Mark Colwell,Russell Frith

a Colwell Geotechnical Services,Caloundra,QLD 4551,Australia

b Mine Advice Pty Ltd.,Beresfield,NSW 2322,Australia

Keywords:Prudent simplification Behavioural mechanisms Support design Delamination Axial stress Buckling

ABSTRACT As per most other earth science engineering problems,the underground coal geotechnical environment and the way in which roof and rib support interacts with the rock mass are complex issues.It is therefore generally recognised that without prudent simplification,the complexity of the problem will overwhelm all current geotechnical methods of modelling,not least for the reason that a rock mass can never be characterised to a level that allows a “non-simplified” analysis.The fact that numerical models,which are commonly purported to be a “simulation” tool and the so-called epitome of advanced geotechnical engineering,always need to be “calibrated” to a known reality is taken to be conclusive proof of this statement.While the problem should not be oversimplified(i.e.the dominant failure mechanisms or critical data input parameters should not be ignored),without question judicious simplification is at the heart of all engineering design,to the point that it has a well-established name–“reductionism”.The hypothesis addressed in this paper,is that horizontal and vertical stress-driven slender beam and column behaviour (which includes unstable Euler Buckling) are respectively the dominant (but not only) roadway roof and ribline behavioural mechanism that (if not controlled) can lead to excessive deformation,failure and eventual collapse.As a part of the Scientific Method,a hypothesis can only be tested via real-world observations,measurements and analyses in establishing it is a credible Theory.Utilising the Scientific Method,this paper demonstrates that slender beam/column behaviour is the dominant instability mechanism within a coal mine roof/rib subject to elevated horizontal/vertical stress conditions and therefore,must be representatively accounted for in any credible empirical,analytical,or numerical approach to coal mine roof/rib stability assessment and associated ground support design.

1.Introduction

Identifying behavioural mechanisms and understanding/applying the associated governing principles is essential to effective engineering in the real world.Furthermore,any attempt to analyse a problem numerically,whether analytically or via modelling software,is likely to produce misleading outcomes if the relevant behavioural mechanisms are not adequately accounted for at a mathematical level.This is deemed to be true of all engineering problems involving the three fundamental elements of:(1) an applied load,(2) the load-bearing capacity of a structure,and (3)resultant displacements leading to the potential for structural failure of some form.

Being able to credibly understand and so analyse both the behaviour of the roof strata above and the coal rib behaviour on each side of a coal mine roadway,is intrinsic to designing effective ground support regimes in the context of the need to achieve both safe mine workings and operational efficiency.The starting point is in demonstrating,beyond a reasonable doubt,the fundamental behavioural mechanisms,irrespective of what approach to engineering design might subsequently be applied (i.e.analytical,empirical or numerical modelling).

In later sections,this paper outlines and details the various coal mine roof/rib behavioural/failure mechanisms which can occur.While more than one behavioural mechanism can conceivably occur,particularly if certain local anomalies are present (e.g.mid-angled planes of weakness),the hypothesis is that one mechanism dominates,namely that of slender beam/column behaviour,which is a process of (1) delamination (or de-coupling) forming slender/thin beams within the roof and columns within the rib which (2) buckle as a consequence of axial loading resulting in(3) shear and tensile failure.

This paper seeks to prove the hypothesis using the rigours of The Scientific Method,so that it can be re-classed as a “theory”,therefore becoming a framework within which observations are explained and predictions can be made.

2.The scientific method

Sir Francis Bacon(1561–1626)is credited with being the first to define the Scientific Method,which was strongly influenced by Nicolaus Copernicus (1473–1543) and Galileo Galilei (1564–1642);and essentially formalised by Sir Isaac Newton (1642–1727) in favour of Bacon’s empirical approach,when he outlines his four “rules of reasoning” in his Principia.

The Scientific Method can be applied to almost all fields of study as a logical,rational,problem-solving method and provides a way of examining the world that allows us to reach conclusions about how it works and that these conclusions can be tested.It is generally an ongoing process,in which researchers review theirs and/or other’s conclusions in the light of new evidence,for example the journey from Newtonian physics to Einstein’s theories of Special and then General Relativity.

With respect to the Scientific Method,some suggest there are six steps while others suggest there are seven with the following considered to be a reasonable summary:(1) make an observation,define a purpose and/or ask a question;(2) construct or propose a hypothesis;(3)design and conduct experiments and collect data to test the hypothesis;(4)analyse the results of the experiments and collected data to form a conclusion;(5) determine whether or not the hypothesis is accepted or rejected and (6) state/communicate the results.

In terms of medical research,Perlmutter simplifies the Scientific Method into four steps as illustrated in the flow chart depicted in Fig.1 (i.e.observe,hypothesize,test and conclude) and indicates that the green clouds to the right of the four steps provide examples of activities involved in each stage,while the pink clouds on the left side are the processes involved in moving through these four stages of the Scientific Method [1].

As noted in Fig.1,clinical trials utilised by the medical profession aren’t simply about assessing potential adverse side effects of a drug,but in fact are an integral component of the Scientific Method employed by the medical profession to help prove or disprove a hypothesis.As Professor Robyn Ward states on the Australian Clinical Trials website,“Knowing what works and what doesn’t is fundamental to the evidence base that underpins medicine.Without it,we are just snake oil salesmen.” Professor Ward’s statement applies to all branches of science and engineering and the absolute need for real-world evidence and justification for the development and use of techniques,processes or interventions for the benefit of humankind.

