1. INTRODUCTION 

Reducing ground failure fatalities and injuries is a 

priority of the National Institute of Occupational 

Safety and Health (NIOSH) mine safety and health 

research program. Ground failures have historically 

accounted for up to 50% of the fatalities in 

underground mines, and nonfatal injuries due to 

ground failure are almost always severe. Ground 

failures helped trigger recent mine disasters in 

Alabama (2001) and Utah (2000) by disrupting 

ventilation that led to gas explosions. Together, 

these incidents claimed the lives of 15 coal miners. 

So far in 2006, six coal miners have lost their lives 

in four roof falls, a rib fall and a coal mine bump. 

To reduce fatalities and injuries due to ground 

failure, NIOSH researchers are working toward 

improved understanding of rock mass failure 

mechanics using numerical analysis models. 

Promoting more widespread use of numerical 

models for ground control engineering may lead to 

the desired safety improvements; however, several 

barriers exist toward that end. Considerable 

guidance is needed for collecting necessary input 

data, setting up a model and finally interpreting the 

analysis results. Such guidance should have the 

agreement of all parties involved in practical ground 

control including mining companies, consultants, 

suppliers and regulatory authorities. To enable 

better communication among mining engineers 

working in coal mine ground control, NIOSH 

researchers have made progress toward a set of 

input parameters for use in FLAC [1] that result in 

very realistic models of coal mine rock behavior 

and rock bolts. Finally, the suggested guidance is 

not intended as a substitute for sound engineering 

judgment. 

Obtaining the input parameters requires collection 

of certain information from rock core. The input 

parameters include material properties for a strainsoftening, ubiquitous-joint constitutive model, rock 

bolt properties and model initialization and loading. 

 Use of these input parameters appears to lead 

automatically to (1) realistic modeling of the failure 

mechanics, (2) calculation of displacement and 

stress that are consistent with field measurements 

and (3) a reasonable forecast of the effectiveness of 

rock support alternatives. This paper discusses a 

core logging procedure to obtain numerical model 

input parameters, presents a suite of input 

 

 

Numerical modeling procedures for practical coal mine design 

Zipf, Jr., R. K. 

NIOSH – Pittsburgh Research Laboratory, Pittsburgh, PA, USA 

 

ABSTRACT: A method is presented for creating realistic numerical models for practical coal mine ground control. The method 

includes procedures to collect the necessary mechanical input parameters from a geologic core log, procedures to set up a model

and procedures to interpret calculation results. The input parameters come from a detailed geologic core log and extensive point 

load tests of estimate rock layer strength. A suite of material property input parameters is proposed which allow the user to go 

from core log to numerical model inputs. Rock bolt anchorage properties are also linked to the material properties of each 

geologic layer in the model. Following this procedure leads to very realistic calculations of the rock failure process and rock 

support system behavior. These calculations in turn enable realistic comparison of the effectiveness of alternative rock support 

systems. 
parameters for practical coal mine models and 

demonstrates their use with a practical example. 

2. CORE LOGGING FOR INPUT PARAMETERS 

Obtaining meaningful results from a numerical 

model begins with the collection of adequate 

geologic information. The method described for 

translating a geologic core log into input parameters 

for a numerical model follows a philosophy 

developed by Gale and Tarrant [2] of “letting the 

rocks tell us their behavior.” For numerical 

modeling of coal mines, the logger must record two 

essential details, namely, individual geologic layers 

of homogeneous character and the strength of those 

geologic layers. Figure 1 shows a typical section of 

core with several distinct layers and other essential 

features to record. 

The logging detail necessary depends on the scale 

of the numerical model. Small-scale models of coal 

mine entry behavior may require logging geologic 

layers as small as 50 mm. Larger-scale coal mine 

models for subsidence prediction may require less 

logging detail. Of particular importance to note are 

the soft clay layers or major bedding planes with 

weak infilling as indicated in figure 1. 

Having defined the geologic layering in sufficient 

detail, the logger must next estimate the strength of 

those layers, including the strength of the rock 

material and the strength of bedding plane 

discontinuities. Unconfined compressive strength 

(UCS) tests, triaxial tests or multi-stage, triaxial 

tests on core specimens oriented both perpendicular 

to bedding and at a 30-degree angle to bedding are 

the best way to measure cohesion and friction angle 

for the rock material and bedding plane 

discontinuities. However, conducting extensive 

tests is rarely a feasible option. Index tests are the 

preferred option and have the distinct advantage of 

providing multiple strength estimates for each 

geologic layer. Basic soil and rock descriptions of 

the ISRM [3] can provide a crude estimate of 

strength. Other options include simple hammer 

blow tests [3, 4] or the Schmidt Hammer test for 

stronger materials [5]. The Point Load Index [6] 

appears to be the simplest and most reliable method 

at present to estimate rock material and bedding 

plane strength through an axial or diametral point 

load test, respectively. Based upon thousands of 

tests, reliable correlations between Point Load 

Index and UCS have been developed for a variety 

of coal mine rocks throughout the U.S. [7]. 

