards a methodology for rock mechanics modelling. Int J Rock Mech Min 

Sci Geomech 25(3):99–106. 

Tukey JW [1962]. The future of data analysis. Ann 

Math Stat 33(1):1–67. 

Vijayakumar S, Yacoub TE, Curran JH [2000]. A 

node-centric indirect boundary element method: threedimensional discontinuities. Int J Comput Struct 74(6): 

687–703. 

61 

 

 

 

 

 

 

 

 

 

AN OVERVIEW OF CALIBRATING AND USING THE LAMODEL PROGRAM 

FOR COAL MINE DESIGN 

By Keith A. Heasley, Ph.D.1 

1

West Virginia University, Department of Mining Engineering, Morgantown, WV. 

ABSTRACT 

The LaModel program was developed from the 

displacement-discontinuity variation of the boundaryelement method. It is used mainly to model the stresses 

and displacements on thin tabular deposits such as coal 

seams. As with most numerical programs, the accuracy of 

a LaModel analysis depends entirely on the accuracy of the 

input parameters. Therefore, the input parameters need to 

be calibrated with the best available information, either 

measured, observed, or empirically or numerically derived. 

In recent years, a common systematic method of developing accurate input parameters for LaModel has been 

greatly desired by the mining industry. In response to this, 

several new algorithms have been developed for calibrating the most critical input parameters in the program. 

In particular, algorithms for calibrating the rock mass 

stiffness against the expected abutment load extent, the 

gob properties against the expected amount of abutment/ 

gob loading, and the coal strength based on the 

expected/desired pillar behavior have been developed and 

are presented in this paper. Also, to demonstrate the 

application of LaModel and the new calibration techniques 

to coal mine design, a case study of a pillar retreat mining 

section is presented. 

INTRODUCTION 

Some 15 years ago, the kernel of a laminated overburden model was programmed into a relatively simple 

program, LaModel, for calculating the displacements and 

stresses on thin, tabular deposits such as coal mines 

[Heasley 1998]. The mathematical basis of the program 

was the displacement-discontinuity variation of the 

boundary-element method. This approach allowed the program to easily model relatively large areas of the mines 

(compared to volume-element methods) and to easily 

model multiple seams. The original desire for the laminated overburden model was that it might provide more 

realistic displacement calculations than the homogeneous 

elastic overburden models that were then state of the art. It 

was even hoped that the laminated overburden model 

would allow accurate calculation of displacements and 

stresses at both the seam level and the surface [Heasley 

and Salamon 1996]. Indeed, the LaModel program did 

provide more realistic displacement calculations at the 

seam level than a homogeneous elastic model, and it did 

provide realistic surface subsidence calculations, although 

simultaneously calculating accurate displacements and 

stresses underground and accurate surface subsidence with 

the same material properties is a goal that the program did 

not achieve [Heasley 1998; Heasley and Barton 1999]. 

The original laminated overburden program, LaModel 

1.0, had just the basic components for performing the seam 

displacement and stress calculations. The input overburden 

parameters, seam parameters, and mine grid were 

manually typed into a text file with rigid formatting. Then, 

the DOS-based LaModel program performed the calculations and put the results into a formatted output file for 

manual analysis. The output consisted of calculations for 

displacement, stress, multiple-seam stress, overburden 

stress, and surface-effect stress. This original program provided a 250 × 250 grid for defining the seam geometry and 

allowed six different material models (linear-elastic coal, 

strain-softening coal, elastic-plastic coal, linear-elastic 

gob, bilinear hardening gob, and exponentially hardening 

gob) for use in 26 different materials for the in-seam 

element behavior. The original LaModel could analyze up 

to 4 different seams using a maximum of 20 steps, and it 

allowed an off-seam plane for calculating remote displacements such as surface subsidence. Also, the original program allowed the input of a topography file for modeling 

the stress effects of a variable topography [Heasley 1998]. 

Over the years, LaModel has been upgraded and 

modernized as operating systems, programming languages, 

and user needs have evolved. The present LaModel 2.1 

program is written in Microsoft Visual C++ and runs in the 

MS Windows operating system. It uses a forms-based preprocessor for inputting the overburden and seam parameters and a graphical spreadsheet-type interface for 

creating the mine grid. The preprocessor, LamPre 2.1, 

also includes a wizard for automatically calculating coal 

pillars with a Mark-Bieniawski pillar strength and another 

wizard to assist with the development of “reasonable” gob 

properties [Heasley and Agioutantis 2001]. Presently, the 

program can analyze a 1,000 × 1,000 seam grid, and an 

interface with AutoCAD has been developed to allow the 

seam and overburden grids to be automatically imported 

from the mine plans and overburden contours in AutoCAD 

drawings [Heasley et al. 2003]. The output from LaModel 

is analyzed with a graphical postprocessor, LamPlt 2.1, 

63
 
 

 

 

 

 

 

 

that quickly and easily generates colored-square plots, 

cross-sectional graphs, history graphs (which show element changes over the steps), and three-dimensional 

fishnet plots. For enhanced analysis and display, an interface has been developed to download the LaModel output 

into AutoCAD and overlay it on the mine map [Wang and 

Heasley 2005]. In recent years, element and pillar safety 

factor calculations, and intraseam subsidence and the 

associated slope and strain calculations have been added to 

the program [Hardy and Heasley 2006]. Also in recent 

years, the laminated overburden model has been programmed into a simple two-dimensional version, LaM2D 

[Heasley and Akinkugbe 2005], and the LaModel output 

has been combined with geostructural features and geology 

to create a comprehensive stability mapping system 

[Heasley et al. 2007; Wang and Heasley 2005]. 

As a result of the Crandall Canyon Mine collapse in 

2007 and the desire in the industry to develop a standardized or best-practice calibration process for LaModel, 

a number of new enhancements to the program are 

currently being developed. These include a rock mass 

stiffness wizard for developing a calibrated lamination 

thickness, a gob stiffness wizard for developing a calibrated gob modulus, and a strain-softening coal wizard for 

developing calibrated postfailure coal parameters. An 

energy release rate calculation, a local mine stiffness 

calculation, and an overburden fault model are also being 

added to the program. In addition, with the next release 

(LaModel 3.0), the grid size will be increased to 2,000 × 

2,000, and a number of general enhancements will be 

made to the grid editor and postprocessor. 

LAMODEL CALIBRATION 

The devastating pillar failure at the Crandall Canyon 

Mine in 2007 [Gates et al. 2008] brought coal mine pillar 

design back to the forefront of mine safety research and 

raised many questions about the proper techniques for 

designing mines with numerical models and for developing, or calibrating, input parameters for the models. With 

LaModel, as with most numerical models, the accuracy of 

an analysis depends entirely on the accuracy of the input 

parameters. Therefore, the input parameters need to be 

calibrated with the best available information, either measured, observed, or empirically or numerically derived 

[Heasley 2008]. 

When actually generating a LaModel input file, the 

geometry of the mining in the seam (or seams) and the 

topography are fairly well known and can be accurately 

discretized into LaModel grids with the AutoCAD utility. 

Therefore, the seam and topography grids do not generally 

pose an accuracy problem. The most critical input parameters with regard to accurately calculating stresses and 

loads, and therefore pillar stability and safety factors, are 

the input material properties, specifically: 

• Rock mass stiffness 

• Gob stiffness 

• Coal strength 

These three parameters are always fundamentally important to accurate modeling with LaModel, particularly in 

simulations analyzing abutment stress transfer (from gob 

areas) and pillar stability. During model calibration, it is 

critical to note that these parameters are strongly interrelated, and because of the model geomechanics, the 

parameters need to be calibrated in the order shown above, 

since changing the value of one parameter affects the value 

of the others. The model calibration process as it relates to 

each of these parameters is discussed in more detail below. 

Rock Mass Stiffness 

The stiffness of the rock mass in LaModel is determined mainly by two parameters: the rock mass modulus 

and the rock mass lamination thickness. Increasing the 

modulus or increasing the lamination thickness will 

increase the stiffness of the rock mass. With a stiffer rock 

mass, (1) the extent of the abutment stresses will increase, 

(2) the convergence over the gob areas and the gob stress 

will decrease, and (3) the multiple-seam stress concentrations will be smoothed over a larger area. When calibrating 

for realistic stress output, it is recommended that the rock 

mass stiffness be calibrated to produce a realistic extent of 

abutment zone at the edge of the critical gob areas. Since 

changes in either the modulus or the lamination thickness 

generally cause a similar response in the model, it is most 

efficient and logical to keep one parameter constant and 

only adjust the other. Generally, when calibrating the rock 

mass stiffness, it has been found to be most efficient to 

initially select a rock mass modulus (often a thicknessweighted average) and then solely adjust the lamination 

thickness for the model calibration. 

To determine a realistic extent for the abutment zone 

for calibrating the lamination thickness, it would be best to 

use specific field measurements of the abutment zone from 

the mine. However, these field measurements are often not 

available. In that case, visual observations of the extent of 

the abutment zone can often be used. Most operations 

personnel in a mine have a fairly good idea of how far the 

stress effects can be seen from an adjacent gob. Without 

any good field measurements or observations, general 

historical field measurements can be used. For instance, 

the field measurements used in developing the ALPS and 

ARMPS pillar design programs indicate that the average 

extent of the abutment zone (D) at depth (H) (with both 

terms expressed in feet) for the case study mines was 

[Peng 2006]: 

64 
D = 9.3 H (1) 

or that 90% of the abutment load (D.9) should be within 

[Mark and Chase 1997]: 

D.9 = 5 H (2) 

Once the extent of the abutment zone (D) at a given 

site is determined from the best available information, the 

following equation, derived from the fundamental laminated overburden model, can be used to determine the 

lamination thickness (t) required to match that abutment 

extent [Heasley 2008]: 

( )⎛ ⎞

2

2 E 12 1 − υ2 D n − d

t = s ⎜ ⎟ ⎜ ( ) ⎟ (3) E h ⎝ ln 1 - n ⎠ 

where E = elastic modulus of the overburden; 

 υ = Poisson’s ratio of the overburden; 

 Es = elastic modulus of the seam; 

 h = seam thickness; 

 d = extent of the coal yielding at the abutment

 edge; 

and n = percentage of the abutment load. 

In Equation 3, the major parameter that is not 

necessarily known ahead of time is “d”, the extent of the 

yield zone at the abutment edge. This value can be 

developed by field measurements or observations, or by 

running LaModel and determining the calculated yield 

zone for the given conditions. To help get a first approximation of the yield zone extent, one can find the distance 

into the abutment where the stress gradient implied by the 

Bieniawski coal strength formula [Mark 1999] is equal to 

the abutment stress level implied by the laminated overburden [Heasley 2008]. The initial estimate of the yield 

zone distance (x) is then the solution to the following 

equation: 

2 E

P 2 E − s x E λ h q s S e − 2.16 i x − 0.64 Si = 0 (4) 

2 E λ h h 

where q = in situ stress; 

P = width of the panel;

 Si = in situ coal strength (psi);

 x = distance into the abutment; 

and: 

t 

λ = 

12 ( 1 − ) (5) 

υ

2 

Gob Stiffness 

In a LaModel analysis with gob areas, an accurate 

input stiffness for the gob (in relation to the stiffness of the 

rock mass) is critical to accurately calculating pillar 

stresses and safety factors. The relative stiffness of the gob 

determines how much overburden weight is carried by the 

gob and therefore not transferred to the surrounding pillars 

as an abutment stress. This means that a stiffer gob carries 

more load and the surrounding pillars carry less, while a 

softer gob carries less load and the surrounding pillars 

carry more. 

In LaModel, three material models are available to 

simulate gob behavior: (1) linear-elastic, (2) bilinear 

hardening, and (3) exponentially strain-hardening. Based 

on laboratory tests that show that gob is generally 

exponentially strain-hardening, this is, as a rule, the preferred model for accurately simulating gob behavior

[Pappas and Mark 1993]. In the strain-hardening model, 

the stiffness of the gob is primarily determined by 

adjusting the “final modulus” parameter [Heasley 1998; 

Zipf 1992]. A higher final modulus gives a stiffer gob, and 

a lower modulus value produces a softer gob material. 

Given that the behavior of the gob is so critical in 

determining the pillar stresses and safety factors, it is 

unfortunate that our knowledge of in situ gob properties 

and stresses is very poor. 

For calibrating LaModel, it is imperative that the gob 

stiffness be calibrated with the best available information. 

The first thought might be to use laboratory or field 

measurements of gob material to obtain the final modulus 

value. However, it is generally very difficult to get an 

accurate in situ final modulus value directly from smallscale laboratory tests, and direct in situ measurements are 

quite rare. In lieu of direct measurement, it is recommended that the final gob modulus be calibrated from gob 

load or abutment load measurements performed at that 

particular mine. However, these types of field measurements are also fairly rare (and sometimes of questionable 

accuracy). Also, visual observations are not very useful for 

estimating abutment loads or gob loads. Therefore, general 

empirical formulas are quite often the only available information on gob loading. 

For coal mining, the most common technique for 

estimating abutment/gob loads is probably the abutment 

angle concept (see Figure 1). Using this concept, the 

abutment load is the weight of the rock contained within 

the wedge of overburden defined between a vertical line at 

the edge of the panel and the angled line defined by the 

“abutment angle” on the inside of the panel [Mark 1990, 

1992]. 

65 
H 

Mined out panel 

LS 

- Abutment Angle 

- Side Abutment Load 

H tan β 

β 

P 

L SS

P/2 

β 

Supercritical Subcritical 

Figure 1.—Conceptualization of the abutment angle. 

Using the abutment angle concept (Figure 1), the 

average gob stress (σgob-sup-av) for a supercritical panel can 

be calculated as: 

⎛ H × δ
⎞⎛ P − (H × tanβ)⎞

σgob-sup−av = ⎜ ⎟⎜ ⎟ (6)
 ⎝ 144 ⎠⎝ P ⎠ 

and the average gob stress (σgob-sub-av) for a subcritical 

panel can be calculated as: 

P
 ⎛ 1 ⎞⎛ δ
 ⎞

σ
 gob-sub−av = ⎜ ⎟⎜ ⎟ (7)
 4
 ⎝ tanβ ⎠⎝144
 ⎠ 

where P = panel width (ft); 

 β = abutment angle; 

 H = seam depth (ft); 

and δ = overburden density (lb/ft3

). 

In the ALPS and ARMPS programs, an average 

abutment angle of 21° was determined from a large 

empirical database and is recommended as a default [Mark 

and Chase 1997; Mark 1990]. 

When calibrating LaModel, determining a realistic gob 

or abutment loading is rather difficult without precise field 

measurements. In general, it has been found that Equations 

6 and 7 with an abutment angle of 21° provide fairly 

conservative estimates of abutment and gob loading and 

can generally be used [Chase et al. 2002; Heasley 2000]. 

However, regardless of what value is chosen for the 

gob/abutment loading, it is clear that a realistic gob loading is critical to realistic model results. This means that the 

gob stiffness, gob loading, and abutment loading results 

from a LaModel analysis should be carefully analyzed and 

seriously debated in any analysis of possible errors. 

Certainly, gaining a better understanding of the true 

gob/abutment loading in retreat coal mining is an area for 

future research. 

66 

Coal Strength 

An accurate in situ coal strength is another value that is 

very difficult to obtain, yet remains critical to designing a 

coal mine and to determining accurate pillar safety factors. 

The first thought might be to use laboratory measurements 

of the strength of coal samples to obtain an in situ strength. 

However, it is very difficult to get a representative sample 

from the coal seam to test in the lab, and scaling the 

laboratory values to accurate in situ coal pillar values is 

not very straightforward or precise [Mark and Barton 

1997]. 