Fig.1.The Scientific Method (after [1]).

3.Formulating the hypothesis based on observation

To start with,researchers draw up an idea that leads to a hypothesis based on available evidence,such as the results of previous experiments,their own observations and the observations of others.

For example as Galvin[2]states,“In coal mines,the immediate roof and floor strata are usually bedded due to the sedimentary origin of coal deposits.Bedding planes are characterised by low to zero tensile strength normal to the bedding planes and low shear strength relative to that of intact rock.Hence,bedding planes constitute potential slippage planes and can effectively divide the roof strata into an assembly of thin rock beams.”

An example of a physical model of a coal mine roadway (faithfully representing the above observation) is illustrated in Fig.2,which is taken from Hoek and Brown[3]where they state that this figure,“illustrates the buckling of slabs in the roof and floor of an excavation in a high horizontal stress field.This type of failure was observed in model studies conducted by the Australian Coal Industry Research Laboratory (ACIRL) in an attempt to simulate the structural and stress conditions in the coalfields near Sydney,Australia.”

Fig.2.ACIRL coal mine roadway physical model (after [3]).

Hoek and Brown go on to state [3],“In jointed or bedded rock masses,the presence of structural features parallel to the excavation surfaces will result in the formation of plates and slabs,Whatever the reason for the presence of these slabs,it takes little imagination to visualise that they are susceptible to buckling under axial stress.”

With respect to U.S.underground coal mines Mark and Molinda state[4],“Bedding was the factor that was most consistently cited as causing roof problems in coal mines.The two most common examples were weak laminations in shale and thinly interbedded sandstone and shale.” They go on to explain that the issue of bedding(or grain alignment)is further complicated because some rock types may appear massive,but are actually highly laminated.

For this reason,they emphasised the need for testing of the rock material to determine bedding plane/laminae strength even when the bedding is not readily visible and,in this regard,diametral point load testing of borehole core is strongly recommended by Colwell[5].As Hill also points out[6],diametral point load testing on vertically orientated core is highly relevant to assessing the potential for roof buckling due to horizontal stress.

Molinda and Mark detail several possible roof failure mechanisms including horizontal stress driven deformation (similar to that illustrated by Fig.2) of interbedded sandstone and shale layers,which in the U.S.is referred to as “stackrock” [7].

In relation to stackrock,Molinda and Mark state[7],“While this rock unit can be relatively strong perpendicular to bedding(CMRR=40–60),it is often very weak parallel to bedding”.The reality is the strength of the individual sandstone and siltstone matrix will not vary significantly normal or parallel to the bedding.Rather,it is the geometry of the individual beams within the stackrock that causes the significant variation in the strength of the unit(as a whole) when comparing the Uniaxial Compressive Strength(UCS,MPa) as measured in the laboratory normal to the bedding,to its in situ lateral/horizontal load-bearing capacity which dictates the unit’s ability to resist horizontal stress.Other failure mechanisms identified by Molinda and Mark [7] included:(1) “skin failure” which is generally readily controlled by the use of steel roof mesh.(2)roof defects(e.g.faults,low to mid-angle or slickensided discontinuities etc) resulting in block failures.(3) “cutter” roof,or guttering as it is referred to in Australia,typically occurring at the corner or intersection of the roof and ribline,but as noted by Molinda and Mark [7] can occur in the centre or anywhere across the roadway and once again this is driven by horizontal stress and generally associated with laminated material.(4)roof spalling or fall of rock between bolts which progresses upwards and can be due to 1) poor bedding cohesion or a weak rock matrix allowing separation and scale to form between bolts and is driven by horizontal stress or gravity or 2) weathering of moisture-sensitive rocks and(5)roof sag,being the delamination of the roof as a result of gravity.

Molinda and Mark [7] explain that a thorough examination of roof falls will often reveal the contributing factors to the fall,which is not disputed.All of the above have been observed by the authors and are essentially described and discussed by Colwell and Frith[8].However,the hypothesis is that horizontal stress-driven slender beam behaviour (which includes unstable Euler Buckling) is the dominant roadway roof mechanism leading to excessive deformation,failure and significant roof falls (i.e.not simply skin failure).

In developing the roof support design methodology ARBS(Analysis of Roof Bolt Systems),Mark et al.[9]explain that with respect to their research,the “starting point” was an industry that had more than 1,500 roof falls occur each year in United States (U.S.)underground coal mines.The relevant finding to the aims of this paper is that in the development ARBS,the two major factors affecting the outcome(i.e.the level of roof support required)were found to be the Coal Mine Roof Rating(CMRR)and the cover depth,which as Mark [10] states is used as a “surrogate” for horizontal stress because at that time horizontal stresses were rarely measured in U.S.underground coal mines.This U.S.finding is entirely consistent with the hypothesis being examined.The mechanistic link between the CMRR of the bolted interval in the roof and slender-beam behaviour will be addressed in more detail later in the paper.

Based on the previous discussion,in terms of horizontally bedded roof,the major structural feature is clearly the bedding and/or laminae along which delamination (i.e.tensile failure leading to subsequent relative horizontal/shear movements)occurs resulting in thinner (or slender) beams,which can buckle under sufficient horizontal stress with ensuing shear failure of the rock.Fig.3 is photo taken of a roof fall cavity associated with a Queensland colliery and clearly illustrates the formation of slender beams,their thickness(in this instance)dictated by the spacing of the carbonaceous laminae.