Techniques to estimate rock layer strength based on 

downhole geophysical measurements are also well 

developed [8]; however, the methods have never 

been adopted widely by the U.S. coal industry. 

Figure 2 shows estimates of the rock material and 

bedding plane strength for each geologic layer 

based on point load tests. 

Detailed geologic logging for numerical modeling 

purposes has a relation to the CMRR classification 

used to describe coal mine roof rock in practical 

ground control [9]. The CMRR Unit Rating for 

each rock layer is comprised of two parts. The UCS 

rating for the rock material strength ranges from 5 

to 30 for a range of strengths between 0 and 

138 MPa as determined from axial point load tests. 

The discontinuity rating for the bedding plane 

strength ranges from 25 to 60 corresponding to 

strength of about 6 to 52 MPa based on diametral 

point load tests. 

3. MATERIAL PROPERTIES 

For general modeling of rock behavior in coal mine 

ground control, Itasca’s FLAC program [1] contains 

many useful features, in particular, the SU 

constitutive model. SU stands for the strainsoftening, ubiquitous joint model and is ideal for 

simulating laminated coal measure rocks. In 

essence, this constitutive model allows for strainsoftening behavior of the rock matrix and/or failure 

Fig. 1. Photograph of core showing different rock layers and 

a prominent clay layer from 1.4 to 1.5 feet. 

Fig. 2. Typical strength data along rock core from axial and 

diametral point load tests. 

0

5

10

15

20

25

0 20 40 60 80 100 120 140

UCS from axial and diametral PLT

height into roof - m .

Axial PLT Diametral PLT
along a pre-defined weakness plane such as bedding 

planes. Failure through the rock matrix or along a 

bedding plane can occur via shear or tension, and 

the dominant failure mode can change at any time. 

The “state” variable within FLAC tracks the failure 

mode in each model element as either shear or 

tensile failure through the rock matrix or along a 

bedding plane. 

The SU constitutive model requires four major 

input parameters, namely, cohesion, friction angle, 

dilation angle and tensile strength for both the rock 

matrix and the bedding planes. Based on a MohrCoulomb strength model, the UCS of a rock 

depends on cohesion and friction angle as 

 (1) 

where c is the cohesion and φ is the friction angle. 

Careful geologic core logging along with point load 

testing to estimate the UCS of each rock layer 

provides a rational basis to estimate the most 

important input parameters to the SU constitutive 

model. 

Tables 1 and 2 summarize the name, UCS and the 

initial value for input parameters of a proposed suite 

of “numerical rocks” along with a corresponding 

geologic description of the rock. The UCS values 

indicated in tables 1 and 2 are field-scale or modelscale values that are reduced from the laboratoryscale values determined from point load tests during 

geologic logging. Following the lead of Gale and 

Tarrant [2] again, these laboratory values of UCS 

for rock and coal, but not soil, are reduced by a 

factor of 0.56 to produce the field-scale UCS and 

hence the input parameters to the numerical model. 

This scaling factor works well for rock masses 

associated with coal mining; however, it does not 

apply outside this narrow scope. 

The material suite shown in tables 1 and 2 includes 

very weak soils and clay-like materials with a UCS 

of 0.02 MPa and weak, medium and finally strong 

rocks with a UCS of about 150 MPa. Also included 

is coal, which ranges from the most friable with a 

UCS of 2 MPa to a strong coal with a UCS of 

12 MPa. The soil material models are isotropic, 

that is the soil matrix properties are the same as 

those for the horizontal weakness plane. However, 

the rock models exhibit anisotropy since the 

strength along bedding planes is less than the UCS 

of the rock matrix. Following results of point load 

tests by Molinda and Mark [4], weak rocks are the 

most anisotropic with the strength along bedding 

planes about 50% of the rock matrix UCS, while 

stronger rocks have less anisotropy with the 

strength along bedding planes being about 90% of 

φ

φ

1 sin

2 cos

− = c UCS

Table 1. Initial values for rock material input parameters

Material 

Name Description Lab UCS (MPa) 

Field UCS 

(MPa) 

