The Ground Response Curve, Pillar Loading and Pillar Failure in 

Coal Mines

 E.

Mark, C.

Murphy, M.

Essie Esterhuizen, Senior Service Fellow

Chris Mark, Principal Research Engineer, Mining Engineer

Michael M. Murphy, Research Engineer, Mining Engineer

Ground Control Branch 

NIOSH, Office of Mine Safety and Health Research 

Pittsburgh, PA

ABSTRACT

The response of the surrounding rock mass to the creation of 

mining excavations determines the ultimate load on a pillar support 

system. In conditions where the ground is relatively soft and 

weak, the full overburden weight can be transferred to the pillar 

system. However, in stiffer and stronger rocks, a greater portion 

of the overburden load is transferred to the unmined coal barriers 

or abutments, and the pillar stress is reduced. This paper makes 

use of numerical models to examine the interaction between typical 

pillar systems and the surrounding rock mass for weak and strong 

geological conditions at various spans and depths of cover. The 

concepts of structural failure and functional failure of pillars are 

used to assess pillar performance when pillars are deformed beyond 

their peak resistance. The results show that the span-to-depth 

ratio is an important factor in determining the pillar stress and the 

ultimate deformation of pillars. The ultimate pillar strain appears 

to be closely related to the functional success of pillar systems.

INTRODUCTION

The National Institute for Occupational Safety and Health 

(NIOSH) was requested by Congress to study the safety of retreat 

pillar mining following the Crandall Canyon Mine disaster that 

took place near Price, Utah in August, 2007. As a part of this study, 

an investigation was made to better understand how the rock mass 

responds to the creation of mining excavations and how the loads 

are distributed among the pillars and the surrounding abutments 

or barriers. The outcome of these investigations contributed to the 

development of a modified loading model for the ARMPS-2010 

(Mark, 2010) method of retreat mining pillar design.

Structural and Functional Failure of Pillars

Pillar design is typically conducted by estimating the pillar 

strength and stress, and then sizing the pillars so that an adequate 

margin of safety exists between the expected strength and stress. 

The pillar strength can be defined as the maximum resistance 

of a pillar to axial compression (Brady and Brown, 1985). If 

a pillar is loaded beyond its peak strength, load shedding or 

yielding can occur, and the pillar is considered to have failed as 

a structure. Structural failure generally refers to a loss of loadcarrying capacity.

Pillars that have a width-to-height ratio of less than 4.0 typically 

exhibit a clear peak resistance when loaded followed by a rapid 

decrease in resistance if the loading continues. For these pillars, 

the point of structural failure can be identified relatively easily 

on a stress-strain curve. When the width-to-height ratio of pillars 

becomes large, pillars may yield at a constant stress or may exhibit 

strain hardening behavior. In these cases, it is difficult to determine 

a particular “peak” value of the pillar strength and structural failure 

becomes hard to define.

In some mining applications, structurally failed pillars are 

desired. For example, yield pillars have been used for many years 

in deep coal mine layouts (Mark et al., 1988; Iannacchione and 

Zelanko, 1995) and in hard rock mines (Barrientos and Parker, 

1975; Ryder and Ozbay, 1990). Although these pillars may be 

structurally failed, they are considered to be successful from a 

“functional” point of view. Functional failure refers to the state 

of not meeting a desired objective. Yield pillars in longwall gate 

entries would be considered to be functionally failed if they no 

longer meet the objective of providing safe access to the longwall 

face. The evaluation of functional failure usually requires the 

consideration of an entire system rather than just one component 

or structure within the system. For example, functional failure of 

a pillar system may be related to roof damage or floor punching 

and not only the failure of the pillar as a structure. The Analysis 

of Longwall Pillar Stability (ALPS) pillar design method for 

longwalls (Mark, 1993; Mark et al., 1994) and the Analysis of 

Retreat Mining Pillar Stability (ARMPS) method for retreat mining 

pillar design (Mark and Chase, 1997; Mark, 2010) both consider 

pillar stability and local roof geology to evaluate the “functional” 

success of a pillar design.