The rock type associated with the roof fall cavity depicted in Fig.3 is sandstone with abundant carbonaceous laminae (as illustrated in Fig.4)extending some 5 m above the roofline,which correlated directly with the height of the fall.This type of roof unit(i.e.highly laminated rock;sometimes referred to as laminites and in the U.S.as “stackrock”) is commonly associated with Australian collieries.

In relation to the sandstone unit depicted in Fig.4;the Sonic Derived UCS was approximately 50 MPa.In terms of the Laboratory or Sonic Derived UCS (both of which are measured normal to the laminae) this would be considered a moderately strong to strong rock with respect to coal mine roof strata,however in terms of the approximate average 50 mm thick roof beams associated with Figs.3 and 4 their lateral load bearing capacity over a 5 m wide roadway span is only in the order of 1 MPa.

Fig.5 illustrates another common roof type which displays a roof sandstone unit with substantial laminae.The only core break identified by the exploration geologist is circled in blue,however under sufficient horizontal load(and if there is an underlying void into which the strata can move) this rock unit would also readily delaminate along those laminations circled in red.

Fig.3.Photograph of a roof fall cavity displaying the formation of slender beams.

Fig 4.Photograph of roof core adjacent to roof fall site.

Fig.5.Photograph of sandstone roof core with substantial laminae.

In relation to the Queensland colliery associated with Fig.5;it was found that the roof units typically comprise reasonably competent sandstone (UCS typically 20 to 40 MPa) and it is the frequency and spacing of the laminae that predominantly causes the variation to the CMRR within the typical range of 40–50.

While a more detailed explanation of the CMRR is provided later,at this point it is worth noting that based on the CMRR calculation process,the Effective Fracture Spacing (FSeff,mm) can be determined.TheFSeffclosely approximates the resultant average beam thickness associated with a rock unit which undergoes delamination due to horizontal stress and/or roof sag.

Irrespective of the type of laminae (i.e.carbonaceous,micaceous,siltstone etc.),such laminated or interbedded roof rock units(with varying intensity of laminae/bedding)as well as highly laminated bituminous/humic roof coal units are extremely common to Australian collieries (and most coalfields worldwide).Coal (typically being a highly laminated rock) is in fact the dominant rock/roof unit within the Australian databases associated with ALTS 2009 (Analysis of Longwall Tailgate Serviceability,Colwell and Frith [11]) and ADFRS (Analysis and Design of Faceroad Roof Support,Colwell and Frith [8]).Furthermore,in relation to Australian longwall operations,at any one time it is found that the primary bolted interval associated with approximately 40% to 50% of the mines is either completely coal or contains a significant coal unit.

To further reinforce the laminated nature of coal mine roof;a review of the ADFRS database involving 26 longwall operations was undertaken.The database contains 201 roof rock units associated with at least the first 5 m above the roofline.It was found that the averageFSeffwas 164 mm,while 71 units had anFSeff<50 mm,139 units had anFSeff<100 mm,168 units had anFSeff<200 mm and 188 units(or ≈94%)hadFSeff<500 mm and with respect to the immediate roof (i.e.roof Unit 1),72 of 94 units (or 77%) theFSeff<100 mm.

In terms of the Australian underground coal industry,historically there has never been anywhere near the level of roof falls as that experienced in the U.S.and this is not because Australian collieries’roof is on average“stronger”(e.g.in terms of the CMRR)in fact just the opposite or mine at shallower depths;it is because Australian collieries typically install the required level of roof support on development to prevent such an unacceptable outcome as well as generally employing cut and bolt development(resulting in less roof movement prior to installation of roof support) as opposed to cut and flit development routinely/historically employed by U.S.coal mines.

Most roadway roof falls (and for that matter excessive roof deformation) in Australia are normally associated with longwall retreat and therefore an increase in horizontal stress.With respect to the belt or adjacent travel road that is undeniable,as paraphrasing Newton’s First Law;“a body will remain at rest unless a net force acts upon it” and the only change to the “body” is the approaching longwall face causing a notching of the in situ horizontal stress.

A horizontal stress increase can also occur within the tailgate even though there is an adjacent goaf.However,in this instance the increase in horizontal stress across the roadway is due to Poisson’s Effect as a result of a significant increase in the vertical stress in the adjacent riblines (prior to yield) due to longwall retreat,which has been identified by numerous chain pillar monitoring studies conducted in Australia (refer Colwell [12],Hill et al.[13]and Colwell [14]).

To further understand this dominant axial stress driven deformation (found worldwide),we only need to “turn the problem through 90°” and review ribline performance.

Colwell [15] in “A Study of the Mechanics of Coal Mine Rib Deformation and Rib Support as a basis for Engineering Design”indicates that up to that point in time there had been comparatively little research undertaken(worldwide)in relation to rib support design as opposed to roof support design.However,based on published information,it was in Australia where the bulk of such research had been carried out over the preceding 20 years with four major studies being summarised in the following reports:(1)O’Beirne et al.[16]–Instability and Support of Coal Mine Ribs.ACIRL Published Report 87–3;(2)Fabjanczyk et al.[17]-Summary Report No.2–Factors Affecting Design of Rib Reinforcement,as part of Final Report for AMIRA Project No.P207S–Optimisation of Coal Mine Roof/Rib Reinforcement and Design Methods;(3)Frith and Ditton[18]–Stage 1 and 2 Monitoring Report for Geomechanics of Rib Failure and Development of Appropriate Support Technology,ACIRL Report EGE 3087/1 and (4) Hebblewhite et al.[19]–Rib Mechanics and Support Systems,Final Report–ACARP Research Project C3059.