Young’s 

Modulus 

(GPa) 

Cohesion 

(MPa) 

Friction 

Angle 

(deg) 

Dilation 

Angle 

(deg) 

Tensile 

Strength 

(MPa) 

Soil 1 paste 0.04 0.02 1 0.007 21 10 0.002 

Soil 2 very soft soil 0.07 0.04 1 0.014 21 10 0.004 

Soil 3 soft soil 0.14 0.08 1 0.028 21 10 0.008 

Soil 4 firm soil 0.29 0.16 1.5 0.055 21 10 0.016 

Soil 5 stiff soil 0.63 0.35 2 0.120 21 10 0.035 

Soil 6 very stiff soil 3.6 2.0 2.5 0.69 21 10 0.20 

Rock 1 claystone, fireclay 6.4 3.6 3 1.2 22 10 0.3 

Rock 2 black shale 11 6 4 2.0 23 10 0.6 

Rock 3 black shale, gray shale 18 10 5 3.3 24 10 1.0 

Rock 4 gray shale 25 14 6 4.5 25 10 1.4 

Rock 5 siltstone, gray shale 34 19 7 6 26 10 1.9 

Rock 6 siltstone 48 27 8 8 28 10 2.7 

Rock 7 Siltstone, sandstone 63 35 10 10 30 10 3.5 

Rock 8 sandstone, limestone 77 43 12 12 32 10 4.2 

Rock 9 sandstone 95 53 15 14 34 10 5.2 

Rock 10 limestone 139 78 20 20 36 10 7.7 

Coal 1 banded, bright coal 3.6 2.0 2.5 0.6 29 10 0.17 

Coal 2 banded coal 6.3 3.5 2.5 1.0 30 10 0.29 

Coal 3 banded, dull coal 12 6.7 2.5 1.9 31 10 0.60 

Coal 4 dull coal 17 9.7 2.5 2.7 32 10 0.85 
the rock matrix. The coal models have a similar 

trend in strength anisotropy with the stronger coal 

less anisotropic than the weaker coal. For the 

stronger coal, the ratio of axial strength to strength 

parallel to bedding is about 1.5-to-1; whereas for 

the weaker coal, this ratio is about 2.2-to-1. The 

weaker coal models would apply to more cleated 

coal, i.e. containing more closely spaced joints. The 

extensive material property suite for coal mine 

rocks proposed in tables 1 and 2 is generally 

consistent with a smaller set of properties proposed 

by Reddish [10]. 

Note that in proposing this suite of numerical rock 

properties, the UCS of the rock matrix is 

independent from the strength of the bedding 

planes. In the absence of specific data, the user will 

usually specify the rock matrix and bedding plane 

strength as a pair with strength ratio similar to that 

noted by Molinda and Mark [4] for an extensive 

database of axial and diametral point load tests. 

However, the strength values for the rock matrix 

and bedding planes are independent in the material 

property suite, and the user can specify any value 

for the bedding plane strength up to that of the rock 

matrix UCS. 

In creating the material model suites, friction angle 

for the matrix and bedding planes are assumed to 

vary as shown in tables 1 and 2, respectively. These 

assumptions for friction angle along with equation 

(1) then imply the values for peak cohesion shown 

in tables 1 and 2. Thus, the UCS of the rock matrix 

and the bedding plane strength provide two of the 

four major input parameters to the SU constitutive 

model in FLAC. 

Assumed friction angle values for the rock matrix 

ranges are 21° for soil- and clay-like materials up to 

36° for the strongest rocks. These values may be 

somewhat low compared to published values of 

Jaeger and Cook [11] and Farmer [12]. Later 

revisions of this material property suite may include 

a one friction angle range for application at low 

confinement and another for application at high 

confinement. Assumed friction angle values for the 

bedding plane are 21° for soil- and clay-like 

materials up to 30° for the strongest rocks. These 

values are consistent with data developed by Barton 

and summarized in Hoek, Kaiser and Bawden [13]. 

Other major assumptions within this material model 

suite are as follows: 

1. Moduli for the materials range from 1 to 

20 GPa. Weaker materials have a lower 

modulus, while stronger materials have a higher 

modulus. The ratio of modulus to UCS of the 

rock matrix varies from about 1,000 for the 

weakest to about 100 for the strongest materials. 

The moduli for the material and the modulus-toUCS ratio are consistent with data shown in 

Table 2. Initial values for bedding plane input parameters

Material 

Name Description 

Lab. 

strgt. 

(MPa) 

Field 

strgt. 