Ground Response and Pillar Stiffness

The driver of pillar failure is the response of the surrounding 

rock mass to the extraction of coal. In flat laying deposits, the 

pillar stress is related to the weight of the overburden. When the 

pillar layout consists of a regular array of pillars, the average pillar 

stress can be estimated using the tributary area method, which 

assumes the full weight of the overburden is equally distributed 

over all the pillars. This approach does not consider the fact that 

a portion of the overburden weight may be transferred to adjacent 
unmined barrier pillars or solid abutments. Stress transfer occurs 

to the relatively stiff barriers or solid abutments as the pillars in the 

mined area are compressed by the surrounding strata. The amount 

of pillar compression is determined by the relative stiffness of the 

pillars and the surrounding strata. Stiffer pillars will develop more 

stress, while stiffer surrounding strata will deflect less and impose a 

smaller load on the pillars. The concept of the pillar stiffness and 

strata stiffness is well established in the field of pillar design and 

has been used to evaluate the potential for violent pillar collapse 

(Salamon, 1970; Ryder and Ozbay, 1990; Zipf, 2001).

Understanding the stress and potential failure of pillars, 

therefore, requires consideration of both the ground response and 

the pillar response to mining. In this paper, the structural and 

functional success of pillar systems in coal mines are evaluated for 

various geological settings, panel spans, and depths of cover. The 

evaluations are restricted to the overall success, or global stability, 

of the systems and do not consider local stability issues such the 

failure of the immediate roof or floor between the pillars.

GROUND RESPONSE CURVE DETERMINATION

The concept of a ground response curve was originally 

developed by the civil tunneling industry where the timing and 

method of ground support is determined by monitoring the 

support pressure and excavation convergence during construction 

(Rabcewicz, 1965). The ground response approach has found 

application in both hard rock and coal mining as a method to better 

understand the interaction between the rock mass and the support 

system (Brown et al., 1983; Brady and Brown, 1985; Barczak et al., 

2005; Medhurst and Reed, 2005).

The ground response curve characterizes the rock mass by 

plotting the internal support pressure against the excavation 

convergence, as shown conceptually in Figure 1. If the excavation 

boundaries are subject to support pressure equal to the stress in 

the surrounding rock, no convergence will occur (point A). As the 

support pressure is reduced, the excavation boundaries initially 

converge in an elastic manner and linear response is observed. 

As the pressure is further reduced, the response becomes nonlinear if rock failure occurs and the self-supporting capacity of the 

ground is destroyed (point B). A point is reached (point C) where 

the required support resistance necessary to establish equilibrium 

begins to increase as the failed ground loosens and its dead weight 

must be resisted (point D).

The effect of the support system can also be plotted on Figure 

1. 

A

D

Convergence

Stress

Initial overburden stress

B

C D

Convergence

P

Q

Ground response curve

Support response

R

Figure 1. Ground response curve and support line.

For example, line PQR represents the stress-convergence 

response of a support system consisting of pillars. Initially, at 

zero convergence, the stress in the pillars will be zero. As the 

overburden is allowed to settle onto the pillars, the pillar resistance 

will increase. In the figure, the resistance of the pillar is equal to 

the pressure required to halt the convergence of the overburden at 

point Q.

Modeling Method to Develop Ground Response Curves for 

Coal Mine Panels

It is difficult to measure the ground response curve in actual 

underground excavations because of the significant loads 

that would have to be applied to balance the original ground 

pressure. However, numerical models can readily be used to 

estimate the ground response curve by progressively reducing the 

internal pressure in a modeled excavation while monitoring the 

resulting convergence.

The finite difference software FLAC3D (Anon., 2007) was used 

to develop ground response curves for coal mining excavations that 

have dimensions typical of longwall and pillar extraction panels in 

the United States. The software is able to realistically model the 

overburden behavior from the initial elastic response to the large 

displacements and deformations that are associated with rock 

failure and yield. It has the capability to model strength anisotropy 

found in the bedded coal measures and can simulate the strainrelated weakening of failed rock. The software also has a builtin programming language that allows the user to control loads 

and displacements in the model. This facility was used to apply 

internal pressure within the modeled panels so that the ground 

response curve could be determined.