For the in situ coal strength in LaModel, it is strongly 

recommended to use 900 psi (Si) in conjunction with the 

Mark-Bieniawski pillar strength formula as implemented 

in the coal wizard [Mark 1999]: 

⎡ ⎛ w ⎞ ⎛ w 

2 ⎞⎤

S =
 S
 p 0.54
 −
 )
 i⎢0.64 +
 ⎜ ⎟ 0.18⎜

⎜ ⎟⎟⎥ (8

⎣ ⎝ h ⎠ ⎝ lh ⎠⎦ 

where Sp = pillar strength (psi); 

 Si = in situ coal strength (psi); 

 w = pillar width; 

 l = pillar length; 

and h = pillar height. 

The 900-psi in situ coal strength that is recommended 

for LaModel comes from the databases used to create the 

ALPS and ARMPS programs and is supported by considerable empirical data. In the author’s opinion, in situ 

coal strengths calculated from laboratory tests are not any 

more valid than the default 900 psi due to the inaccuracies 

inherent to the testing and scaling process for coal 

strength. If the LaModel user chooses to deviate very 

much from the default 900 psi, he/she should have a very 

strong justification, preferably suitable back analyses, 

as described below, or accurate field measurements. 

To determine an appropriate coal strength for LaModel 

based on a back analysis, the user should analyze a 

previous mining situation (similar to the one in question) 

where the coal was close to, or past, failure. The back 

analysis is an iterative process in which the input coal 

strength is increased or decreased to determine the value 

that provides model results consistent with the actual 

observed failure [Gates et al. 2008]. This back analysis 

should, of course, use the previously determined optimum 

values of the lamination thickness and gob stiffness. If 

there are no situations available where the coal was close 

to failure, then the back analysis can at least determine a 

minimum in situ coal strength with some thought as to 

how much stronger the coal may actually be. 
CASE STUDY ANALYSIS 

To illustrate how the LaModel program with the calibration techniques described above would be applied to 

coal mine design, a recent retreat mining analysis is presented here. In this analysis, the active mine was proposing 

to retreat the #1 Mains (see Figure 2), which were located 

in between the longwall gobs of the 1 North and 1 South 

gate roads. The design of the Crandall Canyon Mine area, 

which collapsed in August 2007, was somewhat similar to 

the design of the #1 Mains at this mine, where pillars were 

planned to be extracted in between two longwall gobs 

[Gates et al. 2008]. Because of this similarity and because 

of the management’s desire to ensure the safety of the 

mine’s operation, a detailed review of the proposed retreat 

mining pillar plan in the #1 Mains was performed. This 

review included a comprehensive analysis of the stability 

of the barrier pillars to the north and south of the #1 Mains 

and of the section pillars on retreat. Since the stress in this 

future mining area was a complex combination of the overburden stress, the abutment stresses from retreat mining, 

and the multiple-seam stress transfer from the overlying 

mine, the boundary-element program LaModel was an 

obvious choice for calculating the stress values and safety 

factors. 

In the #1 Mains area, the overburden ranges from 600 

to 1,200 ft, with the deepest overburden lying over the 

middle of the panel (see Figure 2).

Overlying Mine 

1200 

1000 

800 

600 

1000 

800 

600 

2 North 

1 North 

#1 Mains 

1 South 

Active Mine 

2 South 

Model Boundary 

Figure 2.—#1 Mains section at the case study mine. 

 Also in this area, the 

active mine is overlain by a previous mine some 400 ft 

above. The #1 Mains were originally driven in the 1980s 

with four entries and pillars on 90- by 100-ft centers. 

Recently, in preparation for extracting these pillars, the 

section was rehabilitated and an additional entry was 

driven into the south barrier using 60- by 100-ft pillars. So, 

in the #1 Mains before pillar retreat, the barrier pillar to the 

north was 80 ft wide (rib to rib) and the barrier pillar to the 

South was 140 ft wide (rib to rib). The 1 South and 

1 North gate roads adjacent to these barrier pillars were 

driven with two pillars on 90- by 100-ft centers. 

For the LaModel simulation of the #1 Mains, the 

seams were discretized with 10-ft square elements (which 

fit the dimensions of the entries and pillars very well) in a 

500 × 300 element grid with the model boundary as shown 

in Figure 2. The model area covers a panel and a half to 

both the north and south of the #1 Mains section in order 

to include a full abutment stress from the adjacent panels. 

Also, the model area extends a fair distance past the mining boundaries of the active section to both the east and 

west in order to move the edge of the grid outside of the 

area of influence of the active mining. Symmetric boundary conditions were implemented on all four sides of the 

model. The grids for both the active and the overlying 

mine were automatically generated from the AutoCAD 

mine maps of these mines with some manual oversight. 

Similarly, the topographic grid was automatically 

generated from the AutoCAD topographic lines. The 

topography was discretized with 50-ft elements on a 140 × 

100 element grid that extended 1,000 ft beyond all four 

sides of the displacement-discontinuity grids. The interburden between the seams was set at 400 ft, and the rock 

67 
mass was simulated with an average modulus of 3,000,000 

psi. For the active seam, the extraction thickness was set at 

6 ft; for the overlying seam, the extraction thickness was 

set at 4 ft. For both coal seams, the element strengths were 

determined using an in situ coal strength of 900 psi in 

conjunction with the Mark-Bieniawski pillar strength formula as implemented in the coal material wizard in 

LaModel [Heasley and Agioutantis 2001], and the coal 

elastic modulus was set at 300,000 psi. 

In the final LaModel simulation, three mining steps 

were analyzed: (1) the final development of the #1 Mains, 

(2) the #1 Mains retreated under maximum cover, and 

(3) the #1 Mains completely retreated. 

Calibration 

For calibrating the lamination thickness for this model 

using Equation 3 above, it can be determined that the 

lower overburden thickness of 600 ft gives an abutment 

extent around 120 ft and suggests a lamination thickness 

around 180 ft and that the highest overburden thickness of 

1,200 ft gives an abutment extent around 170 ft and suggests a lamination thickness around 370 ft. Observations at 

the mine confirm that the 120- to 170-ft abutment extent 

was fairly close to reality, but in this design analysis, it 

was also desired to emphasis the multiple-seam stresses on 

the retreat panel, so a somewhat thinner lamination thickness of 100 ft was ultimately chosen. 

For calibrating the gob moduli in this model, the average gob stress values suggested by Equation 7 for 1,200 ft 

of cover and a 21° abutment angle were examined. For the 

700-ft-wide longwall gob, Equation 7 suggests an average 

gob stress of 500 psi. For the 340-ft-wide #1 Mains gob, 

the abutment angle concept suggests an average gob stress 

of 243 psi. Under deeper cover such as in the #1 Mains, it 

is believed that the abutment angle concept gives lower 

gob stresses than are actual seen in the field [Heasley 

2000], so modeled gob stresses that are a little higher than 

the calculated values above were deemed reasonable. In 

order to determine the appropriate gob moduli to use, 

a single-seam model of the #1 Mains was run with a range 

of gob moduli from 50,000 to 300,000 psi. From the 

results of these models, the average gob load versus the 

gob moduli in both the longwall and #1 Mains was 

calculated. Ultimately, a final gob modulus of 75,000 psi 

(an average gob stress of 680 psi) was chosen for the 

longwall gob, and a final gob modulus of 250,000 psi (an 

average gob stress of 260 psi) was chosen for the gob in 

the #1 Mains. 

For the coal strength in the model, the 900-psi default 

value was used. To better understand the appropriateness 

of this value, a back analysis of a previously mined section 

of the mine was performed. In this previous section, the 

cover was similar (1,300 ft) and similar values for the 

lamination thickness and gob stresses were used. For 

pillars in the previous section that were adjacent to the 

gob, a pillar safety factor of 0.76 was calculated, and for 

pillars one row outby the gob, a safety factor of 1.64 was 

calculated. According to mine personnel, 2 years after 

mining, these pillars showed signs of stress and had 

significant rib sloughing, but were still stable as bleeder 

pillars and did not require any systematic standing support 

to maintain the entries. This back analysis result suggests 

that the 900-psi coal strength was reasonable and may even 

be a bit conservative. Using the previous section for a 

relative comparison, the #1 Mains section should be stable 

if the pillar line safety factors are ≥ 0.76 and 1.64 for the 

first and second pillar rows from the gob, respectively. 

LaModel Output 

Once all of the input parameters were developed, as 

discussed above, and the input file was generated in 

LamPre, the model was executed in LaModel and it ran for 

several days on the computer. A number of the important 

output values from the LaModel run are plotted below in 

order to analyze the stability of the #1 Mains section. 

Overburden Stress 

The first output to be analyzed is the overburden stress, 

as shown in Figure 3. The main reason for plotting and 

analyzing the overburden stress is to check the overburden 

input grid for accuracy. As seen in Figure 3, the overburden stress on the active seam is consistent with the 

overburden contours. The maximum overburden stress on 

the model is around 1,350 psi at the center of the model, 

and the overburden stress diminishes as the overburden 

drops toward the northeast and southwest edges. The 

“smoothing” of the overburden stress at depth can also be 

seen in Figure 3. The stress under the valleys is a little 

higher than the direct overburden value due to the adjacent 

slopes, and the stress under the ridges is a little lower than 

the exact overburden value due to the adjacent valleys. 

Multiple-Seam Stress 

The next output from the model to be analyzed is the 

multiple-seam stress (see Figure 4). In this plot, only the 

change in stress on the active seam due to the mining of 

the upper seam is shown. With the irregular room-andpillar panels in the overlying seam, the multiple-seam 

stress exhibits a very irregular pattern. Under the larger 

pillars between the extracted panels in the overlying seam, 

the additional abutment stress on the active seam reaches 

up to 520 psi (an additional 40% over the virgin overburden stress). Under the middle of the extracted panels in 

the upper seam, the overburden stress on the active seam is 

partially relieved, up to 760 psi. 

68 
1200 

1000 

800 

600 

1000 

800 

600 

Overburden 

Stress (psi) 

1400 

1300 

1200 

1100 

1000 

900 

800 

700 

600 

500 

400 

Model Boundary 

Figure 3.—Overburden stress. 

Overlying Mine 

Multiple Seam 

Stress (psi) 

500 

380 

260 

140 

20 

-100 

-220 

-340 

-460 

-580 

-700 

Figure 4.—Multiple-seam stress on the active mine from the overlying mine. 

Premining In Situ Stress 

The next stress value to be analyzed is the premining 

in situ stress on the active seam (see Figure 5). This stress 

value is created by adding the overburden and multipleseam stresses together, and it shows the effects from both 

stress components. This premining in situ stress essentially 

represents the level of stress that will be encountered as the 

active seam is extracted. As seen in Figure 5, the highest

in situ stress is above 1,860 psi (compared to the nominal

1,320 psi overburden stress), and it occurs with a 

combination of the deepest cover and the high multipleseam stresses from the abutment pillars in the overlying

seam. 

69 
2 North 

InSitu 

Stress (psi) 

2000 

1800 1 North 

1600 

1400 

1200 

#1 Mains 1000 

800 

1 South 600 

400 

200 Active Mine 

0 

2 South 

Figure 5.—Element safety factors in the #1 Mains. 

Of particular concern with the in situ stress are two 

very high-stress areas that fall within the #1 Mains—one in 

the middle of the panel and one on the south side on the 

outby third of the panel. These high-stress areas will 

probably not affect the global stability of the section since 

they are local in size and adjacent to lower-stress areas. 

However, these local high-stress areas may certainly cause 

localized high-stress conditions on the retreat pillar line. In 

the outby third of the panel, it would probably be best from 

a ground control perspective to pull the pillars from south 

to north to minimize stresses on the retreat line. 

Total Vertical Stress 

The next stress item to be analyzed from the LaModel 

runs is the total vertical stress on the coal seam after the 

#1 Mains has been retreated about halfway and the retreat 

line is at the high in situ stress area (see Figure 6). This 

total vertical stress is essentially the outcome of the 

overburden, multiseam, and tributary area stresses in the 

model. It shows the final resultant vertical stress on the 

in-seam elements. As seen in Figure 6, the highest stresses 

occur in the core of the gate road pillars, which have 

considerable abutment stress on them from the adjacent 

panels. Also, the abutment stress from removing the 

#1 Mains pillars can be seen on the pillars on the retreat 

line and on the barrier pillars to the north and south. 

To maintain global stability in the #1 Mains, the north 

barrier pillar between the 1 North gate road and the south 

barrier pillar between the 1 South gate road need to remain 

stable. In Figure 6, the abutment stresses from the longwall 

panels and the #1 Mains retreat section can be seen 

overriding these barrier pillars. In the south barrier (which 

is 140 ft wide), the abutment stresses do not increase the 

stress of the pillar core very much, and this pillar shows 

considerable stability. However, in the narrower (80-ftwide) barrier pillar to the north, the abutment stresses are 

causing 2,000–4,000 psi of stress in the barrier pillar core. 

Also, the pillars on the retreat line are showing stresses up 

to 5,000 psi. These high-stress areas cause concern, and 

the best way to further evaluate the stability in that area is 

to examine the pillar safety factors in these areas, as presented in Figures 7 and 8. 

Pillar Safety Factors 

The next outputs to be examined from the LaModel 

analysis are the pillar and element safety factors. Using the 

Bieniawski coal pillar formula with a 900-psi in situ coal 

strength gives a peak strength for each element. This peak 

strength is then compared with the actual stress on the 

element to derive an element safety factor. For the pillar 

safety factors, the LaModel program takes the element 

safety factor of each element in the pillar and averages 

them to get the overall pillar safety factor. This algorithm 

gives a conservative (low) safety factor since a pillar that 

has not failed completely through the core can have a 

safety factor less than 1.0 due to the low safety factors of 

the failed edge elements bringing the average safety factor 

down. 

70 
2 North 

Vertical 

Stress (psi) 

10000 

9000 

1 North 8000 

7000 

6000 

5000 #1 Mains 

4000 

1 South 3000 

2000 

1000 

Active Mine 

0 

2 South 

Figure 6.—Vertical stress on the active mine. 

2 North 

Safety 

Factor 

2.50 

2.25 

1 North 

2.00 

1.75 

1.50 

1.25 #1 Mains 

1.00 

1 South 0.75 

0.50 

0.25 

Active Mine 

0.00 

2 South 

Figure 7.—Pillar safety factors in the #1 Mains. 

In the safety factor plots in Figures 7 and 8, many of 

the gate road pillars (1 North, 2 North, 1 South, and 

2 South) show very low safety factors, as would be 

expected for bleeder and isolated conditions. However, in 

this analysis, the safety factors of the barrier pillars and 

retreat line pillars are the keys to global and local stability, 

respectively. 

71 
2 North 

Safety 

Factor 

2.50 

2.25 

1 North 

2.00 

1.75 

1.50 

1.25 #1 Mains 

1.00 

1 South 0.75 

0.50 

0.25 

Active Mine 

0.00 

2 South 

Figure 8.—Element safety factors in the #1 Mains. 

As seen in Figure 7, the average safety factor for the 

north barrier is above 2.25. However, this value is 

averaged over the entire length of the barrier pillar. In 

Figure 8, it can be seen that the edges of the north barrier 

have a considerable number of elements with safety factors 

less than 1.0, but the core still maintains elements with 

safety factors greater than 2.0. To determine the practical 

barrier pillar stability with more detail, the average safety 

factor for a one-element-wide section of the isolated 

barrier pillar between the #1 Mains and 1 North was 

calculated as 1.23. This calculation was performed at the 

worst location in terms of overburden and multipleseam stress, and although the safety factor seems low, the 

pillar should remain stable, in particular, because nearby 

sections of the barrier have much higher safety factors. 

Moreover, the analysis is probably a little conservative on 

the value of the coal strength and gob loading, and failure 

of the barrier pillar in the gob will not directly affect the 

stability of the retreat line pillar. The average safety factor 

of the barrier pillar adjacent to the retreat line has a value 

of 3.72, which is well above recommended values. 

Next, the local stability of the retreat line is analyzed. 

From Figures 7 and 8, the average safety factor for the 

middle pillar in the first row of the retreat line in #1 Mains 

can be calculated as 0.91, and the safety factor of the 

middle pillar in the second row can be calculated as 1.82. 