(MPa) 

Young’s 

Modulus 

(GPa) 

Cohesion 

(MPa) 

Friction 

angle 

(deg) 

Dilation 

angle 

(deg) 

Tensile 

strength 

(MPa) 

Soil 1 paste 0.04 0.02 1 0.007 21 10 0.002 

Soil 2 very soft soil 0.07 0.04 1 0.014 21 10 0.004 

Soil 3 soft soil 0.14 0.08 1 0.028 21 10 0.008 

Soil 4 firm soil 0.29 0.16 1.5 0.055 21 10 0.016 

Soil 5 stiff soil 0.63 0.35 2 0.120 21 10 0.035 

Soil 6 very stiff soil 1.4 0.80 2.5 0.27 21 10 0.080 

Rock 1 claystone, fireclay 2.7 1.5 3 0.5 21 10 0.15 

Rock 2 black shale 5.4 3.0 4 1.0 22 10 0.30 

Rock 3 black shale, gray shale 10 5.7 5 1.9 23 10 0.60 

Rock 4 gray shale 18 10 6 3.3 24 10 1.0 

Rock 5 siltstone, gray shale 25 14 7 4.5 25 10 1.4 

Rock 6 siltstone 32 18 8 5.5 26 10 1.7 

Rock 7 siltstone, sandstone 41 23 10 7 27 10 2.3 

Rock 8 sandstone, limestone 59 33 12 10 28 10 3.3 

Rock 9 sandstone 86 48 15 14 29 10 4.8 

Rock 10 limestone 123 69 20 20 30 10 6.8 

Coal 1 banded, bright coal 1.6 0.9 2.5 0.3 25 10 0.08 

Coal 2 banded coal 2.9 1.6 2.5 0.5 26 10 0.15 

Coal 3 banded, dull coal 6.4 3.6 2.5 1.1 27 10 0.30 

Coal 4 dull coal 12 6.7 2.5 2.0 28 10 0.60 
Jaeger and Cook [11] and Gale and Fabjanczyk 

[14] 

2. Cohesion decreases from its peak value given in 

tables 1 and 2 to a residual value of 10% of peak 

over 5 millistrains of post-failure strain. It is 

this decrease in cohesion with post-failure strain 

that gives rise to strain-softening behavior of 

both the rock matrix and the bedding planes. 

3. Friction angle remains constant at the values 

shown in tables 1 and 2, even in the post-failure 

regime. 

4. Tensile strength is equal to cohesion for the 

soils materials and decreases to 0 over 

1 millistrain of post-failure strain. 

5. Tensile strength values are generally about 10% 

of UCS. It also decreases to 0 over 1 millistrain 

of post-failure strain. This strength ratio is 

again consistent with rock strength data shown 

in Jaeger and Cook [11] and Farmer [12]. 

6. Dilation angle is initially 10° and decreases to 

0° over 5 millistrains of post-failure strain. 

4. ROCK BOLT PROPERTIES 

In addition to its robust constitutive models, FLAC 

also includes various structural support elements. 

The structural element called “cable” represents 

rock support as an axial force along a line, and this 

approach suffices for most rock or cable bolts in 

practical coal mining applications. If the shear or 

moment resistance of a rock bolt is significant, the 

“pile” structural element may be a more appropriate 

choice. 

Properties required by the “cable” element are the 

structural characteristics of the steel, namely elastic 

modulus, cross-sectional area and yield strength, 

along with the structural characteristics of the 

anchor. Resin along with some cement grout now 

dominates most anchors used with rock and cable 

bolts in U.S. mines [15]. Two properties represent 

the anchor characteristics in FLAC, namely 

“Kbond” which is the stiffness of the grout and 

“Sbond” which is its cohesive strength. 

Kbond or anchorage stiffness depends on grout 

properties and the annulus thickness, i.e., hole 

radius minus bolt radius. Based on numerical 

studies by Saint John and Van Dillen [16] of the 

grout-rock interface, the FLAC manuals [1] suggest 

the following expression for a practical estimate of 

Kbond for use in FLAC: 

 (2) 

where G is the grout shear modulus, D is the bolt 

diameter and t is the annulus thickness. 

Farmer [17] reports a value of 2.25 GPa 

(455,000 psi) for the Young’s modulus of resin 

grout. For a typical 19 mm (3/4 inch) rock bolt in a 

28.6 mm (1.125 inch) hole, Kbond is approximately 

1.4 x 109 N/m/m. Over the practical range of rock 

bolt and hole diameters and the likely range for 

grout modulus, Kbond varies at most from about 1 

to 2 x 109

 N/m/m. 