The input parameters used to simulate the coal pillars and the 

surrounding rock mass were extensively calibrated against field 

monitoring results to ensure that realistic large-scale behavior of 

the overburden and coal pillars was achieved (Esterhuizen et al., 

2010). The coal was modeled using the Hoek-Brown material type 

available in the FLAC3D software, while the overburden rocks 

were modeled as a strain-softening ubiquitous joint material. The 

ubiquitous joints were used to simulate the bedding weaknesses 

in the strongly bedded strata. The ubiquitous joints were also 

used to model vertical joints in massive rock types, such as 

sandstone or limestone, that did not contain well-developed 

bedding weaknesses. The gob was modeled as a strain hardening 

material that follows a hyperbolic stress-strain curve after the 

results of Pappas and Mark (1993). The horizontal stress in the 

models consisted of a depth-dependent component and a tectonic 

component that depends on the stiffness of the strata layers. 

Details of the input parameters, model calibration, and comparisons 
of model results to field measurements are given in Esterhuizen et 

al. (2010).

The ground response curve for a particular panel was determined 

by modeling the panel, the unmined coal, and the surrounding 

strata up to the ground surface. The distribution of support 

pressure within the panel has an impact on the shape of the ground 

response curve. Therefore, the internal support pressure in the 

panels was not modeled as a constant pressure, as one would do 

when modeling support systems, but rather by simulating an 

array of pillars in the panel. The resulting “support pressure” 

distribution in the panel more accurately represented the effect of a 

system of pillars with higher stress near the center of the panel and 

lower stresses near the edges. The elastic modulus of the pillars 

was reduced in stages, simultaneously at all points, to simulate 

decreasing support pressure in the excavation. The model was run 

to equilibrium at each stage and the support pressure at the pillar 

in the center of the panel and the convergence at that location were 

recorded. This procedure produces the ground response curve at 

the center of the panel. It is possible to create ground response 

curves for any pillar location if desired. However, for the single 

panels modeled here, the pillar at the mid-span is the most critical 

one because the deformations are the largest at this location. All 

ground response curves presented in this paper were calculated at 

the mid-span of the mined panels. The panels were all assumed to 

be surrounded by an adequately large extent of unmined coal. The 

potential impacts of adjacent mining and barrier pillar yield were 

not considered.

EFFECT OF GEOLOGY, DEPTH, PANEL WIDTH, 

AND PILLAR EXTRACTION OF THE GROUND 

RESPONSE CURVE

Ground response curves were developed for 300-m (1,000-

ft) wide coal mine panels with a mining height of 2.4 m (8 ft) 

in two different geologies at depths of 150 m and 450 m (500 ft 

and 1,500 ft). At 150-m (500-ft) depth, the panels are considered 

to be supercritical, because the span-to-depth ratio exceeds 

1.2. At a 450-m (1,500 ft) depth of cover, they are considered 

to be subcritical, having a span-to-depth ratio of 0.67. The first 

model simulates “weak overburden” that consists of 75% weak 

rocks, such as shale or clay stone, and 25% strong rocks, such as 

sandstone or limestone beds. The gob was modeled as a weak 

material that followed the “shale” gob response after Pappas and 

Mark (1993). The weak overburden model is representative of 

some of the coal measures found in the eastern United States. The 

second model simulates “strong overburden” containing about 

50% strong rocks, typical of the stronger coal measures found 

in southern Appalachia, Colorado, and Utah. The geology was 

modeled by simulating alternating layers of weak and strong rocks, 

having bed thicknesses of between 5 m (16 ft) and 10 m (33 ft), 

based on actual geological profiles of operating mines in the two 

geographic areas. The gob was modeled as a stronger “sandstone” 

material. Figure 2 shows one of the models indicating the general 

model layout and the geologic layering in the model.