The study of O’Beirne et al.[16]highlighted two distinct failure mechanisms namely:(1) buckling of plates,slabs or columns due to vertical closure between the roof and floor over the ribside and/or an increase in the vertical stress;(2)existing cleat and mining induced fracture(MIF)interaction,resulting in granular and/or blocky spall.

In relation to the four Australian studies listed;while there is some minor difference of opinion between the researchers in relation to the driving force behind rib degradation,all (except Fabjanczyk et al.[17]) would appear to agree that buckling due to axial loading is a common failure mechanism and all do agree on the negative impact that weak stone bands can have on rib deterioration.

Unlike O’Beirne et al.[16],the actual ribline deformation mechanisms are not clearly identified by Fabjanczyk et al.[17] other than some figures suggesting that slender columns within the ribline will form due an increase in the vertical stress and illustrating the impact of weak claystone bands(refer Fig.6).The initial tensile failure forms a slender column,where the weathered claystone band modifies its end-fixing condition making it more susceptible to buckling which then allows further bucking to occur followed by kinematic or planar failure of the ribline.It is also worth noting that failure commences in the outer rib and progresses further into the rib/pillar which is predominantly the case.

The significant and potentially detrimental impact of weak claystone bands and/or weak coal/roof and coal/floor interfaces on ribline behaviour is well documented,particularly where translation along these weak bands is allowed.Fig.7 illustrates where initial blockside ribline displacement occurs along a weak to very weak 40–50 mm thick carbonaceous claystone band (boxed in red)located approximately 500 mm from the top of seam,with subsequent significant ribline deterioration requiring remedial support.It was found that the greater the lateral movement allowed along the claystone band,the more likely greater levels of overall ribline deterioration.

Fig.6.Effect of weak bands on coal rib deformation (after [17]).

Fig.7.Effect of weak band on blockside rib behaviour.

As Colwell [15] explains;weak bands within a seam appear to have several roles.Where present they tend to act as the ‘hinge’or apex in relation to bulging in the riblines and/or the end point of the buckling slab.When acting as the end point (as illustrated by Figs.6 and 7) typically these weak bands modify the endfixing condition allowing lateral movement.This increases the Effective Length(Leff)of the coal plates or slabs dramatically lowering the critical load or stress for which buckling can occur.The following is provided to assist in understanding how weak bands can modify the end-fixing condition allowing lateral movement and their impact on rib stability.

Table 1 is adapted from information contained in Standards Australia AS 3600–2001:Concrete Structures[20]and summarises buckling behaviour under various end-fixing conditions and the Theoretical K Value (i.e.the effective length factor) dependent on the end fixing conditions.The critical stress (σcrit) at which a column (pinned at both ends) will buckle is given by Eq.(1):

whereEis Young’s Modulus of the column material;Lthe height;anddthe column thickness.

Where the end-fixing condition of the column is pinned–pinned(refer Columnc,Table 1) it will allow rotation of the end but not translation.Varying the end-fixing condition will affect the length of the column over which buckling occurs and that length is designated as the effective length (Leff) such that:

Table 1K values for buckling columns (after Standards Australia AS 3600–2001 [20]).

Unbraced columns (refer Columnsd,eandf,Table 1) are those in which transverse movement of one end is not prevented.This is commonly observed underground either adjacent to a rock/coal interface (where the seam thickness is less than the development height)or adjacent to a weak low friction stone or bright coal band.This results inKvalues greater than 1,longer effective lengths and as a result a lower critical load or stress for which buckling can occur.It is the effective length,Leff,which is substituted into Eq.(1) forLto calculate the critical stress at which a column will buckle.For example,where theKvalue=2,the critical stress at which movement will occur is reduced by a factor 4 (i.e.1/22).Essentially the initial lateral movement along weak bands is simply a form of buckling due to axial loading,subsequent to which kinematic failures can occur as illustrated in Figs.6 and 7.

Frith and Ditton [18] examined the relative nature of the horizontal rib displacement (Urib) to the vertical roof displacement(Uroof) or more precisely the roof to floor convergence.They point out that if the coal rib were a homogeneous material with no fractures or structure,then prior to failure the outward movement of the rib would simply be a result of Poisson’s Effect and therefore be in the order of 0.25 times the roof to floor convergence adjacent to the ribline.However,based on data associated with the monitoring sites of their project and also those of O’Beirne et al.[16],Frith and Ditton [18] found that in the case of unstable ribs,the amount of outward rib movement can be up to several times that of the roof to floor closure.

A dramatic example of this behaviour is illustrated by Fig.8.This photo is taken in the tailgate (TG) of Dartbrook Colliery looking inbye to the TG intersection with the longwall face.As can be seen there is significant lateral displacement of the chain pillar ribline(i.e.in the order of 300 to 500 mm)and yet the roof is in excellent condition and no floor heave was observed.The principal mechanism which explains this relative deformation behaviour between roof,floor and coal rib is buckling due to axial loading,subsequent to which toppling,wedge and planar (i.e.kinematic)failures can occur.