Numerical modeling of laboratory measurements of 

rock bolt behavior confirms this estimate of Kbond. 

 Numerous researchers [18-21] used strain gauges 

to measure the load distribution along fully-grouted, 

1-m-long rock bolts embedded in large blocks of 

limestone, shale or concrete. Figure 3 shows 

various measured load profiles where the bolt load 

at zero distance along the bolt is the actual applied 

load. Note the exponential decay of bolt load with 

distance that is consistent with analytical models 

proposed by Farmer [17] and Serbousek and Signer 

[19]. A simple FLAC model of these laboratory 

pull tests was used to calculate the bolt load 

distribution for Kbond values of 0.5, 1 and 2 x 109

N/m/m and an applied load of 60 kN. As seen by 

inspection of figure 4, Kbond equal to 1 x 109

N/m/m matches the laboratory measurements well. 

“Sbond” is also known as bond factor, anchor factor 

or grip factor and has a typical value of about 

350 kN/m (1 ton/in) in coal mine rocks. Its value 

depends on the likely failure mode of the bolt 

anchor. If the grout is weak, shear failure occurs 

along the bolt-grout interface, and Sbond depends 

10ln(1 2 / )

2

t D

G Kbond +

≅

π

Fig. 3. Measured and calculated load profiles along rockbolts.

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Distance along bolt - meters

Bolt load - kN .

Reference 18

Reference 19

Reference 20

Reference 21

Kbond = 500,000,000

Kbond = 1,000,000,000

Kbond = 2,000,000,000
on the grout cohesion and the perimeter of the bolt. 

Farmer [17] reports a value of 160 MPa for the 

compressive strength of resin grout. Assuming that 

the cohesion is 1/3 of this value, Sbond at the boltgrout interface for a typical 19 mm (3/4 inch) bolt is 

about 3.2 MN/m. 

However, in coal mine rocks, shear failure typically 

occurs along the grout-rock interface where Sbond 

depends on the lesser of the rock or grout cohesion 

and the perimeter of the hole. From table 1, rock 

cohesion varies from 1.2 to 20 MPa and is even less 

for the occasional thin clay layers. Thus, for a hole 

diameter in the 25 to 35 mm range, Sbond varies 

from 80 kN/m to 2.2 MN/m (0.2 to 4.5 tons/inch) 

depending on the rock material strength. Table 3 

shows the range of Sbond values for various rock 

materials. For practical coal mine modeling with 

FLAC, the user should specify bolt sections that 

correspond to the top and bottom of a geologic layer 

and then assign Sbond value for that section 

consistent with the rock material properties for that 

layer. Table 4 presents Sbond values for various 

rocks either measured directly or else inferred from 

select pull test data. Values range from 77 to 

1,225 kN/m and are consistent with the Sbond input 

parameters shown in table 3. Note that the values 

for Kbond and Sbond discussed here assume a unit 

bolt spacing of 1 meter between rows of bolts. 

These rock bolt properties and others require 

scaling according to the actual rock bolt spacing. 

Table 3. Sbond values for various rock materials 

Material

Name 

Description Cohesion 

(MPa) 

Sbond for 

25 mm hole 

(N/m) 

Sbond for 

35 mm hole

(N/m) 

Soil 1 paste 0.007 559 770 

Soil 2 very soft soil 0.014 1,120 1,540 

Soil 3 soft soil 0.028 2,230 3,080 

Soil 4 firm soil 0.055 4,390 6,050 

Soil 5 stiff soil 0.120 9,580 13,200 

Soil 6 very stiff soil 0.69 55,100 75,900 

Rock 1 claystone, 

fireclay 

1.2 95,800 132,000 

Rock 2 black shale 2.0 160,000 220,000 

Rock 3 black shale, 

gray shale 

3.3 263,000 363,000 

Rock 4 gray shale 4.5 359,000 495,000 

Rock 5 siltstone, gray 

shale 

6 479,000 660,000 

Rock 6 siltstone 8 638,000 880,000 

Rock 7 Siltstone, 

sandstone 

10 798,000 1,100,000 

Rock 8 sandstone, 

limestone 

12 958,000 1,320,000 

Rock 9 sandstone 14 1,120,000 1,540,000 

Rock 10 limestone 20 1,600,000 2,200,000 

Coal 1 banded, bright 

coal 

0.6 47,900 66,000 

Coal 2 banded coal 1.0 79,800 110,000 

Coal 3 banded, 

dull coal 

1.9 152,000 209,000 

Coal 4 dull coal 2.7 215,000 297,000 

Table 4. Measured Sbond in various rocks 

Rock Sbond (N/m) Ref. 