It is not unreasonable to have a safety factor less than 1.0 

for the first row of the retreat line. This is a very short-term 

safety factor; the overall safety factor of the global retreat 

area (the last couple of pillar rows) is what is critical. In 

this case, the average safety factor of the last two rows is 

1.36. These values compare very favorably with the values 

determined in back analyzing the previously mined retreat 

section, which was successful and had a safety factor of 

0.76 for the first row of pillars and a safety factor of 1.64 

for the second row. 

CASE STUDY RESULTS 

The main results of this case study, which were presented to the mine management, are the following: 

• The worst-case value of 1.26 for the safety factor of 

the north barrier pillar indicates that the global stability of 

the #1 Mains section should be adequate. 

• The average retreat pillar line stability factor of 1.36 

indicates that the local stability of the retreat line should 

also be adequate. 

• In some isolated areas of the #1 Mains, the stresses 

encountered due to overmining may be about 40% higher 

than the average in situ stress, and local stability on the 

retreat line may be a problem. 

It was recommended that mine management prepare 

for localized high-stress conditions in these areas and 

adjust the mining process as necessary. 

Following the LaModel analysis, the #1 Mains section 

was indeed retreat mined as modeled. There were no problems observed with the global stability of the section and, 

in general, the pillar retreat line was stable. The mine 

management planned to leave, and did indeed leave, some 

pillars under the highest multiple-seam stress areas. The 

only reported difficulty in the section was some instability 

at the retreat line after the face had been idled for a couple 

of weeks. 

72 
 

 

 

 

SUMMARY 

The LaModel program, developed some 15 years ago, 

is based on the displacement-discontinuity variation of the 

boundary-element method. Because of this formulation, 

the program is able to analyze the stresses and displacements on large areas of single or multiple tabular deposits 

such as coal mines. LaModel is unique among boundaryelement codes because the overburden material includes 

laminations, which give the model a very realistic flexibility for stratified sedimentary geologies and multipleseam mines. Over the years, LaModel has been upgraded 

and modernized. The current LaModel 2.1 uses a formsbased preprocessor for inputting the overburden and seam 

parameters, a graphical interface for creating the mine 

grids, and a graphical postprocessor for generating output 

plots. 

Recent pillar failures in the U.S. mining industry have 

highlighted the need for a standardized, best-practice 

calibration process for LaModel. To meet this need, several new algorithms have been developed for calibrating 

the most critical input parameters in the program. In 

particular, algorithms have been developed for calibrating 

the rock mass stiffness based on the expected extent of the 

abutment load, the gob properties based on the expected 

gob loading, and the coal strength based on back analysis. 

A case study of a pillar retreat mining section was 

presented to demonstrate the application of LaModel and 

the new calibration techniques to coal mine design. In this 

study, the critical input parameters were determined using 

the recommended algorithms, then the LaModel output 

was analyzed to determine the ultimate mine stability. 

During the stability analysis, the utility of using the topographic stress, multiple-seam stress, and safety factor 

calculations in LaModel was demonstrated and highlighted. Ultimately, the LaModel results were shown to 

correlate very well with the actual mining results. 

REFERENCES 

Chase, FE, Mark C, Heasley KA [2002]. Deep cover 

pillar extraction in the U.S. coalfields. In: Peng SS, Mark 

C, Khair AW, Heasley KA, eds. Proceedings of the 21st 

International Conference on Ground Control in Mining. 

Morgantown, WV, West Virginia University, pp. 68–80. 

Gates RA, Gauna M, Morley TA, O’Donnell JR Jr., 

Smith GE, Watkins TR, Weaver CA, Zelanko JC [2008]. 

Report of investigation: underground coal mine, fatal 

underground coal burst accidents, August 6 and 16, 2007, 

Crandall Canyon mine, Genwal Resources, Inc., Huntington, Emery County, Utah, ID No. 42-01715. Arlington, 

VA: U.S. Department of Labor, Mine Safety and Health 

Administration. 

Hardy, R, Heasley KA [2006]. Enhancements to the 

LaModel stress analysis program. SME preprint 06-067. 

Littleton, CO: Society for Mining, Metallurgy, and 

Exploration, Inc. 

Heasley KA [1998]. Numerical modeling of coal 

mines with a laminated displacement-discontinuity code 

[Dissertation]. Golden, CO: Colorado School of Mines, 

Department of Mining and Earth Systems Engineering. 

Heasley KA [2000]. The forgotten denominator: pillar 

loading. In: Girard J, Liebman M, Breeds C, Doe T, eds. 

Pacific Rocks 2000 – Proceedings of the Fourth North 

American Rock Mechanics Symposium (Seattle, WA, July 

31-August 3, 2000). Rotterdam, Netherlands: Balkema, 

pp. 457–464. 

Heasley KA [2008]. Some thoughts on calibrating 

LaModel. In: Peng SS, Tadolini SC, Mark C, Finfinger 

GL, Heasley KA, Khair AW, Luo Y, eds. Proceedings of 

the 27th International Conference on Ground Control in 

Mining. Morgantown, WV: West Virginia University, 

pp. 7–13. 

Heasley KA, Agioutantis Z [2001]. LaModel: a 

boundary-element program for coal mine design. In: Proceedings of the 10th International Conference on Computer Methods and Advances in Geomechanics (Tucson, 

AZ, January 7–12, 2001), pp. 1679–1682. 

Heasley KA, Akinkugbe O [2005]. A simple program 

for estimating multiple-seam interactions. Min Eng 57(4): 

61–66. 

Heasley KA, Barton TM [1999]. Coal mine subsidence 

prediction using a boundary-element program. In: Transactions of Society for Mining, Metallurgy, and Exploration, Inc. Vol. 306. Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 99–104. 

Heasley KA, Salamon MDG [1996]. A new laminated 

displacement-discontinuity program: fundamental behavior. In: Ozdemir L, Hanna K, Haramy KY, Peng SS, eds. 

Proceedings of the 15th International Conference on 

Ground Control in Mining. Golden, CO: Colorado School 

of Mines, pp. 111–125. 

Heasley KA, Agioutantis Z, Wang Q [2003]. Automatic grid generation allows faster analysis of coal mines. 

In: Yernberg WR, ed. Transactions of Society for Mining, 

Metallurgy, and Exploration, Inc. Vol. 314. Littleton, CO: 

Society for Mining, Metallurgy, and Exploration, Inc., 

pp. 75–80. 

Heasley KA, Petrovich MA, Stone R, Stewart CL 

[2007]. Mine stability mapping. SME preprint 07-133. 

Littleton, CO: Society for Mining, Metallurgy, and 

Exploration, Inc. 

Mark C [1990]. Pillar design methods for longwall 

mining. Pittsburgh, PA: U.S. Department of the Interior, 

Bureau of Mines, IC 9247. 

Mark C [1992]. Analysis of longwall pillar stability 

(ALPS): an update. In: Iannacchione AT, Mark C, Repsher 

RC, Tuchman RJ, Simon CC, eds. Proceedings of the 

Workshop on Coal Pillar Mechanics and Design. Pittsburgh, PA: U.S. Department of the Interior, Bureau of 

Mines, IC 9315, pp. 238–249. 

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Mark C [1999]. Empirical methods for coal pillar 

design. In: Mark C, Heasley KA, Iannacchione AT, 

Tuchman RJ, eds. Proceedings of the Second International 

Workshop on Coal Pillar Mechanics and Design. Pittsburgh, PA: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National 

Institute for Occupational Safety and Health, DHHS 

(NIOSH) Publication No. 99–114, IC 9448, pp. 145–154. 

Mark C, Barton TM [1997]. Pillar design and coal 

strength. In: Mark C, Tuchman RJ, eds. Proceedings: New 

technology for ground control in retreat mining. Pittsburgh, PA: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National 

Institute for Occupational Safety and Health, IC 9446, 

pp. 49–59. 

Mark C, Chase FE [1997]. Analysis of retreat mining 

pillar stability (ARMPS). In: Mark C, Tuchman RJ, eds. 

Proceedings: New technology for ground control in retreat 

mining. Pittsburgh, PA: U.S. Department of Health and 

Human Services, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health, 

IC 9446, pp. 17–34. 

Pappas DM, Mark C [1993]. Behavior of simulated 

longwall gob material. Pittsburgh, PA: U.S. Department of 

the Interior, Bureau of Mines, RI 9458. 

Peng SS [2006]. Longwall mining. 2nd ed. Morgantown, WV: West Virginia University, Department of Mining Engineering. 

Wang Q, Heasley KA [2005]. Stability mapping system. In: Peng SS, Mark C, Tadolini SC, Finfinger GL, 

Khair AW, Heasley KA, eds. Proceedings of the 24th 

International Conference on Ground Control in Mining. 

Morgantown, WV: West Virginia University, pp. 243–249. 

Zipf RK Jr. [1992]. MULSIM/NL theoretical and programmer’s manual. Pittsburgh, PA: U.S. Department of the 

Interior, Bureau of Mines, IC 9321. 

74 
 

 

 

 

 

 

 

 

 

DEEP COAL LONGWALL PANEL DESIGN FOR STRONG STRATA: 

THE INFLUENCE OF SOFTWARE CHOICE ON RESULTS 

By Mark K. Larson, Ph.D., P.E.,1

 and Jeffrey K. Whyatt, Ph.D., P.E.1 

1

Spokane Research Laboratory, National Institute for 

Occupational Safety and Health, Spokane, WA. 

ABSTRACT 

Software is often used to construct design models used 

in longwall panel design. These models necessarily reduce 

the abundant variability found in nature to a simplified 

representation that, ideally, captures the relevant characteristics of ground response to mining. The choice of stress 

analysis software is an important step in the modeling 

process. The importance of this step can be easily overlooked, yet assumptions inherent in modeling software can 

have a decisive influence. An appreciation of this step is 

important for both practitioners and users of design model 

results, particularly when decision-makers are integrating 

results into design decisions or evaluating the adequacy of 

design specifications. 

This paper examines four different stress analysis 

programs or tools for analyzing stress around a single 

longwall panel at 610 m (2,000 ft) depth beneath 

overburden containing some strong strata. The four tools 

are: an empirical model that underlies the Analysis 

of Longwall Pillar Stability (ALPS) program; the 

three-dimensional displacement-discontinuity program 

MULSIM/NL; the three-dimensional flexible overburden 

program LaModel, which has largely superseded 

MULSIM/NL; and the two-dimensional volume-element 

program FLAC. 

This study examines key aspects of panel simulation, 

including stress transfer through the gob, stress concentration in abutment ribs, and stress transfer distance 

into abutments. MULSIM/NL and FLAC results were the 

most similar. LaModel results varied greatly in terms of 

peak stress and stress transfer, while ALPS produced the 

least peak stress. This study also examines the transferability of calibrated input properties between MULSIM 

and LaModel. For instance, displacement-discontinuity 

codes have been replaced, at least in part, by LaModel, yet 

considerable experience exists in calibrated models with 

older tools. Whether and how this experience can be incorporated into analyses using other tools is a subject of some 

controversy and must be approached carefully. In all cases, 

selecting models and properties appropriate to site conditions is extremely important. 

INTRODUCTION 

Stress analysis tools such as ALPS, MULSIM/NL, 

LaModel, and FLAC have been used for some time to 

evaluate mine layout design. However, each of these tools 

has underlying assumptions that affect calculated results. 

This study examines the relative performance of these 

tools in building a generic design model for a single deep 

panel in geology typical of western U.S. longwall coal 

mines. The National Institute for Occupational Safety and 

Health has been evaluating these tools as part of a research 

project on control of bump hazards in deep western mines. 

The questions posed for this study are as follows: 

• Are these tools appropriate for deep western coal 

mines where the overburden includes one or more 

strong members? 

•	 What impacts do underlying assumptions have on 

results? 

• Are there ways to translate experience gained with 

one tool into input for another? 

GENERIC MODEL 

Larson and Whyatt [2009] used a generic site model to 

compare the response of ALPS, LaModel, and FLAC to 

cases with a strong strata member in the overburden 

(Figure 1). The model’s stratigraphic column is typical of 

deep western coal mines. Elastic properties and strength 

properties used for each member were within the range of 

those found in the Wasatch Plateau and Book Cliffs region 

of Utah [Agapito et al. 1997; Haramy et al. 1988; Jones et 

al. 1990; Maleki 1995; Maleki 1988; Maleki et al. 1988; 

Maleki 2006; Pariseau 2007] and are presented in Table 1. 

These properties were used in the FLAC models. Elastic 

properties for the displacement-discontinuity codes were 

averaged from these properties according to the equivalent 

stiffness method and the weighted thickness method 

described by Larson and Whyatt [2009]. Only a single 

panel with 244-m (800-ft) width was considered. The 

study was expanded to include results of MULSIM/NL for 

this paper. 

In this study, Salamon’s [1966] nonlinear reconsolidation model with shale gob parameters as determined by 

Pappas and Mark [1993] was used as the constitutive law 

for gob in FLAC. In the case of MULSIM/NL and 

LaModel, the linearly hardening gob model was used, with 

parameters fit to the shale gob model used in FLAC. 

75
 
 Figure 1.—Stratigraphic column of generic model with 

indicated thickness of members used in models. 

 

Table 1.—Estimated properties of materials as used in the generic and FLAC models 

Property Soft shale Sandstone Shale Coal

Young’s modulus, GPa 10.3 34.6 13.8 3.45 

Young’s modulus, million psi 1.50 5.00 2.00 0.50 

Poisson’s ratio 0.35 0.25 0.35 0.30 

Density, kg/m3

 2,310 2,310 2,310 

Density, lb/ft3 144 144 144

1,280

80

Cohesion, MPa 20.5 33.8 20.5 7.09 

Cohesion, psi 2,970 4,910 2,970 1,030 

Friction angle, ° 30 25 30 30 

Dilation angle, ° 5 5 5 5 

Tensile strength, MPa 2.07 5.03 6.89 2.07 

Tensile strength, psi 300 730 1,000 300 

Ubiquitous joint angle, ° 0 — 0 — 

Ubiquitous joint cohesion, MPa 1.4 — 1.4 — 

Ubiquitous joint cohesion, psi 200 — 200 — 

Ubiquitous joint friction angle, ° 25 — 25 — 

Ubiquitous joint dilation angle, ° 5 — 5 — 

Ubiquitous joint tensile strength, MPa 0.83 — 0.83 — 

Ubiquitous joint tensile strength, psi 120 — 120 — 

TOOL CAPABILITIES AND ASSUMPTIONS 

Numerical stress analysis tools are used in most cases 

to evaluate mining layout designs. For any given case 

where there is an excavation and adjacent pillars and 

abutments, three key points of information are determined 

by that model. Figure 2 illustrates these three points: 

(1) the fraction of overpanel weight that is transferred to 

the abutment versus the gob, (2) the distance into the 

abutment that the overpanel weight is transferred, and 

(3) the peak stress in the remaining pillars or abutment and 

its location.

 Figure 2.—Vertical cross-section across the width of a 

panel showing important concepts of stress redistribution 

resulting from excavation of a single panel. 

Each tool simplifies the problem with underlying 

assumptions. For any specific case, the user must evaluate 

whether the underlying assumptions of a tool are appropriate. If a software tool is used without considering the 

underlying assumptions, the tool may give erroneous 

results. A brief summary of each tool with its capabilities 

and assumptions follows. 

76 
ALPS 

Mark [1987] used case studies to empirically calibrate 

a simple estimate of stress distribution around a retreating 

coal panel. This method, called ALPS, considers a longwall panel across its width in vertical cross-section. 

Analysis of Retreat Mining Pillar Stability (ARMPS) is its 

equivalent for room-and-pillar retreat mining [Mark and 

Chase 1997]. ALPS considers no geology, only width of 

the excavation and overburden height to determine a stress 

distribution on the coal seam. Load on pillars and their 

stability factors are then calculated. Mark [1990] defines 

the stability factor as the load-bearing capacity of the pillar 

system divided by the design loading. A database of stability factors for various cases and their classification of 

“satisfactory” or “not satisfactory” allows the user to compare the case at hand with many others. Thus, deficiencies 

in estimation are “corrected” by using experience to define 

the critical stability factor. 