Colwell [15] found that the ribline displacement profile would readily match the type,level and effectiveness of the rib support.Fig.9 is a photo taken of Crinum colliery’s tailgate chain pillar ribline (utilising steel bolts and mesh) just outbye of the tailgate intersection with the longwall face.The shape of the ribline displacement profile is consistent with Column (a) of Table 1,such that the steel bolts are modifying the end-fixing condition of the buckling ribline resulting in aKvalue <1.

The field investigations associated with Colwell [21,15],which resulted in the Analysis and Design of Rib Support (ADRS) design methodology,involved the collection of information from 26 collieries with seven of those collieries also participating as instrumentation sites involving 33 monitoring locations resulting in a large body of data in terms of observation,measurement and analysis.

Fig.8.Dartbrook colliery ribline behaviour under TG loading conditions.

Fig.9.Chain pillar ribline just outbye of TG intersection–Crinum colliery (after [21]).

A review of the Australian ribline database found that the average face cleat spacing was 125 mm and that 13 of the 26 collieries had a cleat spacing of <50 mm,while for 18 of the 26 the cleat spacing <100 mm.When mining-induced fractures are included;then as Hoek and Brown [3] indicate,it is clearly evident slender columns can readily form and buckle due to axial loading.

The extensometry and stress cell data also confirmed the visual observations,such that Colwell [15] formed the strong view that the dominant behavioural mechanism associated with ribline degradation is a process of delamination(or de-coupling)occurring along the cleat,coal joints as well as mining-induced fractures forming slender columns which buckle as a result of axial loading(i.e.vertical stress) eventually resulting in shearing through the buckled columns (as illustrated in Fig.10),subsequent to which toppling,wedge and planar (i.e.kinematic) failures can occur.It was also recognised that other far less common behavioural mechanisms can also occur under specific conditions.

Fig.11(a photo from a U.S.coal mine)is another dramatic illustration of the horizontal stress-driven roof failure mechanism previously described (i.e.delamination,buckling with ensuing shear failure of the rock).Figs.10 and 11 clearly reinforce the previously referred to statement of Hoek and Brown[3],“In jointed or bedded rock masses,the presence of structural features parallel to the excavation surfaces will result in the formation of plates and slabs,Whatever the reason for the presence of these slabs,it takes little imagination to visualise that they are susceptible to buckling under axial stress.”

Therefore,based on the substantial real-world observations of the authors and others (including physical modelling) this would strongly support the hypothesis and the Scientific Method then continues with experimentation,measurement and analysis.

Fig.10.Blockside ribline buckling–Appin colliery (after [21]).

Fig.11.Coal mine roadway roof displaying buckling and shear failure due to horizontal stress (after [22]).

4.Experimentation,measurement and analysis

With respect to the underground coal industry,the measurement and analysis of actual roof and ribline behaviour is primarily obtained via extensometry data and in terms of experimentation,similar to the medical profession,statistical analysis can be utilised help prove or disprove the hypothesis.Several independent databases have been formulated in Australia and overseas utilising the CMRR for both roof support and chain pillar design,which provide invaluable insights in relation to the aims of this paper.

4.1.Extensometry–Measurement and analysis

As the roadway is developed,the in situ stress reorientates and there is a natural tendency for the surrounding strata(i.e.roof,ribs and floor) to move towards the roadway centre.It is generally at this point (i.e.as the surrounding strata moves towards the roadway centre) that ground support (in the form of primary roof and rib bolts) is introduced into the rock mass system to reinforce the rock and coal so as to restrict this displacement to operationally acceptable levels.

Hoek and Brown[3]state,“...thin plates will buckle more easily than thick plates.This suggests that an effective method for reinforcing an underground excavation in which slab buckling is considered to be a problem is to pin the slabs together by means of short rockbolts.”

Fig.12 is a sonic probe roof extensometer plot (where the anchors are at approximately 0.3 m intervals) which illustrates the behaviour (or response) of a section of maingate roof prior to and during longwall retreat.Fig.12 clearly illustrates both how the roof delaminates into thinner beams and also how the 1.8 m bolts (that were utilised to reinforce the immediate roof) modify the beam behaviour via the roof reinforcement mechanism of“beam building”.The concept being that the bolts and cables create“thicker” beams within the reinforced section (or the primary bolted interval) and that a thicker beam will have a greater axial load bearing capacity than a thinner beam,this being consistent with the above statement of Hoek and Brown [3].Similar roof behaviour to that displayed in Fig.12 is found routinely where significant roof displacement has occurred.

Based on measured roof behaviour using sonic probe extensometry,Fig.13 illustrates a commonly held model for the development/progression of roof softening,which is detrimental to overall roof stability.The main point of note in relation to Fig.13 is that roof softening progresses higher into the roof as a series of discrete “steps” with such steps only occurring once certain levels of total roof displacement (TRD,mm) have been exceeded in the underlying roof strata.

The behavioural logic behind this is that roof buckling at any given horizon in the roof can only occur if there is an underlying void into which the strata can move.Therefore for buckling of higher roof measures to take place,the underlying strata must have displaced vertically by a certain amount (i.e.only 10 to 20 mm TRD is required),resulting in a void within the strata into which higher measures can move.As previously indicated,this process is described as one of strata “de-coupling.”