Shale-concrete 77,000 22 

Plaster 126,000 22 

Chalk 193,000 23 

dark gray fireclay 220,500 24 

layered dark gray shale 252,000 24 

Sandstone 289,000 23 

Concrete blocks 290,000 25 

thinly banded gray shale 290,500 24 

clay, claystone 304,500 24 

dark gray shale 364,000 24 

Coal 385,000 23 

Gypsum 385,000 26 

Limestone 400,000 26 

Anhydrite 526,000 26 

Limestone 1,225,000 23 

Coal / Shale 300,000 to 900,000 27 

Sandstone / limestone 1,000,000 to 2,500,000 27 

Additional simple FLAC models calculated the 

minimum anchor length to hold 100 kN (about 

10 tons) without slipping. Again, these models 

consider a 19 mm bolt of varying length and 

assumed yield strength for the steel of 200 kN to 

insure anchorage slip and not steel failure. 

Consistent with expectations, the critical anchor 

Fig. 4. Anchor length required for 100 kN capacity for various

Sbond. 

0

20

40

60

80

100

120

140

0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05 6.00E+05 7.00E+05 8.00E+05 9.00E+05 1.00E+06

Sbond of Anchor - N/m

Anchor Length for 100 kN - cm .

Anchor slip in this region 

Steel yield in this region 
length ranged from 1 m at a low Sbond value of 

100 kN/m down to 10 cm with a high Sbond value 

of 1,000 kN/m as shown in figure 4. For a given 

Sbond, a bolt with anchor length more than this 

critical value will fail by yield of the bolt steel and 

with anchor length less than this critical value, 

anchor slip will occur. Figure 4 suggests that for 

stronger rocks with Sbond more than 350 kN/m 

(1 ton/inch), short encapsulation pull tests with 

anchor length of much less than 30 cm (1 foot) are 

necessary to measure Sbond directly. 

5. INITIALIZATION AND LOADING 

CONDITIONS 

A recent summary of horizontal stress 

measurements in U.S. coal mines by Dolinar [28] 

demonstrated that the horizontal stress magnitude 

depends on the elastic modulus of the rock layers. 

Horizontal stress varies according to the relative 

stiffness of each geologic layer, such that stiff 

limestone or sandstone layers attract higher 

horizontal stress than less stiff black shale or 

claystone layers. 

To initialize horizontal stress in a model, the analyst 

must first calculate the average horizontal strain as 

 (3) 

where σH average is the average horizontal tectonic 

stress and Εaverage is the average modulus. Using 

Dolinar’s approach [28] a tectonic strain could also 

be used directly for the initial far field boundary 

condition. Alternatively, if the horizontal stress and 

modulus are known for a particular layer within a 

model, the horizontal strain can be calculated on 

that basis. 

Horizontal stress for each layer in the model has a 

tectonic component and a Poisson component and is 

calculated as 

 (4) 

where Εi is the Young’s modulus for a layer, υ is 

the Poisson’s ratio and σνi is the vertical stress in a 

layer. Vertical stress in each layer depends on 

depth in the usual way. Figure 5 shows a layered 

model of coal mine rocks initialized with this 

procedure. Average initial vertical and horizontal 

stress is 5 and 8 MPa. 

average

H average

H average E

σ

ε =

( ) 1 ( )( ) H i H average Ei σ V i

υ

υ

σ ε ⎟

⎠

⎞ ⎜

⎝

⎛

− = +

Fig. 5. Initial horizontal stresses. Warm colors indicate high horizontal stress in stiffer layers, and cool colors indicate low 

horizontal stress in less stiff layers. The future entry is shown at center. 
Table 5. Going from core log to numerical model input 

parameters 

Height 

into 

roof 

(m) 

Rock 

type 

UCS 

axial 

PLT 

(MPa) 

Bedding 

strength 

diam. PLT 

(MPa) 

Rock 

matrix 

code 

(table 1)

Bedding 

plane 

code 

(table 2) 