The original ALPS did not take into account the condition of the roof. Molinda and Mark [1994] developed the 

Coal Mine Roof Rating (CMRR). ALPS stability information was then modified to incorporate roof conditions. 

Mark et al. [1994] noted that the line 

 ALPS SF = 1.76 − 0.014 CMRR (1) 

separated “successful” cases from “not successful” tailgate 

cases in 82% of the case histories in the database. 

Advantages of this tool are: 

•	 It is quick and easy to calculate the stability 

factors. 

•	 It has a large database for comparison with other 

cases. 

The assumptions of this tool are: 

•	 Caving and load transfer fit a simple model. Figure 3 depicts supercritical and subcritical vertical 

sections showing a wedge volume with unit 

thickness of the overpanel weight that is transferred to the abutment.

 Figure 3.—Vertical cross-section across the width of mined 

panels showing geometry of supercritical (left) and subcritical 

(right) panels (after Heasley [2008a]). The subcritical geometry 

is used by Mark [1987] in ALPS. 

 That wedge is defined by 

the angle, β. No differences in geology are directly 

considered. The overpanel strata between the triangles are assumed to cave, and their weight is 

fully supported by the gob. 

• Mark [1990] found for six cases in the Eastern 

United States, β ranged from 10.7° to 25.2° and 

recommended that β be assumed as 21°. That 

assumption is constant in the ALPS database. 

Maximum load transfer distance is represented by the 

following equation [Pariseau 2007]: 

D = 9.3 H , (2) 

where D = maximum load transfer distance (ft); 

and H = overburden height (ft). 

 The vertical stress profile on the seam is represented 

by 

⎛ 3L

σ
 s ⎞ a =
 ⎜ 3 ⎟(D −
x )

2

, (3) ⎝ D
 ⎠ 

where σa = abutment stress distribution function; 

 x = distance from the edge of the panel; 

and Ls = total side abutment load. 

MULSIM/NL 

Boundary-element techniques, pioneered in the late 

1960s and early 1970s, have a computational advantage 

over volume-element techniques for problems in infinite or 

semi-infinite domains in that the system of equations to 

solve is much smaller for the same problem [Crouch and 

Starfield 1983]. However, the equations are not sparse, 

as with volume-element tools, meaning that there are not 

many zero coefficients in the system of equations that must 

be solved. The displacement-discontinuity method is a 

subset of the boundary-element method, which solves the 

problem of a discontinuity in displacement between opposite surfaces of a crack over a finite length in an infinite 

elastic medium. Such a solution can be applied to a tabular 

deposit, such as a coal seam, where the behavior of the 

deposit is simulated with the crack. The seam is represented by a grid, and each square or block in that grid is 

assigned its own set of properties, strengths, and constitutive law. Constitutive laws for seam elements include 

linear elastic, strain softening, elastic-plastic, bilinear 

77 
hardening, strain hardening, and linear elastic gob. The 

off-seam material is isotropic elastic only. 

Crouch and Fairhurst [1973] developed software 

implementing the technique for mine structural analysis. 

St. John [1978] used the technique in his code, 

EXPAREA. Sinha [1979] used the technique in the 

development of three computer programs, one of which 

(MULSIM) analyzes cases of multiple, parallel seams. He 

included the ability to subdivide coarse blocks into finer 

mesh so that the scheme was computationally more efficient. Beckett and Madrid [1986, 1988] developed additional features for MULSIM (their version was called 

MULSIM/BM), such as additional seam materials like 

gob, pack walls, and cribs; graphical development of grids; 

and an increase in the number of coarse blocks and the 

number of blocks that could be subdivided into finer mesh. 

Donato [1992] converted MULSIM/BM to a PC environment. Itasca Consulting Group added the ability to consider multiple mining steps [Zipf 1992b]. Zipf [1992a,b] 

added nonlinear seam materials such as strain-softening, 

elastic-plastic, bilinear hardening, and strain-hardening 

(MULSIM/NL). 

MULSIM/NL can handle up to four parallel seams dipping at some angle to horizontal as specified by the user. 

Initial three-dimensional stress conditions and stress gradients with depth are specified. Once the system of equations 

is solved iteratively, the full stress tensor and displacement 

vector components are output for each element and at userspecified locations in the surrounding ground. 

The DOS version (or Zipf version) of the tool uses 

coarse mesh to streamline calculations. For problems in this 

study (68 × 68 coarse blocks with fine mesh in the middle 

50 × 50 of the coarse blocks), a stress threshold of 1 psi 

served as the equilibrium convergence criterion so that the 

number of iterations typically ranged from 250 to 350. 

The Windows version (or Heasley version) of the tool 

lacks the coarse mesh, but allows a 400 × 400 fine mesh. 

Meshes of this size were initially used in this study, but all 

iterations were stopped at 90. Use of this version in this 

study was eventually abandoned because of long run time. 

Advantages of this tool are: 

• Calculation time with the Zipf version is relatively 

short. 

• The full stress tensor is output. 

•	 Nonlinear in-seam behavior is available, as mentioned earlier. 

Assumptions of this tool are: 

• Overburden and underburden behavior can be 

adequately simulated with a one-material, elastic 

medium. 

• Interaction between an elastic off-seam material 

and a nonlinear seam will adequately and realistically simulate gob-roof displacement and caving 

behavior. In short, the roof does not fail and cave. 

Instead, elastic sag of the overburden and appropriate in-seam gob constants can provide realistic 

load to the gob. 

LAMODEL 

Heasley [1998] developed LaModel, a displacementdiscontinuity modeling tool that uses the thin-plate or 

lamination formulation [Salamon 1991]. Each layer is 

separated by parallel, frictionless joints in the overburden 

and underburden at even intervals specified by the user. 

Heasley also included the same nonlinear models used in 

MULSIM/NL. The frictionless joints make the overburden 

less stiff, increasing closure of excavated areas of the 

seam. Heasley found this formulation tracked stress distributions in a coal seam and provided a better match to 

subsidence observations than an elastic model [Heasley 

1998]. However, he cautioned that the user must calibrate 

for displacement or stress, and calibrating for one entity 

may not provide realistic results for the other [Heasley 

2008b]. 

Solutions are completed about the same or faster than 

the Zipf version of MULSIM/NL. Off-seam calculations 

take a much longer time. Horizontal stresses are not 

computed. In addition, the seam can only be horizontal. 

Overburden and underburden are assumed to consist of 

layers of elastic material interspersed with horizontal, 

frictionless, cohesionless joints. The result is an increase in 

mechanical flexibility and the amount of predicted surface 

subsidence compared to the MULSIM/NL model, which 

assumes elastic behavior of the overburden. 

Heasley [2008b] suggested a method for calibrating a 

LaModel simulation. He recommended adjusting the overburden Young’s modulus so that 90% of the load transferred to the abutment lies within 

D .9 = 5 H , (4) 

where H = seam depth (ft). Then Heasley recommended 

using a layer thickness according to 

2Es 12(1−ν 2) ⎛ 5 H − d ⎞

2

 

t = ⎜ ⎟ , (5)
 

E h ⎜

⎝ ln(0.1) ⎟⎠

where E = elastic modulus of the overburden; 

ν = Poisson’s ratio of the overburden; 

Es = elastic modulus of the seam; 

h = seam thickness (ft); 

d = extent of the coal yielding at the gob 

 edge (ft); 

and H = seam depth (ft), as in Equation 4. 

78 
 

If Es , ν, h, H, and d are maintained constant, then 

Equation 5 can be reformed to find the product, tE, that is: 

 tE = constant (6) 

In fact, this product is the actual overburden “property,” i.e., calculated results will be the same as long as 

this product is constant. 

Advantages of the tool are: 

• Calculation time is relatively short. 

•	 Nonlinear in-seam behavior is available. 

Assumptions of this tool are: 

•	 Overburden and underburden behavior can be 

adequately simulated with a one-material, elastic 

medium with embedded frictionless, cohesionless 

joints. 

• Interaction between an elastic off-seam material 

with embedded frictionless, cohesionless joints and 

a nonlinear seam will adequately and realistically 

simulate gob-roof displacement and caving 

behavior. In short, the roof does not fail and cave. 

Instead, elastic sag of the overburden and appropriate in-seam gob constants can provide realistic 

load to the gob. 

EQUIVALENCY OF MULSIM/NL AND LAMODEL 

The transition from an elastic overburden mass in 

MULSIM/NL to overburden with frictionless, cohesionless 

joints in LaModel begs the question whether MULSIM/NL 

and LaModel can produce equivalent or similar results for 

appropriate inputs. Gates et al. [2008, Appendix V], based 

on Heasley’s [1998] formulation, proposed defining 

equivalent properties by matching midpanel closure. Solutions for the two methods, assuming cracks rather than 

coal seams, are: 

sh ( ) x = 4( q 1 − υ2 ) (L 2 − x

2 ) and (7) E ,

() 12(1 − υ 2 ) q sl x =	 ( L 2 − x 

2 ) , (8) 

 t E 

where sh = seam convergence of the homogeneous 

 (MULSIM/NL) case; 

sl = seam convergence of the laminated case; 

x = distance from the panel centerline; 

ν = rock mass Poisson’s ratio; 

t = layer or lamination thickness; 

q = overburden stress; 

E = rock Young’s modulus; 

and L = half-width of longwall panel. 

Combining these, Gates et al. [2008, Appendix V] found 

3 E

t	 = homogeneous L

(9) 4 E 2

 − , laminated 1 υ 

or 

tElaminated = kEhomogeneous (10) 

Gates et al. [2008, p. V-1] present Equation 9 as a 

method for finding the “required thickness” for translating 

a calibrated elastic overburden modulus to LaModel overburden properties. More specifically, they state that Equation 9 “could be used to estimate properties that would 

equate the laminated strata behavior with the homogeneous 

rock mass used in other boundary element programs” 

[Gates et al. 2008, p. 115]. This suggests that Equation 9 

may provide equivalence beyond closure at centerline of 

the panel. Such an equivalence would be a valuable link 

between tools, even though limited to a particular panel 

width (2L). 

A simple test was devised to explore the extent of this 

equivalence. An elastic model was constructed for both 

MULSIM/NL and LaModel with layer thickness calculated according to Equation 9. Young’s modulus of coal 

was set high (207 GPa (30,000,000 psi)) to minimize seam 

contribution to closure. Figure 4 shows the stress and closure profiles for a case with panel half-width set at 122 m 

(400 ft), Poisson’s ratio set at 0.35, and Ehomogeneous = 

Elaminated = 10.3 GPa (1.5 million psi); and thus t = k = 

113 m (370 ft). At midpanel, LaModel calculated closure 

to be 9.8% higher than MULSIM/NL. This difference 

likely is a result of effects from element size and edges 

[Heasley 1998, 2009; Zipf 1992b]. However, the stress 

profile within 46 m (150 ft) of the panel differed significantly. Thus, this “equivalence” is extremely limited and 

should not be used if abutment stresses are a concern, 

which is usually the case. 

FLAC OR VOLUME ELEMENT 

The concept of volume-element discretization for 

stress analysis has been around for a long time, but has 

become increasingly important since the advent of computers. For example, the finite-element method was 

developed in the aerospace industry in the 1950s 

[Segerlind 1976]. Turner et al. [1956] are credited with 

being the first to use the method in solid mechanics in 

1956. Finite-difference concepts have also been long 

known to the mathematical world [Dahlquist and Björck 

1974]. Dr. Peter Cundall first used the technique in his 

FLAC computer code to solve solid mechanics problems 

specifically for geomaterials in 1986. 

79 
 Figure 4.—A, Vertical stress profile; B, closure profile for 

a purely elastic case with large Young’s modulus for coal. 

The closures at centerline of panel were expected to be 

equivalent. 

 

FLAC, as with most volume-element codes, calculates 

stress for each discretized volume element and displacement at each grid point that defines the volume elements. 

Each element has its own constitutive law and properties, 

including the possibility of material yielding and plastic 

flow. With FLAC version 5.0, used in this study, care must 

be taken in choosing mesh size and strength properties. If 

an element exhibits too much localized plastic flow, 

numerical instability may result. To detect such an 

impending situation, FLAC stops calculations if any triangular subzone of an element has an area below a 

threshold fraction of the entire element volume. However, 

FLAC version 6.0 includes the capability of dynamic 

meshing, thus eliminating this instability under large plastic deformations. 

Volume-element models discretize all modeled space, 

so boundaries are needed to limit model size. As a result, 

model boundaries must be far away from the area of 

interest to avoid influencing results, but close enough to 

limit problem size. Generally, this method needs a large 

number of elements and, thus, the size of the model can be 

very large. 

Advantages of FLAC are: 

• Each member of the stratigraphic column can be 

represented according to an appropriate constitutive law, specific elastic properties, and specific 

strength properties. 

• Failure of elements is determined by the code, not 

by the user. 

•	 The code has an embedded simple computer language, FISH, that permits the user much versatility 

in model construction, model running, and inclusion of user-defined constitutive laws. 

• Complex boundary conditions and initial conditions can be input to the model. 

Assumptions of this tool are: 

•	 In the case of a two-dimensional model, the vertical cross-section of the model is far enough from 

panel ends that a plain-strain condition exists. 

• The first-order volume-element response (in the 

elastic formulation, terms with exponents greater 

than 2 are neglected) adequately represents material behavior. If beamlike behavior is important in 

an analysis, then the grid must be fine to calculate 

accurate deformations and stresses. 

GENERIC MODEL RESULTS 

The generic model study with each of the four tools 

considered estimated three aspects of stress redistribution 

resulting from panel mining, as shown in Figure 2. These 

are (1) the fraction of overpanel weight that is transferred 

to the abutment versus the gob, (2) the distance into the 

abutment that the overpanel weight is transferred, and 

(3) the peak stress in the remaining pillars or abutment and 

its location. 

Overpanel Weight Transfer to Abutment 

or to Gob 

Figure 5 shows the range of overpanel weight fraction 

transferred to the abutment for roughly “equivalent” 

properties. The range for MULSIM/NL was very small— 

approximately 0.94–0.96 for the whole range of overburden properties used. MULSIM/NL and FLAC results 

are similar. The larger range of FLAC results was likely 

caused by various degrees of failure in the set of models. 

The full range of LaModel results with the same 

overburden elastic properties (E, ν) was less than that of 

MULSIM/NL. Stress transfer with LaModel using a 

lamination thickness on the order of the overburden 

thickness was clearly not the same as that calculated by 

MULSIM/NL. The fraction of overpanel weight transferred to the abutment by ALPS for β = 21° was 

approximately 0.73—clearly below that of FLAC and 

MULSIM/NL. The upper value of 38° was chosen to test 

the impact of increased bridging of strata on results. 

80 
 Figure 5.—Chart showing the range of proportion of overpanel weight shifted to abutments for three numerical modeling tools and ALPS for a panel width of 244 m (800 ft) and an 

overburden thickness of 610 m (2,000 ft). The locations of 

numbers in the LaModel column represent average results 

for that layer interval, where the interval is in feet. 

 

 

Peak Stress and Location 

Figure 6 shows the vertical stress profile on the coal in 

the first 46 m (150 ft) from the edge of the abutment for 

two generic model cases.

 Figure6.—Vertical stress profile on abutment for the 

generic model case of 61 m (200 ft) of roof sandstone. Gob is 

modeled. A, No immediate roof shale; B, immediate roof shale 

thickness is 15 m (50 ft). 

 Results from LaModel were calculated with 1.5-m (5-ft) elements with eight yield rings, 

while the results from MULSIM/NL were calculated with 

3.0-m (10-ft) elements and four yield rings. Results from 

FLAC were calculated using 0.76-m (2.5-ft) elements. 

While these element sizes are not the same, they represent 

the best results one can get for a single panel model within 

the constraints of each numerical tool. 