Effect of the Geology and the Depth-to-Span Ratio

Figure 3 shows the resulting ground response curves at midspan of the panel for the weak and strong geologies at 150- and 

450-m (500- and 1,500-ft) depths. Considering the results at a 150-

m (500-ft) depth, in which both panels are supercritical (span-todepth ratio is 2.0), it can be seen that the ground response curves 

are nearly horizontal and are almost equal to the cover stress 

of 3.8 MPa (550 psi). There is almost no initial linear section 

of the curve, because overburden failure starts at an early stage 

of deformation. This represents a near “dead-weight” loading 

condition, and, clearly, no arching of the strata is occurring over 

these supercritical panels. The support system would be required 

to carry almost the full overburden weight. If pillars are used for 

support, this situation would approach the classical tributary area 

loading condition. There is little difference between the weak 

and strong overburden results because of the near dead-weight 

loading conditions.

The results for 450-m (1,476 ft) depth show a different picture. 

Here, the span-to-depth ratio is 0.67 (subcritical), and there is 

considerable difference between the weak and strong overburden 

response. The response of the strong overburden is initially 

nearly linear, followed by a curved section, which is related to the 

development of failure in the overburden. When the convergence 

is about 20 cm (0.66 ft), the curve flattens out at about 50% of the 

initial overburden stress. This implies that arching is occurring in 

the overburden, and about 50% of the weight of the overburden 

is being carried by the support system, while the remainder is 

transferred to the solid abutments. The arching mechanism is 

often referred to as a “pressure arch” in rock engineering practice 

(Barrientos and Parker, 1975).

In the weak overburden model, the ground response is flatter 

and arch formation is not as developed as in the stronger rock 

model. Only about 25% of the overburden load is transferred to 

the abutments, while about 75% would be carried by the support 

system. The “support system” might be a system of pillars or the 

gob if full extraction mining is carried out.

These results clearly show that the geological composition of 

the overburden and the span-to-depth ratio both have a significant 

impact on the stress that is carried by the support system, be it 

pillars or gob. Under weak overburden materials the arching 

mechanism is not as pronounced and greater load is transferred 

to the support system, while strong overburden is able to form a 

more developed arch and a lesser amount of stress is carried by the 

support system.

Effect of the Span

The strong overburden model was used to further investigate the 

effect of the mining span on the ground response. Models were 

created to simulate mining at a depth of 450 m (1,500 ft) and the 

panel spans were set at various dimensions from 300 m (1,000 ft) 

(span-to-depth ratio = 0.67) down to 25 m (80 ft) (span-to-depth 

ratio = 0.06). The resulting ground response curves are shown in 

Figure 4. It can be seen that as the panel span is decreased from 

300 to 25 m (1,000 to 80 ft), the ground response becomes stiffer 

(steeper slope) and the arching effect becomes more pronounced. 

For example, when the spans are 150 m (500 ft) (span-to-depth 

ratio = 0.33) or less the curve flattens at 1–2 MPa (145–290 psi), 

which is considerably lower than the overburden stress of 11.3 

MPa (1,600 psi). This indicates that significant arching of the 

overburden stress to the solid abutments is occurring.

These results for relatively strong overburden rocks show that 

the mining span and arching of the roof strata over the excavation 
will have a significant impact on the final stress in the support 

system. In weaker overburden, the effect of arching is less 

pronounced and the resulting loading of the support system is likely 

to be greater.

Figure 2. Example of a numerical model layout showing location of mined panel and geological layering.

Ground Response at the Pillar Extraction Line

The ground response curve is dramatically affected if pillar 

extraction is performed. The prevailing stress is considerably 

increased and the presence of the adjacent gob will affect the 

ground response. The results of a fully three-dimensional 

model that simulated a 150-m (500-ft) wide panel under strong 

overburden are presented. The ground response curve was 

determined at the mid-span pillar on the extraction line for a case 

where the pillars in half of the panel had been extracted. The 

600-m (2,000-ft) long extracted portion of the panel was filled 

with an appropriate gob material, after Esterhuizen et al. (2010). 