3.00 sandy bl sh 33.70 12.40 RM5 RBP3 

2.90 sandy bl sh 33.70 12.40 RM5 RBP3 

2.80 sandy bl sh 33.70 12.40 RM5 RBP3 

2.70 sandy bl sh 33.70 12.40 RM5 RBP3 

2.55 sandy bl sh 33.70 12.40 RM5 RBP3 

2.40 coal 12.00 6.70 CM3 CBP3 

2.30 coal 12.00 6.70 CM3 CBP3 

2.20 coal 12.00 6.70 CM3 CBP3 

2.10 coal 12.00 6.70 CM3 CBP3 

2.03 coal 12.00 6.70 CM3 CBP3 

1.90 bl sh + coal 18.00 4.00 RM3 RBP2 

1.80 bl sh + coal 18.00 4.00 RM3 RBP2 

1.69 bl sh + coal 18.00 4.00 RM3 RBP2 

1.60 clayst 8.00 2.00 RM2 RBP1 

1.50 clayst 8.00 2.00 RM2 RBP1 

1.40 clayst 8.00 2.00 RM2 RBP1 

1.30 clayst 8.00 2.00 RM2 RBP1 

1.18 clayst 8.00 2.00 RM2 RBP1 

1.08 bl sh 18.00 4.00 RM3 RBP2 

0.98 coal 12.00 6.70 CM3 CBP3 

0.88 coal 12.00 6.70 CM3 CBP3 

0.76 bl sh 18.00 4.00 RM3 RBP2 

0.64 bl sh 18.00 4.00 RM3 RBP2 

0.52 coal 12.00 6.70 CM3 CBP3 

0.40 coal 12.00 6.70 CM3 CBP3 

0.28 bl sh 18.00 4.00 RM3 RBP2 

0.16 bl sh 18.00 4.00 RM3 RBP2 

0.00 coal 12.00 6.70 CM3 CBP3 

6. PUTTING IT ALL TOGETHER – AN 

EXAMPLE 

This example demonstrates the complete modeling 

procedure for a coal mine gateroad entry in the 

Pittsburgh coalbed that is first subject to initial 

development loading, then additional loading from 

mining the first longwall panel and finally more 

loading as a second longwall panel approaches. 

Again, figure 2 shows estimates of axial and 

diametral point load strength as measured along a 

core. The point load tests used to estimate the UCS 

of the rock matrix and the bedding plane strength 

lead directly to material property assignments based 

on tables 1 and 2. Table 5 summarizes a section of 

the geologic column, strength values from point 

load tests and the resulting material property inputs 

for the model. Figure 5 reflects the layering detail 

in the overall model. Initial horizontal stress 

magnitude applied to the model generally correlates 

to high or low strength rock layers. The rock bolts 

in the model are composed of many sections where 

each section corresponds to the top and bottom of a 

geologic layer. Each bolt section is then assigned a 

Sbond value consistent with the rock material 

properties for that layer. 

Table 6 indicates the average horizontal and vertical 

stress applied to the model at different stages. The 

stresses indicated in table 6 are a two-dimensional 

approximation to a complex three-dimensional 

problem. In the gateroad development phase, 

applied stresses are the same as in situ stresses. 

Mining the first longwall panel effectively induces 

higher horizontal and vertical stresses far field from 

the model coal mine entry. The approaching second 

longwall panel and passage of that second panel 

induces additional horizontal and vertical stresses. 

Again, the stress path indicated in table 6 is only a 

simple two-dimensional approximation of the actual 

complex three-dimensional stress field applied to 

the coal mine entry. 

Table 6. Applied stress path at model boundary 

Loading 

condition 

Average 

horizontal 

stress (MPa) 

Average vertical 

stress (MPa) 

Development 8 5 

1st panel mining 14 9 

2nd panel mining 17.6 11.4 

Post mining 20 13 

To apply these additional horizontal and vertical 

stresses to the model, equivalent average strains are 

calculated based on a weighted average modulus for 

the model. Based on the overall model dimensions, 

equivalent displacements at the model boundary are 

calculated. These displacements are then achieved 

in the model by slowly applying a velocity at the 

boundary for a prescribed number of computational 

steps. Velocity at the model boundary is then set to 

zero for additional computational steps to achieve 

equilibrium. 

The modeling analyzes two alternative support 

systems, namely 2.4-m-fully-grouted rock bolts 

alone and with 4-m-long cable bolts. Figures 6 

(top) and 6 (bottom) compare these alternatives by 

showing rock bolts loads, rock bolt anchor slip, rock 

bolt breakage and rock mass shear failure 

superimposed on the UCS of the rock matrix. 

Different colors represent rock layers of different 

rock matrix strength. Generally in the Pittsburgh 

coalbed, the immediate roof rock is low strength 

black shale, thin coal layers and claystone. Above 

the immediate roof rock is somewhat higher 

strength gray shale and siltstone beds. Rock mass 

failure has occurred throughout the immediate roof. 