Fig.12.Roof behaviour adjacent to longwall extraction.

Fig.13.Roof softening progression with displacement (after [23]).

Conversely,if softening of the roof above a certain level can be prevented by limiting roof displacements (in the lower roof),the higher de-coupling process can be prevented.Accepting that allowing roof softening to progress higher into the roof detracts from roof stability,it is self-evident that limiting the displacement of the lower or immediate roof should be a primary objective of effective strata control.

The other significant point of note with respect to Fig.13 is that the curves rapidly extend to around 2 to 3 m above the roofline for total roof displacements of 10 to 20 mm and then tend to flatten off.This suggests that roof softening to 3 m can occur quite rapidly at relatively low roofline displacement levels providing the condition by which buckling of the roof layers(due to horizontal stress)within this zone can occur,however an equilibrium (or load balance)is reached prior to shear failure such that further vertical displacement is controlled.

Fig.13 also demonstrates that softening above 3 m becomes increasingly more difficult to propagate as disproportionately higher levels of roof displacement in the lower roof are required all of which is consistent with Fig.12.Furthermore,if one assumes that the shear stress distribution and deformation is parabolic in the roof,then the maximum height of softening should be approximately 2/3 of the span(i.e.approximately 3 m for a 5 m span)with higher softening only then occurring if the immediate 3 m roof section is allowed to displace excessively.

Typically with 10 to 20 mm of total roof displacement the roof is still under reasonable control (i.e.the roof achieves a load balance equilibrium),however it is once these levels are exceeded that there is a far greater likelihood for a loss of control leading to a roof fall.For this reason AMCMRR (Analytical Model for Coal Mine Roof Reinforcement [24]) employs a design process to reinforce those slender beams that would form in the immediate 3 m roof section,via the reinforcement mechanisms of“beam building”(i.e.bolts and cables) and mechanical advantage associated with longer pre-tensioned cables anchored well above the 3 m roof section,so as to resist buckling and provide an adequate Factor of Safety (FOS) to prevent further roof deterioration that could lead to a roof fall.The interested reader is referred to Colwell and Frith[8,24] for a complete description of how these reinforcement mechanisms and the related mathematical equations are readily employed.

To further reinforce the above discussion,with respect to the critical nature of the 3 m roof section to overall roof stability,further evidence is to found via ACARP Project C19008 from which the ADFRS design methodology was developed(refer[8]).With respect to the two-pass faceroad dataset(involving 207 cases)it was found that for the 134 satisfactory cases the average TRD was 13.9 mm with an average height of softening (HOS) of 2.99 m,while for the 33 manageable cases the average TRD was 42.5 mm with an average HOS of 5.20 m and for the 40 unsatisfactory cases the average TRD was 101.7 mm with an average HOS of 5.84 m.

Colwell and Frith[8]also found the AMCMRR 1st Pass FOS to be an excellent predictor of the overall success of the fully widened faceroad.Within ADFRS it is referred as the 1st Pass Reinforcement Index (RF5m-yield) and provides both an analytical/mechanistic and empirical basis in relation to the roof reinforcement required in respect of (in this instance) the 5 m roof section associated with the 1st pass drivage prior to widening to ensure a successful outcome.

Fig.14 illustrates measured movements within a coal mine(Angus Place colliery) rib being subjected to increasing vertical stress during longwall extraction [21].While remembering that the average development height in Australia is approximately 2 m less than the average roadway width and therefore the relative parabolic nature of softening is less;the general similarity with the measured roof and rib displacement behaviours contained in Figs.12 and 14 is stark,which strongly infers that the behavioural mechanisms,and hence the general geotechnical drivers,within a deteriorating coal rib are likely to be no different to those at work within the roof strata.

Fig.14 details the resultant chain pillar rib displacement for both the maingate (following the passage of LW 26) and tailgate loading conditions with LW 26 N faceline level with the instrumentation site.A more detailed examination of the measured ribline behaviour provides further evidence that buckling due to axial loading is the dominant behavioural mechanism.

Following the passage of LW 26 the total ribline displacement was approximately 50 mm,with increasing displacement occurring during the approach of LW 26 N.Then with the LW 26 N faceline 8 m inbye of the monitoring site there is a dramatic increase in total ribline displacement from ≈90 mm to 170 mm,however there is very little movement with respect to the other rib extensometer anchors.It is worth noting that the adjacent roof extensometer recorded only 5 mm of total roof displacement (TRD)and there was no observed floor heave (i.e.minimal roof to floor closure) and yet significant lateral rib displacement consistent with buckling due to axial loading.

While it is possible that σcritwas exceeded for the coal plate/slab(s) that had been formed,it is far more likely that the coal plate/slab(s) within the immediate (0.75 m) rib separated into two or more thinner slabs (similar to that illustrated in Fig.10)resulting in a sudden and rapid increase in horizontal rib displacement i.e.further buckling.If for example a coal plate/slab separates into two thinner slabs of equal thickness then based on equation(1),σcritdrops by a factor of 4.

Fig.14.Chain pillar rib extensometer–Angus Place colliery (after [21]).