The ground response curve was determined by reducing the 

pillar stiffness simultaneously in all the remaining pillars in the 

panel in a stepwise manner and determining the pillar stress and 

associated convergence at the mid-span pillar on the extraction line 

at each step. Figure 5 is a schematic diagram showing a partially 

extracted panel, the pillars, the extraction line and the gob. It 

also shows the location of the pillar where the ground response 

was determined. Figure 6 displays the resulting ground response 

curve at the extraction line and the ground response curve under 

normal development loading conditions. It can be seen that the 

ground response curve at the pillar extraction line initiates at a 

much higher stress because of the abutment loading effects. At 

the extraction line, the stress required to achieve equilibrium for a 

given convergence is much greater than under normal development 

loading conditions. Convergence is also seen to be greater for any 

given stress value.

ADDING PILLAR STRESS-STRAIN CURVES

The interaction between the overburden loading system and 

a system of pillars can be assessed by adding pillar stress-strain 

curves to the ground response charts to represent the “support 

system” illustrated in Figure 1. Numerical models were used to 

generate a representative set of pillar stress-strain curves using 

adequately calibrated input parameters (Esterhuizen et al., 2010). 

The models simulated coal pillars that are located between strong 

roof and floor strata, so that failure or punching into the roof or 

floor would not occur. Therefore, the resulting pillar strength 

is based on failure within the coal material only. The models 

were designed to follow the Bieniawski strength equation up 

to a width-to-height (W:H) ratio of 8.0. At greater W:H ratios, a 

clear peak strength is not identifiable, because the pillars become 

strain hardening.

Equivalent Support Pressure

In order to plot the pillars on the ground response curve, the 

equivalent “support pressure” of the pillars is calculated. Since 
 

the pillars do not contact the full excavation surface, the equivalent 

pillar stress, Pe

, (or “support pressure”) is calculated by assuming 

the pillar stress is applied over the full excavation surface. This 

can easily be calculated as:

Pe = σ × (1− e) (1)

where σ is the average pillar stress and e is the extraction 

ratio. Figure 7 shows the ground response curve for the strong 

overburden model at a depth of 450 m (1,500 ft) with the pillar 

response curves added, after converting the pillar stress to an 

equivalent support pressure. In this chart, the strain is expressed as 

ground convergence over the pillar height of 2.4 m (8 ft), to allow 

the ground response curve and the stress-strain behavior of the 

pillars to be plotted on the same set of axes.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Stress (MPa)

Convergence (m)

450-m depth weak overburden

150-m depth weak overburden

150-m depth strong overburden

Overburden stress at 450 m

Overburden stress at 150 m

Stress transferred to 

abutments by arching

Stress transferred to 

abutments by arching

Figure 3. Ground response curves at the center of a 300–m- (1,000 ft) wide panel in weak and strong overburden strata at 150 m and 

450 m (500 ft and 1,500 ft) depth of cover.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Stress (MPa)

Convergence (m)

Overburden stress 

Stress transferred to 

abutments by arching

Figure 4. Ground response curves at mid-span of panels with 

various spans in strong overburden strata at 450-m (1,500-ft) 

depth of cover.

Initial Support Pressure

The pillar stress-strain curves in Figure 7 all have an initial 

stress value when the strain is zero. This point represents the 

starting condition of the FLAC3D models, where the convergence 

is held at zero and the rooms are excavated. At this initial stage, 
 

before any convergence takes place, the stress in the pillars is still 

equal to the original overburden stress. The initial support pressure 

exerted by the pillars at this stage is calculated using Equation 1 

and can be seen to be lower than the overburden stress of 11.3 MPa 

(1,600 psi). This imbalance causes the roof and floor to converge 

until the pillar response curve meets the ground response curve and 

equilibrium is established.

 

Extraction line ground 

response was 

recorded at this pillar

Gob

Extraction line

Ground response determined by 

softening all the pillars in the 

panel simultaneously

Figure 5. Schematic diagram showing a partially extracted panel and the location of the pillar that was used to determine the ground 

response at the pillar extraction line.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Stress (MPa)

Convergence (m)

Ground response at the extraction line

Ground response under development conditions

Figure 6. Ground response curves at mid-span of a 150-m- (500-

ft-) wide pillar extraction panel, showing the ground response 

under development conditions and at the pillar extraction line. 