The peak stresses and their locations are significantly 

affected by element size. To adequately compare results 

using the Mark-Bieniawski formula (MULSIM/NL and 

LaModel) and an equivalent-strength, elastic-perfectlyplastic constitutive law (FLAC), the elements would need 

to be the same size and probably smaller (0.76-m (2.5-ft) 

or smaller). 

For cases where only the seam is extracted (no immediate roof shale caves (e.g., Figure 6A)), FLAC tends to 

calculate higher peak stress than MULSIM/NL and 

LaModel. However, FLAC, MULSIM/NL, and LaModel 

with layer thickness set at overburden height calculate 

similar peak stresses and stress profiles. 

FLAC, MULSIM/NL, and LaModel handle material 

failure near the rib differently. In FLAC, zones stressed 

beyond the elastic limit undergo plastic flow, thus reducing 

the stiffness near the rib and shifting overburden weight to 

stiffer coal farther from the rib. MULSIM/NL and 

LaModel impose an elastic limit according to the MarkBieniawski formula and allow more closure of the seam in 

an element if stresses are above the limit. These two 

methods are not equivalent and thus can affect the amount 

of peak stress calculated. It is, therefore, not surprising 

when FLAC peak stresses are significantly different from 

either MULSIM/NL or LaModel. ALPS, of course, has no 

ability to simulate failure of seam material near a rib. 

Where it is assumed that immediate roof shale caves and 

forms gob (FLAC results in Figure 6B), the location of the 

top of the seam with respect to the geometry of the 

opening affects the amount of peak stress. Such geometry 

is not possible in the boundary-element codes, where fullheight extraction of the seam only is assumed. 

81 
Stress Transfer To Abutment 

Figures 7 and 8 show the range of locations in the 

abutment where total vertical stress returns to 150% and 

200%, respectively, of premining vertical stress for 

reasonable ranges of input for each tool.

 Figure 7.—Distance from gob where vertical stress on coal 

is 150% of premining vertical stress. Results include immediate shale thickness of 0, 3.0, and 15 m (0, 10, and 50 ft) and all 

LaModel layer intervals modeled. 

 Figure 8.—Distance from gob where vertical stress on coal 

is 200% of premining vertical stress. Results include immediate shale thickness of 0, 3.0, and 15 m (0, 10, and 50 ft) and all 

LaModel layer intervals modeled. 

 It is, in essence, 

a map of accessible solutions. LaModel lamination thickness significantly affects stress transfer distance. Results 

with lamination thickness of 7.6-m (25-ft) plot at the 

bottom of the LaModel range, while results with lamination thickness of 610-m (2,000-ft) plot at the top of the 

LaModel range. MULSIM/NL stress transfer distance 

seems to be at approximately midrange of the LaModel 

results. MULSIM/NL stress does not seem to transfer as 

far into the abutment as ALPS, FLAC, or LaModel with 

layer thickness set at the overburden thickness. However, 

FLAC results with smaller roof sandstone thickness plots 

near corresponding MULSIM/NL results. 

Equivalency of MULSIM/NL and LaModel: 

Generic Model Results 

Equivalence of MULSIM/NL and LaModel tools was 

also tested for the generic model to see if some combination of input parameters might produce essentially equivalent stress distributions. This was addressed by applying 

generic model E and varying t in LaModel. 

82 

Figure 9 shows stress profiles for the generic case 

where immediate roof shale thickness is 0 m and roof 

sandstone thickness is 61 m (200 ft). 

 Figure 9.—Vertical stress profiles across half-width of 

panel and abutment for MULSIM/NL and LaModel for the 

same overburden properties and various layer thicknesses 

for LaModel. Properties were determined by the weighted 

thickness method for shale = 0 m and sandstone = 61 m 

(200 ft). 

Stress profile equivalency does not seem possible for this practical example 

with inelastic rib properties. When layer thickness was set 

to overburden thickness, peak stress calculated by the two 

tools was nearly the same. However, LaModel results 

showed more load closer to the opening than those of 

MULSIM/NL. It seems that no value of the constant tE 

will produce a LaModel stress profile equivalent to that 

from MULSIM/NL. 
 

 

 

 

 

 

Discussion 

These results show that the underlying assumptions of 

each of these stress analysis tools (ALPS, MULSIM/NL, 

LaModel, and FLAC) significantly influenced results. Of 

these, FLAC and MULSIM/NL with averaged overburden 

properties provide the most similar results. The main 

difference is that FLAC transfers overpanel weight slightly 

farther into the abutment. The recommended β = 21° for 

ALPS, which controls the portion of overpanel weight 

transferred to the abutment, underestimates abutment load 

transfer relative to FLAC and MULSIM/NL. Larger values 

of β provide closer results, but nonstandard input to ALPS 

makes comparison with the ALPS database invalid. 

LaModel produces the widest range of possible 

solutions and thus is most sensitive to input parameters. 

Heasley [2008b] addresses this by recommending a 

specific input development process. However, in deep 

western conditions where the stratigraphic column includes a strong, stiff member, overpanel weight may be 

transferred farther [Barron 1990; DeMarco et al. 1995; 

Gilbride and Hardy 2004; Goodrich et al. 1999; Kelly 

1999; Maleki 2006] than Equation 2 would indicate. In 

such a case, observations or measurements of load transfer 

would be necessary to determine the maximum load 

transfer distance. 

In this study, the gob model was not varied. However, 

accurate simulation of gob behavior is perhaps the input 

that most significantly affects stress transfer to the abutment. All four tools may be able to adequately simulate 

site-specific gob behavior where detailed observations or 

measurements have been made of strata behavior, subsidence, extent of cave, gob loading, etc. However, not all 

tools can simulate important mechanisms. For example, 

a strong, stiff overburden member may result in arching of 

stress over the excavated panel and subsequent sudden 

collapse. Displacement-discontinuity models cannot simulate that mechanism or its effects. Only models that 

simulate the behavior of individual stratigraphic members 

can simulate and/or predict this mechanism. 

When moving between MULSIM/NL and LaModel, 

it may be possible to get equivalent closures at midpanel 

by limiting error resulting from edge and element size 

effects, but equivalent stress profiles cannot be achieved in 

this case. Equivalence seems to be approached, but not 

attained, as lamination thickness is increased to 

overburden depth. The user’s choice between these two 

tools should be motivated by measured behavior or 

characteristics of the stratigraphic column, such as the 

strength of beds, bedding plane properties, thickness of 

beds, etc. 

CALIBRATION TO STRESS MEASUREMENTS 

Comparison to actual conditions is the only way to 

evaluate the validity of a model. It can also be used to 

“calibrate” model input, i.e., results of the previous section 

show only relative performance, not which is “best.” 

Figures 7 and 8 show ranges of stress transfer distance that 

each tool can achieve for a given geology. Therefore, it is 

best, where possible, to assess whether a tool is appropriate 

for a specific site. 

As an example, Larson and Whyatt [2009] compared 

stress in the abutment calculated with ALPS, LaModel, 

and FLAC with borehole pressure cell measurements of 

stress induced by mining at two sites. Figures 10 and 11 

show the same results with MULSIM/NL calculations 

added. Gate road entries were not included in the models 

for convenience. However, aside from local perturbations 

around entries, each tool can be optimized to provide the 

best possible approximation of the measured stress 

distribution. 

While the borehole pressure cells were not located 

close enough to the rib to capture the actual peak stress, 

the ALPS stress distributions do not simulate the rapid 

change in stress near the gob. Calibrated MULSIM/NL 

stress change profiles reasonably matched the changes in 

stress measurements. LaModel stress profiles varied 

greatly, with either the peak stress too high or the stress 

not decreasing as quickly as the measurements with 

distance from the gob. FLAC models were not built to 

closely simulate stratigraphy because stratigraphic members or their properties was not sufficiently described 

[Barron 1990; Koehler et al. 1996]. Instead, generic model 

geometries with actual panel widths and overburden 

heights were used to approximate actual site conditions. In 

these cases, calculated vertical stress profiles with roof 

sandstone thicknesses of 3 m (10 ft) and 15 m (50 ft) are 

reasonably close to the changes in stress measurements, 

suggesting that calculated results likely would match stress 

change measurements closely if the actual stratigraphic 

columns were modeled. 

83 
 Figure 10.—Mining-induced stress around the 6th Right 

gate roads at a Utah Mine [Koehler et al. 1996]. A, ALPSassumed stress distribution function and measurements; 

B, MULSIM/NL and LaModel results; C, FLAC results with 

measurements. (BPC = borehole pressure cell; Sh = shale; 

SS = sandstone; YM = Young’s modulus.) 

 

 

 

 Figure 11.—Mining-induced stress around the 9th East 

gate roads at a Utah Mine [Barron 1990]. A, ALPS-assumed 

stress distribution function and measurements; 

B, MULSIM/NL and LaModel results; C, FLAC results 

with measurements. (BPC = borehole pressure cell; 

Sh = shale; SS = sandstone; YM = Young’s modulus.) 

 

The importance of calibrating tool input properties to 

site conditions is emphasized by these results. This point 

was also underscored in a recent Program Information 

Bulletin from the Mine Safety and Health Administration 

[Skiles and Stricklin 2009]. In the bulletin, an eight-step 

general process is outlined for successful calibration to 

specific sites. The bulletin states, in summary:

“Successful numerical simulation requires a substantial 

effort including the observation of in-mine conditions 

in many areas and the often repetitive process of 

calibrating model parameters...It cannot be overemphasized, however, that in order to be of value, 

a numerical model must be validated and provide a 

realistic representation of the underground environment 

for which it is applied.” 

84 
 

 

 

 

 

 

 

 

 

 

CONCLUSIONS 

Empirical, boundary-element, and volume-element 

tools are often used to evaluate mine plans. These tools are 

not interchangeable. Site-specific information must be 

used to calibrate and assess the appropriateness of each 

tool. For instance, LaModel does not consider tectonic 

stress. Thus, it might be a poor choice if high horizontal 

stresses are present and can influence outcomes in the 

mine. For empirical tools, application site conditions 

should be compared with conditions at underlying cases to 

determine whether the tool might be justified. The published database includes a wide variety of geologic and 

stress conditions, but it is possible that cases exist outside 

of database conditions. If possible, additional cases based 

on local experience should be compared to the published 

database to establish validity. 

Generally, a tool’s input properties should be calibrated to site-specific conditions and observations. This 

point is even more important when a strong, stiff member 

is present in the stratigraphic column. Calibration procedures should include achieving the correct abutment stress 

profile and reasonable stress transfer distance. Empirical 

tools are often an exception, as the reference database typically includes a variety of site conditions. However, if 

local behavior or cases depart significantly from the 

underlying database, the user may need to make adjustments. These can include revising coal strength and cave 

angle, for example. Alternatively, a revised critical 

stability factor might be proposed. In either case, 

adjustments delink results from the underlying empirical 

database and the established success criterion, creating, 

in essence, a new empirical method that must be justified 

on its merits. 

Results of the generic model study show that assumptions and features of the tools studied differ too markedly 

for a model constructed with one tool to be “converted” 

into another through application of the same input 

parameters. Thus, care must be taken when taking input 

parameters from past analyses using different modeling 

programs. New models should be calibrated to field observations and, ideally, measurements of critical behavior. 

Results from this study show that if FLAC input 

accounts for individual stratigraphic members and their 

properties, then the seam stress profile that it calculates is 

most similar to results calculated by MULSIM/NL, where 

overburden properties were determined by averaging individual member properties by some reasonable method. 

However, the user should evaluate the stratigraphic column and the properties of its individual members with 

respect to the caving mechanism of the site. An analysis 

tool should be able to simulate the most important effects 

of that mechanism. 

LaModel results are highly sensitive to input parameters and, therefore, careful model calibration, adjusting tE 

to fit observed or measured stress conditions, is required. 

LaModel results did not fit the example cases very well. 

The quick decrease of stress near the rib requires tE to 

be relatively small, but this increases peak stress 

unrealistically. 

ALPS stress distribution significantly underestimates 

peak stress. However, using the default value of β may, 

in many cases, be a reasonable estimate of total load transferred to the abutment. 

In this study, we assumed a model for gob (shale from 

Pappas and Mark [1993]) and kept that constitutive model 

constant for all models. If a stiffer gob were used, less 

stress would be transferred to the abutment. Determining 

the correct gob stiffness relationship is one of the most 

important parts of model calibration because that relationship is the most significant factor in determining amount of 

load transfer to the abutment. 

The user must be very careful when selecting the 

proper analysis tool. If caving behavior can be affected 

significantly by variability in the strength and stiffness of 

stratigraphic column members, then a tool should be used 

that can take that influence into account. This means that 

tools that assume a single off-seam material that is elastic 

may miss details of off-seam strata behavior that may be 

significant. 

ACKNOWLEDGMENTS 

The authors would like to thank Keith A. Heasley, 

Ph.D., West Virginia University, Department of Mining 

Engineering, for discussions that strengthened this paper. 

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PRACTICAL APPLICATION OF NUMERICAL MODELING FOR THE STUDY OF 

SUDDEN FLOOR HEAVE FAILURE MECHANISMS
 

By Hamid Maleki, Ph.D.,1

1

Maleki Technologies, Inc. (MTI), Spokane, WA. 

 Collin Stewart,2

2

Formerly with Bowie Resources, LLC, Paonia, CO. 

Ry Stone,3 and Jim Abshire3 

3

Bowie Resources, LLC, Paonia, CO. 

ABSTRACT 

As mining continues toward deeper reserves in thick 

western U.S. coalfields, the control of mining inducedseismicity has become a priority in many operations in 

Utah, Colorado, and Wyoming. Gradual floor heave, 

common in many coal mines, historically has not been a 

safety issue. However, recent occurrences of sudden floor 

heave accompanied with seismicity in a few deep mines 

have fueled this investigation. The focus is to identify and 

study the mechanisms resulting in sudden heaving of the 

mine floor in western U.S. deep coal mines through analytical calculations and back analyses of an actual event in 

a cooperative mine. 

Based on review of available data in three mines, 

underground observations, and back analyses of an actual 

event, we identified the following contributing factors: 

(1) the presence of stiff stratigraphic units and thick 

seams mined at depths exceeding 1,000 ft (305 m); (2) the 

presence of geological discontinuities, reducing the in situ 

strength of the coal with a calculated factor of safety near 

1 for the mine floor; (3) mining approaching areas of 

higher than normal stress gradient associated with 

previous mining or structural anomalies or surface topographic highs; and (4) an additional source of energy 

triggering sudden failure, such as periodic caving or slip 

along geological discontinuities. 

Detailed FLAC3D modeling of the event has 

improved understanding of the floor heave mechanism. 

Preliminary examination of seismic data for the actual 

event in the cooperative mine and underground observations excluded fault slip at the mining horizon as a major 

triggering mechanism, but highlighted the significance of 

weak, anisotropic strata conditions near the intersection of 

two faults. Numerical investigations at the study site point 

to shear failure of bottom coal during time-dependent 

strain softening. The model response is not very sensitive 

to elevated horizontal stress. Although there is no single 

triggering mechanism for the sudden failure at the study 

site, we can point to the coincidence of several unfavorable factors, including faulting, stiff stratigraphic 

units, and altered stress gradients at the multiple-seam crossing and topographic highs. 

INTRODUCTION 

As mining continues toward deeper reserves in thick 

western U.S. coalfields, the control of mining inducedseismicity has become a priority in many operations in Utah, 

Colorado, and Wyoming. Gradual floor heave, common in 

many coal mines, historically has not been a safety issue. 

However, recent occurrences of sudden floor heave accompanied with seismicity in a few deep mines have fueled this 

investigation. The focus is to identify and study the mechanisms resulting in sudden heaving of the mine floor in western U.S. deep coal mines through analytical calculations and 

back analyses of an actual event in a cooperative mine. Site 

inspections and mining records from two additional mines 

were also reviewed and are included in this paper. 