In terms of civil or static structures,buckling is often described as acatastrophicfailure mechanism,in that there is a sudden change to the configuration of the structural element(i.e.a column or beam either buckles or it doesn’t and this change of state can occur due to a small change in stress or plate dimension),with this behaviour being clearly illustrated via Fig.14.Furthermore,it also demonstrates why in our environment roof,rib and floor can move from a relatively static condition (where the forces are in equilibrium) to that of rapid displacement potentially leading to a fall of ground.

4.2.Empirical (statistical) analyses

As previously indicated,in terms of experimentation and similar to the medical profession,statistical analysis can be utilised help prove or disprove the hypothesis.In relation to this aspect several independent databases have been formulated in Australia and overseas utilising the CMRR for both roof support and chain pillar design.

The CMRR was originally developed by the United States Bureau of Mines(USBM)in the early 1990′s as an engineering tool to quantify descriptive geological data used in coal mine design and roof support selection and was adapted from Bieniawski’s [25] roof mass rating (RMR).

As Mark and Molinda [26] explain;the CMRR was developed because none of the existing rock mass classification systems adequately provided for the layered geology and geologic structures typical of coal mine roof.They go on to state,“It employs the familiar format of Bieniawski’s roof mass rating (RMR),summing the individual ratings to obtain a final CMRR on a zero to 100 scale.It is also designed so that the CMRR/unsupported span/standup time relationship is roughly comparable to one determined for the RMR.To verify the procedure,field data were collected from nearly 100 mines in every major coalfield in the U.S.” The CMRR was first introduced to Australia as a part of the original ALTS project conducted in 1997/8 [12].

The original ALTS design methodology [12] and ALTS II [27]specifically dealt with tailgate design for the vast bulk of tailgates/chain pillars subject to double pass longwall extraction with the focus being the tailgate intersection performance with the retreating longwall face as the design condition.

As a result of the ALTS 2006 project;ALTS 2009 now contains roof support design modules for Maingate Belt Road (MGB) roof support design as well tailgates subject to Single and Super Stress Notch conditions.The interested reader is referred to Colwell and Frith [11] for a more detailed description of ALTS 2009,however for the purposes of this paper the development of the MGB roof support design module within ALTS 2009 will be used in relation to the hypothesis put forward.

4.2.1.Calculating the CMRR

While the calculation of the CMRR is discussed in far more detail by Mark and Molinda [26,28] and Colwell [5];the following summary is provided for the purposes of this paper.

The CMRR consists of individual Unit Ratings (UR’s),which assess the structural competence of individual rock (stone/coal)units within and above the primary bolted interval,and adjustments which consider the geotechnical competence of all the units in association with one-another.

The UR’s are the basic building blocks of the CMRR.Units are defined as rock intervals with distinct structural characteristics.While units are also commonly distinct lithological types,it is stressed that the individual rock units are distinguished by geotechnical,not geological,characteristics.The UR is calculated based on the following information specifically associated with the rock unit under consideration:

(1) The UCS (MPa),averaged over the unit thickness which is converted to a UCS Rating.

(2) Geotechnical logging of the core which results in the calculation of the Rock Quality Designation(RQD)Index(Deere&Miller[29])and Fracture Spacing(FS,mm),specifically with respect to the unit under consideration.

(3) The FS had been defined as the average spacing (mm) of actual core breaks or fractures within the geotechnical unit(e.g.if there are 8 pieces in a 1 m long section of core then the FS=125 mm).However,as will be discussed,this definition has been modified to benefit this assessment.

(4) RQD and FS Ratings are then determined and the lower of the two is the resultant Discontinuity Spacing Rating (DSR).

(5) Diametral point load testing of the core resulting in the diametral point load test (Diametral PLT) strength index(DiametralIs(50),MPa),which is averaged over the unit thickness,such that the Average DiametralIs(50)is then converted to the Diametral PLT Rating.

(6) The lower of the DSR and Diametral PLT Ratings is typically used as the Discontinuity Rating.

(7) An estimate of the rock unit’s moisture sensitivity,which is converted to Moisture Sensitivity Deduction being a negative value.

Individual Unit Ratings are then determined based on the above where;Unit Rating=UCS Rating+Discontinuity Rating+Moisture Sensitivity Deduction.

The Moisture Sensitivity Deduction is applied only if a unit is moisture sensitive and is exposed to a level of moisture that would cause structural deterioration of the unit.Where this does occur,it can have a significant impact on roof stability and a deduction of up to 15 points can be applied for rocks that rapidly disintegrate in contact with water.

It is fully recognised that where these factors coincide (i.e.moisture sensitive roof units that are exposed to a level of moisture that would cause structural deterioration of the units) this can become the dominant mechanism leading to roof deformation;however,Australian collieries typically experience mostly dry conditions and therefore while assessing the Moisture Sensitivity Deduction is crucially important;it is generally not a major factor with respect to the individual UR calculations associated with the Australian databases.

The Thickness-Weighted Average of the UR’s within the bolted interval (Roof Ratings Weighted–RRw) is then adjusted for the effects of the Strong Bed,Unit Contacts,Groundwater and the Surcharge to determine the CMRR,such that;CMRR=RRw+Strong Bed Adjustment+Unit Contact Adjustment+Groundwater Adjustment+Surcharge Adjustment.

Like the Moisture Sensitivity Deduction;it is crucially important to properly assess the abovementioned adjustments as recommended by Colwell [5] prior to calculating the CMRR;however,in terms of the Australian databases associated with ALTS and ADFRS(as opposed to a specific colliery)the adjustments typically have a secondary impact on the CMRR calculation.