Depth of cover is 450 m (1,500 ft) under strong overburden strata.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0% 2.0% 4.0% 6.0% 8.0% 10.0%

Stress (MPa)

Strain

W:H = 6

W:H = 4

W:H = 3 Span 25 m

Figure 7. Pillar stress-strain curves and ground response curves 

at mid-span of panels with various widths at 450-m (1,500-ft) 

depth of cover under strong overburden strata.

PILLAR PERFORMANCE AND GROUND RESPONSE

The results plotted in Figure 7 can be used to explain pillar 

performance in a number of situations and can help to explain 

why pillars can be functionally successful while they may be 

structurally failed.

Loading of Stable Pillars

Consider the response of the pillar with W:H = 8 in Figure 7. 

For a span of 300 m (1,000 ft), the pillar and surrounding rock 

mass will come to equilibrium when the support pressure is 10.8 

MPa (1,560 psi), which is 96% of the tributary area stress. The 

equilibrium point can be seen to occur at decreasing stress values 

as the span is reduced. For example, when the panel span is 45 m 

(148 ft), equilibrium is reached when the stress is 9.4 MPa (1,360 

psi), which is 83% of the tributary area stress. A similar pattern is 

seen for the W:H = 10 pillar, but the impact of the span would not 

be as significant as a result of the increased pillar stiffness.
 

 

The W:H = 6 pillar would be considered to be a structurally 

failed pillar, because its peak resistance is less than the overburden 

stress and its safety factor would be less than 1.0 using the tributary 

area method. However, the ground response curve for the 150 m 

(500 ft) wide panel is seen to intersect the pillar response curve just 

prior the peak, which is considered to be a stable, although near 

critical, situation. As the panel span is decreased, the equilibrium 

points are located at lower stress values. Therefore, the figure 

indicates that W:H = 6 pillars might be expected to be stable under 

the modeled geological conditions if the panel spans are less than 

about 150 m (500 ft), in spite of a traditional safety factor of less 

than 1.0.

The figure also shows that when the panel span is 300 m (1,000 

ft), the W:H = 6 pillars will be loaded beyond their peak resistance 

and equilibrium will be reached after about 4.5% vertical strain. In 

mining terminology, these would be called “yield pillars.”

A review of the ARMPS-2010 (Mark, 2010) case history 

database revealed that a limited number of cases exist where pillars 

with W:H ratios of between 5.9 and 6.3 have been successfully 

extracted under strong overburden at depths of 380 to 450 m (1,200 

to 1,500 ft). The panel width in these cases varied between 100 

and 120 m (330 and 400 ft), similar to the example discussed 

above. The pillars had calculated stability factors of less than 1.0 

on development using the tributary area method. Considering the 

ground response curve helps to explain why the pillars were in an 

acceptable condition. The relatively stiff ground response most 

likely resulted in pillar stresses that were lower than the tributary 

area estimates.

This assessment shows that assuming pillars carry the full 

overburden load up to the ground surface can result in overestimation of the pillar stress, particularly when the spans are small 

and strong overburden is involved.

Stability of Yield Pillars

In the western United States, two-entry gate road systems with 

small yielding pillars are often used (Peng, 2008), while in some 

cases small yield pillars are left adjacent to a wider barrier pillar so 

that the longwall would be protected from bump events associated 

with the large barrier (Iannacchione and Zelanko, 1995). These 

yield pillars may have W:H ratios in the region of 3.0 to 4.0. 