This study was initiated in November 2007 to investigate 

geotechnical factors contributing to floor bumps in a relatively isolated portion of the cooperative mine. The mine is 

located in the Somerset Coal Basin, near Paonia, CO, where 

three mining companies have been extracting coal from 

multiple-seam reserves within the last 2 decades. At the study 

site, the operator has been extracting coal reserves from the 

Upper D and Lower and Upper B Seams. After extracting the 

Upper D Seam reserves in the No. 2 Mine, the operator has 

been mining in both the Lower and Upper B Seams located 

approximately 300 ft (91 m) below the D Seam workings. 

The mine has employed the longwall mining method to 

extract the Upper D Seam since 1999 using yield-abutment 

gate pillar designs while monitoring surface subsidence, 

collecting detailed geotechnical data in cooperation with MTI 

staff, and, more recently, monitoring the mining-induced 

seismicity in cooperation with NIOSH. In the gate roads of 

these longwall panels, the operator used yield abutment pillars from 98 to 114 ft (30 to 35 m) wide. Yield pillars were 

37–47 ft (11–14 m) wide, and the longwall face was 824 ft 

(251 m) wide. The mine layout and location of the study area 

are shown in Figure 1, along with historic workings in the 

U.S. Steel Mine and King Mine. Similar gate pillar layouts 

are used in the B Seam while offsetting the position of gate 

roads with respect to D Seam gate roads (Figure 1). 

89
 
Figure 1.—Mine layout and the location of the study area. 

 

 

 

 

 

 

In addition to surface monitoring, the operator implemented a detailed geotechnical program consisting of drilling continuous coreholes from the surface, depositional and 

structural logging of the core, geologic mapping, rock 

mechanics testing, and hydrologic monitoring in cooperation with MTI staff at one location. Overburden characteristics were evaluated using Bieniawski’s Rock Mass 

Rating system, identifying massive overburden units 

capable of transferring loads and reducing differential 

movements for future extraction of the B Seam [Maleki 

et al. 2007]. 

Additional data have been systematically collected near 

the longwall block using interseam core drilling and the 

access from the Upper D Seam, exploring geologic and 

rock strength of the interburden rocks. These activities included lithologic and structural logging, together with 

mechanical property testing of near-seam strata. 

GEOLOGIC SETTING 

The Somerset Coalfield is located on the southeastern 

margin of the Piceance Basin, which lies north of the 

Gunnison Uplift, west of the Elk Mountains, east of the 

Uncompahgre Uplift, and south of the White River Uplift. 

There are six primary coal seams within the Somerset Coalfield ranging from 10 ft (3 m) thick on a single bench of 

coal to over 20 ft (6.1 m) where one or more seams merge 

[Maleki et al. 1997]. An estimated 1.5 billion tons of 

bituminous coal lies within the Somerset field. Coal seams 

B, C, D, E, and F have been mined historically in this basin. 

The coal seams contain a very well developed cleat set 

oriented at N 58° to 75° E [Carroll 2003]. 

The regional structural dip of the Mesa Verde Formation is 3° to 5° to the north-northeast. The predominant 

jointing of sedimentary rocks is N 68° E to N 74° E in the 

basin, with secondary jointing at N 18° W to N 35° W. 

Regional joint patterns have been mapped by Carroll [2003] 

and the authors. 

During extraction of the D1–D9 and WD1–WD3 panels 

in the southwest district, we studied faulting using both surface and underground mapping by the geologic staff. Both 

normal and strike-slip faults have been encountered underground, but only one fault has surface expression. The 

southern portion of the D6 panel and part of D5 gate road is 

traversed by D-5 fault, a N 80° to 90° E left-lateral, strikeslip fault system. The system is a complex array of anastomosing fault planes of variable offsets. Relative motion is 

10° to 15° from the horizontal with 5–10 ft (1.5–3.0 m) of 

total throw down to the south. North of the strike-slip fault, 

the D6–D9 panels are intersected by several N 60° E normal faults with limited lateral extent and displacements 

appearing as tensile gashes. It seems that these faults 

formed as a result of differential movement along the 

strike-slip fault. This assertion is based on observations that 

throw decreases with increasing distance from the fault to 

the north, but no such features are found to the south. 

Where present, kinematic indicators suggest dip-slip movement and little to no shear [Robeck 2005]. 

Additional data were collected more recently at the 

location of the floor bump. As shown in Figure 2, geologic 

structures are projected based on underground mapping in 

the D Seam as well as available exposures within the 

B Seam in close proximity to the study area. The east-west 

oriented D-5 fault shown in Figure 2 has strike-slip 

movements with very limited vertical offset. As it bends to 

the north near the event site, the offset increases to 20 ft 

(6.1 m), becoming near parallel to another set of northwestoriented faults in the study area. Clearly, the geologic and 

stress conditions are complex near the event site, and the 

possibility of abnormal horizontal stress conditions (including reorientation and higher magnitudes) cannot be ruled 

90
 
out. Faulting did not create any significant operational 

problems or seismicity during multiple crossings at the 

Upper D Seam. In the weaker, deeper B Seam workings 

near the bend zone, the faulting has promoted floor heave 

mostly in a gradual manner, but also suddenly under certain 

conditions. 

(A) 

(B) 

 Figure 2.—Mining geometry, geologic conditions near the 

event locations, and observed floor heave in the Lower B 

Seam: (A) first event, (B) final event. 

Figure 3 shows a typical geologic cross-section for the 

two-seam longwall area.

“C” Sandstone 

Rollins Sands tone 

BRL-IP-00-65 Su rface BRL-IP-00-66 

Undif ferentiated 

Upper “D” Seam USS G-15 Lower “D” Seam 

“C” Seam Alluvium Large sand stone Up per “B” Sea m bod ies L owe r “B ” Se am 

Figure 3.—East-west geologic cross-section. 

The major units present are representative of the Cretaceous Age Lower Mesa Verde 

Formation in this area and include the Rollins Sandstone, 

the C-Sandstone (locally referred to as Upper Marine Sandstone), and coal seams A through D-Upper. Horizontally 

bedded mudstone and siltstone sequences, together with the 

cross-bedded to laminar-bedded fluvial sandstone channels, 

are also present, but shown as undifferentiated in the crosssection. The alluvial valley fill is believed to be Quaternary 

in age and is composed of Tertiary Age igneous boulders, 

cobbles, and gravel. 

The coal seams and the Rollins and C-Sandstones are 

the only truly tabular sedimentary bodies in the section. The 

two sandstone bodies are even more laterally continuous 

than the thinner coal seams. Because of strength and lateral 

persistency, these two marine sandstone bodies have by far 

the best characteristics for bearing and distributing loads. 

The C-Sandstone is approximately 90 ft (27 m) thick in two 

parts with a 10- to 15-ft (3.0- to 4.6-m) mudstone-rich zone 

near the center of the unit. 

91 
 

STRATA STRENGTH AND STABILITY 

Figure 4 shows a portion of a lithology and structure 

log for a corehole drilled from the Upper D Seam toward 

the B Seams near the event site. Uniaxial compressive 

strength (in psi) derived from point load tests is also shown 

in the figure.

 Figure 4.—Lithology and strength log for an interseam corehole close to the event site. 

(Depth is given in feet. Uniaxial compressive strength (UCS) is given in psi.) 

 The data indicate the presence of both weak 

but mostly strong rocks near the seam, as well as thick 

sandstone above the Upper B Seam. Using regression 

analyses of strength and elastic modulus, the majority of 

rocks are both strong and stiff. These stiff units have the 

capacity to absorb high stress and release the energy upon 

failure in the form of bounces or seismic events. Mudstone 

cap rock failure is common in the study area and is 

influenced by unfavorable orientation of N 60° E joints 

with respect to the rooms. 

92
 
 

 

 

 

 

 

 

 

 

 

 

There are many stress measurements in the Somerset 

Basin that are generally consistent and thus provide a good 

estimate of far-field horizontal stress. The U.S. Bureau of 

Mines (USBM) originally measured the far-field horizontal 

stress at two locations at the neighboring Orchard Valley 

Mine [Bickel 1993], while the site operator provided 

another measurement more recently in the No. 2 mine in the 

D Seam. 

Regional measurements show excess horizontal stress 

[Maleki et al. 1997, 2007] in the Somerset Coalfield along 

the regional structural trend (N 74° to 80° E). Horizontal 

stress is only gravity-induced along the secondary direction 

(N 10° W). The excess stress is moderate, but increases 

slightly with depth at the study site. The far-field horizontal 

stress is very anisotropic in this basin at mining depths and 

away from drainages. The ratio of maximum to minimum 

secondary principal horizontal stress (P/Q ratio) is approximately 4 to 6. The orientation of maximum principal stress 

is consistent, averaging N 80° E near the study mine. The 

stress field may be different at the study area because of the 

complex structural setting. Maleki et al. [2003, 2006] 

address an appearance of a switch in P and Q under drainages and other geologic conditions. 

The failure occurred on October 2, 2007, accompanied 

by heave of the bottom coal within three rooms (Figure 2A), 

rapid displacement of coal into these rooms, knocking 

down of one stopping, and damage to three other stoppings. 

The failure was accompanied by a seismic event. This event 

registered 2.1 on the seismic system operated on the surface 

by the mining company with support from NIOSH. During 

these initial investigations and modeling, two other events 

registered on the NIOSH system, which resulted in additional floor heave after resumption of mining activities 

(Figure 2B). The study area in B Seam mains remained 

bump-free for the last quarter after mining extended beyond 

the faulted ground. The failure occurred at the vertical 

intersection of the D and B mains, where the overburden 

thickness peaked at 1,700 ft (518 m). 

Because faulting was significant at the study area, we 

briefly reviewed potential impacts and mechanisms. Faulting is known to (1) introduce fluids and thus create difficult 

mining conditions; (2) reduce strata strength; (3) retard load 

transfer across fault planes, causing localized stress concentrations; (4) change the stiffness of the mine loading system, thus contributing to sudden failure; and (5) influence 

periodic cave conditions. 

The impact of faulting in western U.S. coal mines has 

been studied through long-term measurements within panel 

workings and back in the gob [Maleki 1981]. Roof and 

floor stability problems are likely within fault zones 

depending on fault characteristics (displacement, fluids, 

gouge thickness, and composition) and are influenced by 

lower strata strength and higher moisture content. Because 

shear stress cannot transmit easily across many faults, 

localized stress concentration occurs near fault zones, contributing to stability problems during retreat depending on 

the angle of incidence and mining geometry. Based on pressure measurements in the gob, the interaction of faulting 

with sudden, periodic caving has been shown to trigger failure of marginally stable structures in the mine roof or floor 

[Maleki 2006]. 

POTENTIAL FAILURE MECHANISM 

Gradual floor heave historically has not been a safety 

issue at the cooperating mine and at many other deep western 

U.S. operations except where it contributed to asymmetrical 

loading and tilting of cribs [Maleki 1988]. However, recent 

occurrences of sudden floor heave accompanied with seismicity in a few deep mines have fueled this investigation. 

Factors contributing to sudden failure have been studied 

by Maleki et al. [1997] through analyses of violent failure 

from 25 case studies in U.S. mines. Those specifically 

relating to floor heave events are expanded here, including 

(1) the presence of thick seams and stiff stratigraphic units 

within the roof and floor; (2) the presence of geological 

discontinuities, reducing the in situ strength of the bottom 

coal with marginal stability; (3) mining approaching areas of 

higher than normal stress gradient associated with previous 

mining or structural anomalies or surface topographic highs; 

and (4) an additional source of energy triggering sudden 

failure, such as periodic caving or slip along geological discontinuities or reaching topographic highs. 

Preliminary examination of seismic data for the actual 

event in the cooperative mine [Swanson 2008] and underground observations excluded significant fault slip at the 

mining horizon as the triggering mechanism. Although the 

final release of the energy was sudden, we suspect timedependent growth of failure around the excavation during 

the idle time leading to the release of the energy. Such a 

process is likely to be associated with microseismic emissions (rock noise) and thus provides a means of studying 

abnormal areas having the potential to deform suddenly. 

The regional seismic monitoring system operated by 

NIOSH on the surface became a valuable tool for studying 

changes in microseismic activities, confirming a history of 

low-level seismicity at this relatively isolated area at the 

study site. 

Assuming elastic strata conditions, vertical load transfer 

from the D Seam longwalls are expected to be minimal at a 

distance of 1,000 ft (305 m) from the edge of the D Seam 

gob. This distance corresponds to the horizontal distance 

between the nearest gob and the event location. The influence of any abnormal vertical stress gradient was evaluated 

at the site using numerical modeling techniques. Other 

mechanisms relating to diminished ability of the mine loading system [Salamon 1970] to transfer loads in a faulted 

zone was not considered to be significant at the event site. 

93
 
 

 

 

 

Two classic floor heave mechanisms are proposed: 

(1) buckling failure [Aggson 1978] and (2) shear failure. 

For the buckling mechanism, Euler’s equation shows that 

the compressive failure of the floor beam is controlled by 

horizontal stress, beam thickness, and span. This process 

could be facilitated near the event location by anisotropic 

strength of strata, higher suspected horizontal stress 

gradients and reorientation (northwest) near the faults, and 

laminated nature of the coal in the floor and entry spans. 

Numerical modeling is used to study the failure mechanisms and examine the significance of these factors. 

STRESS ANALYSES 

Additional insight is gained by conducting stress 

analyses to identify significant factors contributing to the 

event at the study site. 

The scope of the modeling was as follows: 

1.	 Preliminary evaluation of the sensitivity of strata 

deformation to several parameters, including a 

horizontal stress field and material properties along 

a north-south oriented section (section A) using 

a two-dimensional multilayer FLAC model 

(FLAC2D) (Figure 2A). The intent was to reduce 

the number of potential causal factors in preparation 

for more detailed analyses. 

2.	 Detailed sensitivity analyses and evaluation of 

floor heave failure mechanisms with the threedimensional FLAC analyses (FLAC3D) (Figure 2A). 

Modeling included three different constitutive 

material models and simulation of distinct faulting. 

FLAC2D SENSITIVITY ANALYSES 

The main objective of these preliminary analyses was to 

evaluate the sensitivity of strata deformation to several 

parameters, including an abnormal horizontal stress field, 

higher vertical stress at main crossings, and weak material 

properties as influenced by geologic structure. The modeling 

is completed along an approximately north-south oriented 

section (Figure 2A) using the two-dimensional multilayer 

FLAC code (FLAC2D). These are inelastic analyses that 

considered yielding and redistribution of stress during the 

mining process using the Mohr-Coulomb criteria. 

The modeling scope included preliminary evaluation 

and ranking of causal factors that were suspected to have 

played a role at the event site: 

•	 Higher vertical stress gradient with a worst-case 

assumed scenario of 40% increase. 

•	 Twice higher horizontal stress gradient. 

•	 Twice lower horizontal stress gradient. 

•	 Weaker floor rocks as influenced by faulting and 

simulated by reducing the cohesion of floor. 

•	 Bedding planes with low shear strength properties 

at the Lower B Seam contact and 12 ft (3.7 m) 

below as simulated using the interface model 

embedded in FLAC. 

The far-field horizontal stress has been measured 

underground with the maximum stress oriented near eastwest. Both the orientation and direction of the horizontal 

stress could change at the fault zone. The impact of both the 

higher and lower northwest component of stress is evaluated in these simulations. 

Results mostly excluded from this paper showed the 

calculated floor heave to be sensitive to significant reduction in bottom coal cohesion near the fault, the presence of 

weak bedding planes at the Lower B Seam contact with 

floor rocks, and simulated high horizontal stress. On the 

contrary, the model does not predict the heave to be sensitive to significant changes in vertical stress gradient or 

weak interfaces deeper into the floor (modeled 12 ft (3.7 m) 

below the floor). For the worst combination of these factors, the calculated floor heave approaches reported values 

at the first event location (1 ft (0.3 m)). Since many of these 

significant factors could be associated with northwestoriented faulting, it is this local additional faulting that 

seems to have strongly influenced the floor heave events. 

Typical safety factor is reported under “strength/stress 

ratio” in Figure 5 for an analysis with twice higher horizontal stress gradient. The marginal stability of the mine 

floor and very stable pillar core are noted for the assumed 

conditions. 