 Zone of intense bedding plane slip exist above the 

upper corners of the entry and these zones 
propagate 2 to 3 meters into the roof. Bedding 

plane separation has also developed 1.5, 2.5 and 4.5 

meters into the roof rock as shown in figure 7. 

Compressive failure of the immediate roof rock has 

localized into several “shear bands” as indicated on 

figures 6 (top) and 6 (bottom) with the shear strain 

index parameter in FLAC. These shear bands are 

more developed with the lighter support system 

consisting of bolts alone. The failure has also 

tended to favor one side of the roof more than the 

other. Downward roof movement is much greater 

on the left than on the right. The magnitude of rock 

bolt load is plotted as a percentage of yield strength 

of the steel. For the untensioned, fully-grouted rock 

bolts used in this model, the load increases from 

zero at the bolt head, rises to a maximum 

somewhere in the middle and decreases back to zero 

at the anchorage end. The shape of the load profile 

follows the measured laboratory experiments as 

shown in figure 3. All bolt loads are tensile no 

matter whether the load is plotted left or right of the 

bolt. Anchorage slip is indicated by crosses along 

the bolt. At the highest load applied to the model, 

anchor slip has occurred almost everywhere along 

the rock bolts and the lower portion of the cable 

bolts. Rock bolt or cable bolt breakage can occur if 

load on the bolt equals the yield load and if strain in 

the bolt exceeds 2%. Bolt breakage occurs in the 

left and center bolts for the bolts alone case and 

only in the center bolt if cable bolts are also 

installed. While the broken section of bolt is not 

visible in figure 6, the low axial loads on either side 

of the shear zone mark the location of the broken 

bolt section. 

Figure 7 shows the effectiveness of the two 

alternative rock support systems for controlling 

immediate roof movement under progressively 

higher load conditions. Under development 

conditions with horizontal and vertical stresses of 8 

and 5 MPa, respectively, roof displacement is less 

than 10 mm and both bolt alternatives behave 

identically. Mining the first longwall panel 

increases horizontal and vertical stresses to 14 and 

9 MPa; however, calculated roof displacements 

remain under 30 mm, and there is still negligible 

difference between the two alternatives. When the 

second longwall panel approaches, the necessity of 

the cable bolts becomes evident. In the alternative 

without cables, downward roof displacement at 2-m 

horizon approaches 70 mm, whereas with cables 

movement at this horizon is about 30 mm. Total 

downward roof movement in excess of 50 mm and 

sudden jumps in that movement with small 

increases in the applied load on the model are 

indicative of roof instability and ineffective roof 

support. 

Fig. 6. Support system performance with 2.4 m bolts alone

(top) and 2.4 m bolts with 4 m cables (bottom). Rock layers

of different strength are colored; shear zones are contoured;

maximum shear strain contour is 0.5; rock bolt load is

indicated. 
7. CONCLUSIONS 

This paper presents progress toward a standard 

method for the use of numerical models in practical 

ground control planning. The method includes 

procedures for collecting the needed input data, 

setting up a model and interpreting the results of 

calculations. 

Collecting the input data needed for a numerical 

model begins with development of a detailed 

geologic core log. This core log must capture 

geologic layers of similar mechanical properties and 

also note particular features such as exceptionally 

weak clay layers. Point load testing is a convenient 

method to estimate the UCS of the rock matrix and 

the bedding plane strength for each geologic layer. 

This paper proposes a suite of material property 

input parameters aimed at the SU constitutive 

model in FLAC. This suite of “numerical rocks” 

includes very weak soils and weak rocks to the 

strongest rocks found in coal mining. Having 

estimates of UCS and bedding plane strength for 

each geologic layer, the user can readily create a 

numerical model that correctly reflects the geologic 

situation. The suggested procedure has the distinct 

advantage of being organized and reproducible. In 

principle, two different individuals could examine a 

geologic section, describe it, test it and develop the 

same numerical model inputs for the field 

conditions. 

The paper also presents select properties needed to 

represent rock supports in a numerical model. The 

significant feature of the rock bolt properties is the 

linkage between rock bolt anchorage and the 

specific geologic layer containing that section of the 

rock bolt. Sections of a rock bolt in weak rocks 

have low anchor strength and vice versa in stronger 

rocks. 

A practical example of a numerical model that 

follows the proposed procedure leads to very 

realistic results. The calculations capture the rock 

failure process correctly and agree with failure 

observations in the field. Calculated stresses and 

displacements in the model are consistent with field 

measurements of the same. 

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Fig. 7. Immediate roof displacement response for two rock support alternatives.

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