When mining at depths of cover of 300 to 600 m (1,000 to 2,000 

ft), these pillars are likely to be failed on development, yet they 

are considered to be functionally successful. Referring to Figure 

7, which is applicable for mining at a 450 m (1,500 ft) depth, it 

can be seen that if the excavation span across these pillars (pillar 

width plus two entry widths) is in the region of 25 m (80 ft), a W:H 

= 3 pillar would be loaded beyond its peak strength and would 

be considered to be failed, while a W:H = 4 pillar might actually 

still be in its pre-peak state. If more than one row of yield pillars 

were created, the effective span would increase and the ground 

response will change. If the span across the yield pillars was 

45 m (150 ft) for example, the W:H = 3 pillar will yield up to a 

strain value of about 8% before equilibrium is achieved. This may 

result in unacceptable rib and roof conditions and the yield pillar 

system would be considered to be functionally failed. A yield 

pillar system using W:H = 4.0 pillars would be loaded beyond the 

peak strength and would be considered to be structurally failed, 

but since the vertical pillar strain is less than 2%, the conditions 

may well be acceptable and the system would be considered to be 

functionally successful.

This evaluation shows that yield pillars can be successfully 

used if the ground response is such that the pillars are not driven 

to excessive amounts of strain. The stiffness of the surrounding 

strata plays an important role in determining how far the pillars are 

driven beyond their peak strength. When the span-to-depth ratio 

is small, the ground response is stiffer and yield pillars are more 

likely to be successful.

The transition of a pillar from a pre-peak to post-peak, or 

yielded, condition has received much attention in the literature 

(Salamon, 1970; Ryder and Ozbay, 1990; Zipf, 2001). Comparing 

the local ground response to the post-peak slope of the pillars 

can assist in determining whether the transition will occur in a 

controlled or uncontrolled manner.

Pillars at the Extraction Line

When extracting pillars on retreat, the pillars at the extraction 

line become even more severely stressed; yet pillars are extracted 

successfully in spite of the elevated loading. It is possible to gain 

insight into the performance of the pillars under these conditions 

by comparing the ground response at the extraction line to the 

pillar stress-strain behavior and evaluating the likely success of the 

system using the ARMPS (Mark and Chase, 1997) method.

Figure 8 shows the calculated ground response curves at the 

pillar extraction line and under normal cover loading conditions, 

taken from Figure 6. The ground response curves were developed 

for a 150-m (500-ft) wide panel at a 450-m (1,500-ft) depth under 

strong overburden, which represents a typical deep pillar extraction 

layout. The pillar response curves have also been added to the 

chart. The likely pillar performance of the different pillars plotted 

on the chart can be examined:

a) The W:H = 3 pillars are likely to be wholly unsatisfactory 

because their peak resistance is well below the overburden 

pressure and they would be compressed to a vertical strain in 

excess of 10% while under development conditions, remote 

from the extraction line.

b) The W:H = 4 pillars are also likely to be unsatisfactory, 

the vertical strain will be about 7% when remote from the 

extraction line, and the ground pressure will drive the pillars 

to about 9% strain as the extraction line approaches. The 

ARMPS stability factor for this layout is 0.33, which falls well 

below the recommended value of 0.76 for mining at 450 m 

(1,500 ft) in strong rock, indicating that conditions are likely 

to by highly unsatisfactory.

c) The W:H = 6 pillars will be in a critical state of stability 

during development; they will be loaded just below their peak 

resistance, unexpected variation in the stress or pillar strength 

can result in structural failure of the pillars. As the extraction 

line approaches, the pillars will fail and equilibrium will be 

reached at about 5.5% vertical strain. The ARMPS stability 

factor is 0.55, predicting that it is unlikely that pillar extraction 

will be successful.

d) The W:H = 8 pillars will be in a pre-peak stress state under 

development conditions, remote from the extraction line. 
 

 

As the extraction line approaches, the pillars will be loaded 

beyond their initial peak and post-peak yielding will occur. At 

these relatively high stress values, the ground response is stiff 

and equilibrium is reached at a vertical strain value of 3.2%. 

This level of strain is likely to be acceptable, since several 

case histories exist of successful pillar extraction under similar 

conditions. The calculated ARMPS stability factor for this 

layout is 0.76, which falls just below the recommended value 

of 0.8 for mining at this depth in strong roof conditions.

e) The W:H = 10 pillar will also be in a pre-peak state of stress 

during development and will yield with strain hardening when 

it is located at the pillar extraction line. The vertical strain 

will be 2.4%, which is likely to result in satisfactory ground 

conditions. The ARMPS stability factor for this layout is 1.03, 

which is well above the recommended value of 0.8.