FLAC3D ANALYSES 

FLAC3D (F3D) modeling advances FLAC2D (F2D) 

results by including the anisotropic nature of horizontal 

stress, different material models, as well as threedimensional excavation geometries. The location of the 

analyzed region is shown in Figure 2A, where model 

boundaries are lines of symmetry. As with the F2D 

analyses, we evaluated the impact of higher than normal 

stress gradient. In addition, the anisotropic strength along 

either the face cleat or butt cleat were analyzed together 

with distinct and equivalent modeling of faults. The butt 

cleat was intensified along the northwest-oriented fault 

planes. An observation of significance to F3D modeling 

was the higher pattern of heaving along the rooms and 

crosscuts, but notably absent at the intersections. 

In these analyses, we examined both normal (measured) 

horizontal stress, with the maximum stress oriented parallel 

to the rooms, and high stress gradient. The latter assumes an 

abnormally high horizontal stress field influenced by D-5 

and northwest-oriented faults and simulated by applying up 

to 2.5 times higher horizontal stress parallel to the crosscuts 

(SYY). In addition, we implemented three different constitutive models for the coal, including Mohr-Coulomb 

plasticity, Mohr-Coulomb strain softening, and ubiquitous 

joints. 

94
 
JOB TITLE : Option 2, High Stress Gradient (*10^ 2)

 FLAC (Version 5.00) 

 2.200 

LEGEND

 23-Oct-07 6:56

 step 45978 1.800

 -1.000E+ 01 < x< 2.200E+ 02

 1.000E+ 01 < y< 2.400E+ 02 

strength/stress ratio

 1.00E+ 00 

 1.50E+ 00 1.400

 2.00E+ 00 

 2.50E+ 00 

 3.00E+ 00 

 3.50E+ 00 

 4.00E+ 00 1.000

 4.50E+ 00 

 5.00E+ 00 

 5.50E+ 00 

Contour interval= 5.00E-01

 0.600

 0.200

Maleki Technologies, Inc. 

Spokane, WA (509) 448-7911 0.200 0.600 1.000 1.400 1.800 

(*10^ 2) 

Figure 5.—Typical safety factor plot for high horizontal stress gradient. Note marginal stability of the bottom coal. 

The significance of anisotropic strength properties of 

the coal seam along the face cleat and the butt cleat 

(paralleling the northwest fault trend) was also evaluated. 

At the event site, the geologic staff has mapped weaker, 

slickensided butt cleats at fault planes. In addition, the face 

cleat is known to influence rib movements in the mine due 

to its persistence and small deviation from the orientation of 

rooms (30°). Using the bilinear strain-softening ubiquitousjoint plasticity model embedded in FLAC, we compared the 

model response to observed weakness planes along the face 

or butt cleat. 

Figure 6 compares calculated floor heave for three 

constitutive models supporting gradual strain softening near 

the excavation.

 Figure 6.—Comparison of floor heave for different material 

models. 

 Note higher calculated heave at the 

intersections for the Mohr-Coulomb model, which is 

replaced by significantly higher heave along the rooms and 

crosscuts as the strain-softening model is used for the coal 

and ubiquitous-joint model for the face cleat. By including 

the weaker nature of the coal along the face cleat and using 

the strain-softening ubiquitous-joint model, we come to 

close agreement between observed and measured floor 

heave patterns. This concurs with another comprehensive 

case study including detailed measurements of stress, 

deformation, and floor-bearing capacity [Maleki 1993; 

Maleki and Hollberg 1995]. 

95
Figure 7 compares calculated floor heave for four 

analyses designed to simulate approximate faulting using 

both distinct and equivalent strain-softening zones.

Figure 7.—Calculated floor heave for different methods of simulating faulting in the study area. 

 Using 

an interface to simulate the north-south oriented fault plane, 

the model closely predicted the pattern of floor heave in the 

study site. However, the magnitudes were lower because of 

high-strength values used to overcome model convergence 

issues. Alternatively, by simulating two north-south 

oriented equivalent fault zones using the strain-softening 

model, the model came to replicate significant heave along 

the rooms near the fault crossings. The higher assumed 

north-south horizontal stress makes some improvement in 

predicting floor heave patterns, but the model is rather 

insensitive to simulated changes in the horizontal stress 

(Figure 8). This supports strain softening near the excavation and along the fault planes as the primary factor influencing a large amount of observed heave (Figure 9). 

The model has helped greatly in understanding floor 

heave mechanisms and the significance of faulting. With 

planned additional geotechnical measurements, we intend 

to investigate the source of sudden heaving at the study site. 

With no nearby longwall extraction and evidence of slip, 

noticeable slip along the fault at the mining horizon is 

excluded. Because model response is not very sensitive to 

simulated higher than normal horizontal stress gradients, we 

do not consider high horizontal stress and buckling failure 

to be likely at the site. Although there is no single triggering 

mechanism for the sudden failure, we can point to the 

coincidence of several unfavorable factors, including faulting, stiff stratigraphic units, and altered stress gradients at 

the multiple-seam crossing and topographic highs. 

96
 
Heave (ft)

3.5 sxx=0.5 sigHmax, 

syy=1.5 sigHmax

3 sxx=0.5 sigHmax, 

syy=2.5 sigHmax

sxx=syy=sigHmax

2.5 

2 

1.5 

1 

0.5 

0 

Intersection Room Crosscut 

Figure 8.—Calculated floor heave for different horizontal stress gradients. 

FLAC3D 2.10 ob Title: Floor Heave Analysis, 18' entry, Coal Seam Softening + UJ face cleat 

Step 7527 Model Perspective 

07:04:47 Tue Nov 04 2008 

Center: Rotation:

 X: 7.980e+000 X: 40.000

 Y: 2.457e+001 Y: 0.000

 Z: 1.917e+002 Z: 18.000 

Dist: 2.080e+003 Mag.: 2.92 

Ang.: 22.500 

Contour of Z-Displacement

 Magfac = 1.000e+000 

-5.2720e-001 to -2.5000e-001

 0.0000e+000 to 2.5000e-001

 5.0000e-001 to 7.5000e-001

 1.0000e+000 to 1.2500e+000

 1.5000e+000 to 1.7500e+000

 2.0000e+000 to 2.2500e+000

 2.5000e+000 to 2.7500e+000

 3.0000e+000 to 3.2500e+000

 3.2500e+000 to 3.4699e+000

 Interval = 2.5e-001 

Axes

 Linestyle 

Maleki Technologies, Inc. Y Z

Mining & Geotechnical Engineers
 X 

Figure 9.—Vertical displacement contours for equivalent simulated faulting. (UJ = ubiquitous joint.) 

97
 
 

 

 

 

 

 

 

 

 

 

 

 

COLLECTIVE EVIDENCE FROM OTHER MINES 

We also inspected and studied factors contributing to 

sudden floor heave at two other western U.S. mines at fault 

crossings. Despite many similarities between geologic setting and rock mass conditions, the sudden floor heave 

occurred during longwall retreat at those sites where 

significant changes in stress concentration results about the 

gob cavity. In addition, nonuniform caving and periodic 

collapse of overburden rocks have been measured at one of 

these sites through direct-pressure measurements in the 

gob [Maleki 1981, 2008]. Such events have adequate 

energy to trigger sudden floor heave in marginally stable 

bottom coal in faulted ground with low-strength properties. 

Because the event happened as the longwall face 

approached a distance equal to face width, we suspect that 

the caving provided the additional energy at the mine 

based on past measurements and regional experiences 

[Maleki 1981]. 

CONCLUSIONS 

Common factors identified at all sites include (1) the 

presence of stiff units and thick seams mined at depths 

exceeding 1,000 ft (305 m); (2) the presence of geological 

discontinuities, reducing the in situ strength of the coal 

with a calculated factor of safety near 1 for the mine floor; 

(3) mining approaching areas of higher than normal stress 

gradient associated with previous mining or structural 

anomalies or surface topographic highs; and (4) an additional source of energy triggering sudden failure, such as 

periodic caving or slip along geological discontinuities. 

Preliminary examination of seismic data for the actual 

event in the cooperative mine and underground observations excluded fault slip at the mining horizon as a major 

triggering mechanism, but highlighted the significance of 

weak, anisotropic strata conditions near the intersection of 

two faults. Numerical investigations at the study site point 

to shear failure of bottom coal during time-dependent 

strain softening. The model response is not very sensitive 

to elevated horizontal stress. Although there is no single 

triggering mechanism for the sudden failure at the study 

site, we can point to the coincidence of several unfavorable 

factors, including faulting, stiff stratigraphic units, and 

altered stress gradients at the multiple-seam crossing and 

topographic highs. 

It should be emphasized that faulting is often not 

associated with abnormal far-field stress conditions based 

on measurements by the USBM and decades of mining 

experience. However, there are some complex structural 

settings and stress conditions that are known to be associated with higher than normal stress gradients. The identification and projection of those conditions ahead of mining, 

together with monitoring of roof-floor convergence, play a 

key role in predicting zones with higher potential for 

sudden floor heave. 

Practical research should continue toward improving 

the understanding of sudden failure through site-specific 

measurements and numerical modeling of other events at 

cooperating mines. 

REFERENCES 

Aggson JR [1978]. In-situ stress fields and associated 

mine roof stability. Mini-Symposium Series No. 78–1, 

SME-AIME Annual Meeting, Dallas, TX, 7 pp. 

Bickel D [1993]. Rock stress determinations from 

overcoring: an overview. Denver, CO: U.S. Department of 

the Interior, Bureau of Mines, Bull. 694. 

Carroll CJ [2003]. Fractures in the Mesaverde Group 

at Somerset Coal Field, Delta and Gunnison Counties, 

Colorado. Denver, CO: Colorado Geological Survey. 

Maleki H [1981]. Coal mine ground control [Dissertation]. Golden, CO: Colorado School of Mines, Vol. 1. 

Maleki H [1988]. Ground response to longwall mining: 

a case study of two-entry yield pillar evolution in weak 

rock. Colo Sch Mines Q 83(3). 

Maleki H [1993]. Case study of the inelastic behavior 

of strata around mining excavations. In: Haimson B, ed. 

Proceedings of the 34th U.S. Symposium on Rock 

Mechanics (Madison, WI, June 27–30, 1993), vol. 1, 

pp. 137–140. 

Maleki H [2006]. Caving, load transfer, seismicity in 

four Utah mines. In: Peng SS, Mark C, Finfinger GL, 

Tadolini SC, Khair AW, Heasley KA, Luo Y, eds. Proceedings of the 25th International Conference on Ground 

Control in Mining. Morgantown, WV: West Virginia University, pp. 79–86. 

Maleki H [2008]. In situ pillar strength and overburden 

stability in U.S. mines. In: Peng SS, Tadolini SC, Mark C, 

Finfinger GL, Heasley KA, Khair AW, Luo Y, eds. 

Proceedings of the 27th International Conference on 

Ground Control in Mining. Morgantown, WV: West Virginia University. 

Maleki H, Hollberg K [1995]. Structural stability 

assessment through measurements. In: Proceedings of the 

ISRM Workshop on Rock Foundations (Tokyo, Japan). 

Maleki H Clanton J, Koontz W, Papp A [1997]. The 

relationship between far-field horizontal stress and geologic structure. Rock Support, Oslo, Norway. 

Maleki H, Dolinar DR, Dubbert J [2003]. Rock 

mechanics study of lateral destressing for the advance-andrelieve mining method. In: Peng SS, Mark C, Khair AW, 

Heasley KA, eds. Proceedings of the 22nd International 

Conference on Ground Control in Mining. Morgantown, 

WV: West Virginia University, pp. 105–113. 

Maleki H, Stewart C, Hunt G [2006]. Subsidence 

characteristics for Bowie Mines, Colorado. In: Proceedings 

of the 41st U.S. Rock Mechanics Symposium. Alexandria, 

VA: American Rock Mechanics Association. 

Maleki H, Stewart C, Stone R [2007]. Three-seam 

stress analyses at Bowie Mines, Colorado. In: Peng SS, 

98
 
 

Mark C, Finfinger GL, Tadolini SC, Khair AW, Heasley 

KA, Luo Y, eds. Proceedings of the 26th International 

Conference on Ground Control in Mining. Morgantown, 

WV: West Virginia University, pp. 29–37. 

Robeck E [2005]. The effects of fault-induced anisotropy on fracturing, folding, and sill emplacement [Thesis]. 

Provo, UT: Brigham Young University. 

Salamon M [1970]. Stability, instability and design of 

pillar workings. Int J Rock Mech Min Sci 7:613–631. 

Swanson P [2008]. Monitoring mine seismicity with an 

automated wireless digital strong-motion network. In: 

Peng SS, Tadolini SC, Mark C, Finfinger GL, Heasley 

KA, Khair AW, Luo Y, eds. Proceedings of the 27th 

International Conference on Ground Control in Mining. 

Morgantown, WV: West Virginia University, pp. 79–86. 

99
 

 

ADVANCED NUMERICAL SOLUTIONS FOR STRATA CONTROL IN MINING 

By Axel Studeny1

1

IMC-Montan Consulting GmbH, Essen, Germany. 

 and Carsten Scior2
 

2

DMT GmbH & Co. KG, Mining Service, Essen, Germany. 

ABSTRACT 

Geomechanical-numerical methods are an established 

tool for planning of underground excavations worldwide. 

By describing the interaction between heterogeneous 

layered strata and support elements, it is possible to determine the suitability of alternative support systems. 

The German hard-coal mining industry has more than 

20 years of experience in investigating and using geotechnical parameters to conduct numerical calculations. 

Today, nearly all excavations (shafts, pit bottoms, bunkers, 

coal faces, development drivages, gate roads, etc.) are 

evaluated by geomechanical-numerical tools in combination with empirical planning methods. 

A high accuracy of planning results, which is especially 

required in the German coal industry with its deep-level 

longwalls, bedded and weak surrounding strata, and 

multiple-seam mining layouts, depends on the extensive 

calibration of the numerical models, which was achieved by: 

1.	 Taking a large number of underground measurements with empirical evaluation 

2.	 Carrying out physical modeling 

3.	 Using the characteristic features of the installed 

support elements 

This paper describes the planning approach for 

numerical models in mining and presents the advantages of 

these planning tools. 

INTRODUCTION 

Numerical methods are widely used for solving a wide 

variety of technical problems. They are mainly used in 

applications where analytical and empirical processes 

cannot provide the required degree of accuracy because of 

complex boundary conditions [Junker 2006]. 

The mining industry uses geomechanical-numerical 

models extensively as operational planning tools. Analytical and empirical methods have thus far proved to lack the 

degree of precision required for describing the interaction 

that occurs between heterogeneous strata and various types 

of support elements (rock bolts, standing supports, yielding 

arches, and backfilling) in highly deformed systems. 

Compared with conventional calculation methods, numerical modeling can, for example, provide a detailed analysis 

of the fracture and deformation status of the rock strata 

surrounding a mining excavation. This produces a picture 

of the extent of the strata fracture zone and helps to determine the support measures required. To understand the 

complex mechanical phenomena within the rock mass with 

all its inhomogeneity and separation planes, it is necessary 

to develop and implement various constructive models in 

the form of mechanical equations, which can reproduce the 

stress-deformation behavior of the rock mass with sufficient accuracy. 

DMT has used several numerical programs for solving 

different geomechanical questions for many years. For 

large-scale stress redistributions, the program GEDRU 

developed by DMT is used. For most planning cases, the 

program FLAC (two- and three-dimensional) is applied. In 

special cases, other programs like PFC, UDEC, or Ansys 

are used. The main focal point here is the application of 

the program FLAC to solve several geotechnical questions. 

The German coal industry uses numerical models for a 

wide range of planning assignments, including: 

• Warranty of long-term stability for underground 

openings like shafts, pit bottoms, or main roadways 

•	 Investigation of the deformation behavior of temporary underground openings such as longwalls 

or gate roads 

• Support dimensioning 

• Investigation of mining impact (surface subsidence, damage) 

The numerical modeling process essentially operates 

by reproducing all fundamental support elements (rock 

bolts, standing supports, roadside packs, injection material, 

etc.), along with a wide range of boundary conditions that 

apply to the working of coal seams in geological deposits 

(geology, depth, single- and multiple-seam mining, etc.). 

This paper uses different examples to present the range of 

application of numerical modeling techniques. 

PREPARATION OF NUMERICAL MODELS 

The preparation of geomechanical-numerical models 

for control of underground openings requires a multitude 

of information as initial parameters. This includes: 

• Strata 

◦ Geology 

◦ Geotechnics 

• Type and shape of the underground opening 

◦ Two-dimensional simulation (e.g., roadways) 

◦ Three-dimensional simulation (e.g., junctions) 

101
 
• Rock stress 

◦ Primary rock stress 

◦ Secondary rock stress 

• Rock support 

◦ Support elements 

◦ Support pattern 

◦ Support behavior 

To create models that are as realistic as possible, initial 

information with a high accuracy and model calibration are 

required. To obtain this information, many investigations 

need to be conducted (Figure 1): 

•	 Geologic and geotechnical core logs 

• Rock mechanical lab tests 

• Stress measurements and calculations 

• Underground support tests 

• Laboratory support tests for the support material 

as well as for the installed support elements 

(resined bolts including the rock mass) 

Figure 1.—Information required for calibrating a numerical model. 

The challenge is the modification of the lab parameters 

for use in the continuum-mechanical program FLAC. Due 

to the limitation of implementing every geotechnical element (e.g., joint) in a model, a reduction of these test 

results (e.g., rock strength) is required. Therefore, different 

empirical approaches and experiences are used. An additional point is a mostly limited amount or poor quality of 

initial parameters. For these reasons, calibration of the 

model is required. DMT uses two different methods for 

model calibration [Hucke et al. 2006]: 

•	 Physical modeling of underground roadways 

(1:15 scale) 

• Underground measurements and observation 

The advantage of this extensive calibration process is 

that one gains a comprehensive picture of the complex 

deformation and fracture structure around the underground 

opening. The physical modeling technique especially permits a detailed view into the rock around an opening. 

Thus, it is possible to detect fractures in the rock as well as 

support failure (e.g., bolt failure). 

Based on these considerable initial parameters and 

calibration capabilities, DMT has successfully developed 

numerical modeling as a reliable planning tool that can be 

used worldwide. The following examples describe the 

application of numerical models for different planning 

cases. 

102 
APPLICATIONS 

This section will focus on the various ways in which 

underground openings are used and how this affects the 

numerical modeling process. This will be done using 

examples taken from different mining operations: 

1.	 Gate road at average depth in brittle ground at a 

Ukrainian coal mine 

2.	 Dimensioning of stable pillars to prevent spontaneous combustion in an Italian lignite mine 

3.	 Investigation of rock burst risk for multiple-seam 

extraction in a Czech coal mine 

4.	 Dimensioning of roof bolt support for roadways 

and junctions in a German gypsum mine 

5.	 Dimensional design of shaft and pit bottom 

support systems at a depth of 1,200 m in a German coal mine 

6.	 Investigation of surface subsidence as a result of 

extraction in German coal mines 

7.	 Room-and-pillar design in very weak ground at a 

Russian iron ore mine 

8.	 Planning of shape and driving sequence of a rise 

heading in a German coal mine 

1. Ukrainian Coal Mine: Planning of Gate Roads 

Investigation Focal Point 

The investigation focused on the search for alternative 

roadway support designs combined with roadway shape 

variations with the key objective of substantially reducing 

the considerably high roadway deformations. A special 

feature of this case was the lower strength of the surrounding rock mass compared with the coal, which is the 

main reason for the high roadway deformation under these 

conditions. 

Results 

The numerical setup for the basic model depends on a 

visual evaluation of the in situ strata behavior. Figure 2 

compares the numerical model with the actual deformation 

taking place in the roadway. 

Figure 2.—Roadway deformation structures. The yellow line in the left image indicates the initial cross-section. 

To improve the stability of the roadway and reduce its 

deformations, several variations were investigated based 

on this calibrated model. Two results are presented in 

Figure 3. The left image shows a roadway with backfill 

and yielding arch support, which could improve the roadway stability considerably. The right image shows a rockbolted rectangular roadway, resulting in poor stability and 

high roadway deformation. 

103 
 

 

 Figure 3.—Fracture zones for different investigation cases. 

Outcome: A suggestion for improved roadway support 

was provided based on a “visual model calibration,” taking 

into consideration the specific boundary conditions 

[Studeny and Wittenberg 2007]. 

2. Italian Lignite Mine: Pillar Design 

Investigation Focal Point 

The main objective was the dimensioning of stable 

pillars without fracturing to reduce the risk of spontaneous 

combustion of a high compact layer on the surface. A 

special concern was the improved calculation of pillar 

width with a stable, nonfractured core inside compared 

with simple empirical approaches (pillar width = 10% of 

depth) to optimize the utilization of the deposit. 

Results 

Based on underground observations, a calibrated 

model for one roadway was created first. In the second 

step, the model was extended to reproduce the planned 

situation including extraction and the second roadway. 

Therefore, several pillar widths were investigated. Figure 4 

shows two cases: fractured pillar (left) and stable core in 

the pillar (right). 

Figure 4.—Shear zones around two roadways for different pillar widths. 

The numerical results were compared with those of the 

Analysis of Longwall Pillar Stability (ALPS) program 

(Figure 5). The result shows very good agreement between 

these two calculation tools. 

Outcome: A new approach for designing pillar width 

was developed with a reduction from 10% to 7.5% of the 

mining depth, resulting in higher utilization of the deposit. 

104 
 Figure 5.—Pillar width analysis: comparison between 

numerical model and ALPS calculation. 

 3. Czech Coal Mine: Rock Burst Prevention 

Investigation Focal Point 

The objective of the investigation was to analyze the 

stress situation in a mining seam in different areas to detect 

a potential rock burst risk in the seam, including the 

influence of multiple-seam extraction. Based on largescale stress calculations with GEDRU for the complete 

mining area, small-scale FLAC models need to be determined. These models include mining in different seams as 

well as large-scale stress distribution as initial conditions 

for modeling. 

Results 

The current situation is shown in Figure 6 with a new 

panel next to the excavated area. During the mining process, rock bursts occur. 

The red lines in Figure 6 depict a residual pillar overlying extracted areas.

Figure 6.—Ground view of investigation area with marked model cross-sections (green lines). 

 Based on this, large-scale stress 

analyses were conducted for the whole mining area to 

show potential rock burst risk areas. In Figure 7, two 

sections are presented: next to the extracted area near the 

tailgate (left) and near the main gate (right). The high 

stresses around the extraction near the tailgate were an 

indicator of a rock burst risk. The stresses near the main 

gate are considerably lower. 

Outcome: A map of potential rock burst risk areas 

was compiled, and measures for rock burst prevention 

were developed by rock burst experts based on these findings [Breitenstein et al. 2007; Baltz and Hucke 2008]. 

4. German Gypsum Mine: Support Design 

Investigation Focal Point 

The investigation focused on improving the roof 

stability of roadways and junctions extracted in layered 

strata to avoid cleavage of the roof as a result of thin 

clayey layers. The calculations were done with twodimensional models for roadways and three-dimensional 

models for junctions. 

105 
Figure 7.—Vertical stress during excavation for two investigation areas. 

Results 

The stability problems were the result of thin clayey 

layers in the roof that were very sensitive to moisture. Due 

to loosening at infiltration, the stability of the roof is 

dependent on the moisture of the clay. In particular, the 

junctions are endangered because of the large span. 

Therefore, several three-dimensional calculations with 

different layer strengths were conducted, which resulted in 

a support pattern with Swellex bolts to avoid cleavage of 

the roof (Figure 8). 

Figure 8.—Suggested support pattern for a junction. 

Outcome: By combining the modeling results with 

empirical approaches, the support system could be optimized significantly for the roadways and junctions. 

106 
 

 

 

 

5. German Coal Mine: Pit Bottom 

and Shaft Support Design 

Investigation Focal Point 

The main question was the stability of an installed 

rigid support of a pit bottom, with a cross-section of 

approximately 200 m2

 and a length of 15 m, due to 

changing stress conditions caused by drivage of a roadway 

toward the pit bottom. The challenge was to create a threedimensional numerical model with a demanding geometry, 

layered strata, different stages of excavation, support 

installation, and fault implementation. 

Results 

To solve this task, a complex three-dimensional model 

was required. The geologic-geomechanical conditions and 

the design variations for the connection between the existing roadway system and the already built pit bottom placed 

a high demand on the model. Figure 9 shows a section of 

the model with the layered strata, the shaft, the built pit 

bottom, and first steps of roadway drivage. The roadway 

drivage was planned in two steps—the upper contour, then 

the floor. 

 Figure 9.—Section of the numerical model with drivage 

sequence. 

By means of modeling, a roadway support concept was 

developed for the convergence and breakthrough to the 

existing, rigidly supported pit bottom. Therefore, stress 

analyses were conducted to investigate the pit bottom 

support load for several variations of roadway support. 

Results showed that installing high-powered supports, 

10 m in front of the breakthrough to the pit bottom, would 

protect the existing rigid pit bottom support considerably. 

Outcome: Numerical modeling was used successfully 

to develop a construction concept for such a complex 

underground building. 

6. German Coal Mines: Surface Subsidence 

Investigation Focal Point 

This project investigated the influence of different 

parameters such as extraction, advance rate, seam thickness, strata conditions, panel dimension, and multipleseam mining on surface subsidence and subsidence rate. 

A major point, compared to generally used stochastic 

models for subsidence prediction, was the consideration of 

geologic-geomechanical parameters, as well as mining 

activities. 

Results 

To calibrate the numerical models, subsidence measurements at the surface of several German coal mines 

were used. Therefore, different situations such as singleand multiple-seam extraction, as well as single and multiple panels in one seam, were examined. 

Figure 10 compares numerical calculations and 

measurements for an actual case.

 Figure 10.—Measured and calculated subsidence on the 

surface. 

107 

 In a virgin mining area, 

one panel was extracted, then two more panels next to the 

first were mined simultaneously. Both the lower subsidence after mining the first panel (red line) and the higher 

subsidence after three extracted panels (blue line) could be 

reproduced with the same numerical model without changing any parameters, which is nearly impossible with 

common stochastic subsidence calculation. 
 

 

 

Outcome: A geomechanic-numerical model was 

created that can reproduce the surface subsidence for various mining situations, taking into account the geologicgeomechanical boundary conditions of the strata [Kook 

et al. 2008]. 

7. Russian Iron Ore Mine: Room-and-Pillar Design 

Investigation Focal Point 

The main objective was the planning of a room-andpillar test mining layout in a weak rock mass, including 

room, pillar, and support design, to define the boundary 

conditions for complete extraction of an ore body. A 

special feature was the reproduction of the existing roadways with small deformations in a rock mass, which is 

characterized by behavior and strength similar to a soil, 

at a depth of approximately 600 m. 

Results 

The model calibration was based on underground 

observations in existing roadways in the mine. The iron 

ore rock mass was characterized by a very low strength 

and a high water sensitivity. To reproduce the observed 

roadway deformations, a strength of 1 MPa was used for 

the modeling. With this calibrated model (Figure 11, left), 

a multitude of variants were investigated to design the 

room (with or without support) and the pillar for a test 

mining area. A highly effective mining concept with large 

rooms was not possible because of stability problems with 

the room (Figure 11, center). Therefore, a concept with 

rock-bolted roadways and a pillar width twice the room 

width was recommended (Figure 11, right). 

Figure 11.—Roadway and room deformation for different investigation cases. 

Outcome: A mining concept for a test mining layout 

in highly stressed, weak rock mass was provided to and 

implemented by the mining company. 

8. German Coal Mine: Rise Heading Design 

Investigation Focal Point 

The focus of this investigation was the planning of the 

shape and driving sequence of a rise heading at great depth 

in a highly disturbed rock mass for a RAG mine in 

cooperation with RAG experts. A special feature was the 

implementation of different combined support systems 

(rock bolts, yielding arches, standing support, shield support) and partially combined roadway shapes (arch shape 

with rectangular extension roadway for shield support) in 

one model. 

Results 

Based on experience and empirical approaches, a 

model calibration for the basic roadways (purely archshaped and rectangular roadway) was conducted. These 

calibrated models were used in the investigation of 

different variants of rise heading drivage in RAG coal 

mines. 

Results are shown in Figure 12. The left image shows 

an arch-shaped roadway with a rectangular extension in 

the mining direction. The middle and right images show a 

rectangular roadway also with an extension in the mining 

direction (to the left) with different support systems. The 

middle image has only standing support, while the right 

image has bolts and powered support. It was found that 

only a powerful support with shields and roof bolts could 

reduce the roof fractures and roadway deformation considerably. In the other cases, visible fractures in the roof 

could result in stability problems during mining operation. 

108 
 

 

 

 

 

Figure 12.—Fracture zones around the rise heading for different investigation cases. 

Outcome: Based on experience, plausible models 

were created to support the client (RAG) in choosing a rise 

heading design. 

CONCLUSIONS 

Based on extensive experience over many years in 

underground mining and physical modeling, DMT has 

accumulated a comprehensive understanding of geomechanical processes, especially with regard to the 

interaction of rock stress, rock mass structure, and support 

technology. This knowledge was implemented in 

geomechanical-numerical models and, due to continuous 

calibration and optimization, a high standard of modeling 

is assured. 

As proven by various projects, this advanced modeling 

technique is suitable for solving a wide variety of geotechnical problems in underground openings in different 

kinds of deposits. This confirms that numerical modeling 

is a versatile tool in current mine planning and shows 

increasing importance for safe, economic, and trouble-free 

mining operation in the future. 

REFERENCES 

Baltz R, Hucke A [2008]. Rockburst prevention in the 

German coal industry. In: Peng SS, Tadolini SC, Mark C, 

Finfinger GL, Heasley KA, Khair AW, Luo Y, eds. 

Proceedings of the 27th International Conference on 

Ground Control in Mining. Morgantown, WV: West Virginia University, pp. 46–50. 

Breitenstein K, Huwe HW, Baltz R [2007]. Protective 

seam extraction as a planning measure for the efficient 

mining of rockburst-prone coal seams. In: Proceedings of 

the Fourth International Symposium on High-Performance 

Mine Production (Aachen, Germany, May 30–31, 2007). 

Hucke A, Studeny A, Ruppel U, Witthaus H [2006]. 

Advanced prediction methods for roadway behaviour by 

combining numerical simulation, physical modelling and 

in-situ monitoring. In: Peng SS, Mark C, Finfinger GL, 

Tadolini SC, Khair AW, Heasley KA, Luo Y, eds. Proceedings of the 25th International Conference on Ground 

Control in Mining. Morgantown, WV: West Virginia University, pp. 213–220. 

Junker M [2006]. Gebirgsbeherrschung von Flözstricken (in German). Essen, Germany: Verlag Glückauf 

GmbH. 

Kook J, Scior C, Fischer P, Hegemann M [2008]. Subsidence prediction for multiple seam extraction under consideration of time effects by the use of geomechanical 

numerical models. In: Peng SS, Tadolini SC, Mark C, 

Finfinger GL, Heasley KA, Khair AW, Luo Y, eds. Proceedings of the 27th International Conference on Ground 

Control in Mining. Morgantown, WV: West Virginia University. 

Studeny A, Wittenberg D [2007]. Numerical modeling 

for roadway support systems: a comparison for single and 

multiple seam mining. In: Peng SS, Mark C, Finfinger GL, 

Tadolini SC, Khair AW, Heasley KA, Luo Y, eds. Proceedings of the 26th International Conference on Ground 

Control in Mining. Morgantown, WV: West Virginia University, pp. 42–48. 

109 
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DHHS (NIOSH) Publication No. 2009–141 

June 2009