The above results apply for a depth of 450 m (1,500 ft) and an 

isolated panel with a span of 150 m (500 ft) in strong strata. If 

the panel geometry, the overburden strength, or the depth-to-span 

ratio changes, the location of the ground response curve will also 

change, affecting the final stress and strain condition of the pillars. 

The importance of the slope of the ground response curve is clearly 

seen. When the ground response curve is elevated by an increase 

in the stress at the pillar extraction line, pillars may be driven to 

excessive strain values, which can result in the functional failure of 

the system.

Figure 8. Pillar stress-strain curves and ground response 

curves at mid-span of a panel that is 150-m (500-ft) wide at 450-

m (1,500-ft) depth of cover under strong overburden strata. 

Ground response curves are shown for development conditions 

and at the pillar extraction line.

Pillar Strain and Functional Failure

The assessment of the various panel layouts and pillar types 

shows that pillars that have been loaded beyond their peak 

resistance (structural failure) do not necessarily imply that 

functional failure has occurred. The ground response determines 

whether yielding pillars will be driven to excessive strain values 

and whether the conditions will be acceptable or not.

Comparing the pillar strain values to the ARMPS stability 

factors shows that for the situation modeled, there appears to be 

a relationship between the pillar strain and the ARMPS stability 

factor for yielding pillars at the extraction line. As the ground 

response drives the yielding pillars to greater strain values, 

the conditions are expected to deteriorate and successful pillar 

extraction is less likely to occur. Assessment of the ultimate 

strain of the pillars provides an improved insight into the likely 

functional performance of pillar systems. Further investigation of 

the relationship between the pillar strain and functional failure of 

pillar systems under various geologies and mining situations needs 

to be carried out to determine whether the pillar strain can be used 

as a design criterion for yielding pillars at the extraction line and in 

longwall mining applications.

CONCLUSIONS

The influence of the ground response curve on ultimate pillar 

loading and pillar deformation has been demonstrated. When the 

span-to-depth ratio is small or when the overburden consists of 

stiff-strong rocks, the ground response is stiffer, and pillar stress 

will be reduced when compared to the tributary area calculated 

stress. However, if the span-to-depth ratio increases or the 

overburden material is weaker and softer, the pillar loading may be 

closer to the tributary area stress.

The slope of the ground response curve also determines the 

ultimate deformation to which pillars, and particularly yielding 

pillars, will be driven. If the ground response is stiff, the ultimate 

pillar deformation will be smaller and may result in satisfactory 

mining conditions although the pillars may have yielded and 

would be considered to be structurally failed. However, if the 

ground response is soft, the yielding pillars can be driven to 

excessive deformation values and the mining conditions may 

become unacceptable.

The study confirmed the importance of the panel span on the 

ground response curve and the ultimate loading and deformation of 

pillars in a panel. The span-to-depth ratio has been added as an 

input parameter in the updated ARMPS-2010 design procedure 

(Mark 2010).

The ultimate deformation of a pillar provides insight into its 

likely functional success or failure. A review of pillar strains and 

calculated stability factors using the ARMPS (Mark and Chase, 

1997) method showed that a relationship appears to exist between 

the ultimate pillar strain and the likely success of retreat mining.

Further research will be required to investigate the relationship 

between pillar strain and successful pillar layouts for a range of 

geologies and mining geometries. For example, the pillar stressstrain curves used in this paper assumed failure occurs within the 

coal only. Factors such as the potential impact of weak roof and 

floor strata on pillar response, the impact of side abutment loading 

from adjacent mining, and barrier pillar deformation should also 

be evaluated.
 

DISCLAIMER

The findings and conclusions in this paper have not been 

formally disseminated by the National Institute for Occupational 

Safety and Health and should not be construed to represent any 

agency determination or policy.

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