It is the UCS and discontinuities(and resultant UCS and Discontinuity Ratings)associated with the primary bolted interval which are the principal determinants with respect to the resultant CMRR values associated with the ALTS and ADFRS databases and therefore it is their evaluation and mechanistic impact that are the primary focus of this paper.

Once the Average UCS of the unit has been determined,it is converted to a UCS Rating as graphically illustrated in Fig.15 and ranges from a minimum of 5 points to a maximum of 30.

For coal measure rocks the UCS will typically range between approximately 5 MPa (e.g.weak coal and carbonaceous material)to 80 MPa (e.g.sandstone and strong conglomerates) and therefore,as also illustrated on Fig.15,in practical terms there is typically only a 15 point variation such that for every 5 MPa increase there is approximately a 1 point linear increase in the UCS Rating and accordingly a 1 point increase in the UR.Mark and Molinda[28] indicate that approximately one-third of the CMRR is determined by the UCS Rating.

The Discontinuity Rating is primarily meant to “capture” the very practical and mechanistic effect of how a unit will delaminate(or de-couple) under sufficient horizontal stress.

Once the units have been identified,the RQD and FS are calculated for each unit based on the information recorded while the core is in the“splits”and the core photography is particularly useful in this regard and should always be reviewed.As more than one geotechnical unit may be contained within a core run or a unit may overlap between core runs,it is important that care is taken to calculate the RQD and FS for each unit rather than simply each core run.

Fig.15.UCS (MPa) converted to UCS rating.

Following photographing,boxing of the core and the removal of any samples for laboratory testing;where the core allows then axial and diametral point load testing should be conducted to obtain a representative Average AxialIs(50)and Average DiametralIs(50)values.

As discussed by Mark et al.[30],the RQD,FS,Average DiametralIs(50)are then converted to RQD,FS and Diametral PLT Ratings utilising formulae and rules/limits,which were derived from the original CMRR discontinuity rating tables associated with the Underground Method.The Discontinuity Rating varies between 18 and 60 (or a 42-point spread) and accordingly has a far greater weighting or impact on the UR and CMRR calculations,reinforcing that like most other rock mass classification systems,the CMRR(representing the structural competence of coal mine roof) is determined primarily by discontinuities that weaken the rock fabric.

In relation to assessing the FS,a significant update relates to the following where Mark and Molinda[28]state,“Fracture spacing is easily determined by counting the core breaks in a particular unit,and then dividing by the thickness of the unit.”

To both emphasise the importance of the role of bedding/laminae and realistically account for its effect in assessing the FS,Colwell [5] strongly recommends that for laminated rock types;“if in the opinion of the geotechnical engineer insufficient diametral point load testing has been conducted with respect to the laminae/bedding and/or it is assessed that the laminae/bedding are essentially weak contacts along which delamination will readily occur then these laminae/bedding can be included as fractures within the rock unit and the FS should be recalculated accordingly.” A textbook example as to why this recommendation is made was illustrated in Fig.5,which displays a roof sandstone unit with substantial laminae and yet only one actual core break.

It is also very important to note that the original CMRR discontinuity rating tables associated with the Underground Method can also be used to rate the laminae/bedding to return a Discontinuity Rating.However,in assessing the UR from core,it was considered the above recommendation to be more appropriate.

Fig.16 clearly illustrates the effect of the FS on the resultant Discontinuity Rating.As opposed to the UCS Rating where there is essentially a linear increase of 1 point for every 5 MPa increase from 5 to 80 MPa;Fig.16 reveals a logarithmic relationship where there is rapid increase in the Discontinuity Rating particularly over the initial 200 mm change in the FS.

Fig.16.Discontinuity Rating vs.Fracture Spacing (mm).

As previously indicated,following the process by which the UR is assessed the Effective Fracture Spacing (FSeff,mm) can be determined,which closely approximates the resultant average beam thickness associated with a rock unit which undergoes delamination due to horizontal stress and/or roof sag.

TheFSeffis a data output parameter associated with the geotechnical logging and diametral point load testing of a rock unit.While the Fracture Spacing(FS,mm)is the actual value associated with the geotechnical logging of the core in the“splits”,theFSeffis calculated utilising the unit’s UR and UCS Rating(UCSR)via the following equation and rules:

Rule 1.If the calculatedFSeff>Unit Thickness (UT) then theFSeff=UT.

Rule 2.If the RQD is used to calculate the UR then if theFSeff>FSthen theFSeff=FS.

4.2.2.Maingate belt road analyses

The change and increase in horizontal stress in the roof that occurs about the belt road intersection with the longwall face during retreat extraction is often referred to as Maingate Stress Notching.The magnitude of the resultant stress (in MPa) is denoted as σR-MGB and the interested reader is referred to Colwell and Frith[11] where its calculation is fully detailed.

In developing an empirical model;the initial approach is to clearly identify what is the desired outcome and then to assess(via a literature review and using one’s own experience) what are the important factors affecting (or significant predictors of)that outcome and most importantly the initial concept and the eventual geotechnical design technique developed is consistent with Newton’s Laws,which govern the physical world associated with an underground coal mine.

In terms of an Australian longwall mine’s belt road;the desired outcome is to quantify the level and type of roof support(as well as timing of installation) required to maintain satisfactory roadway conditions during and subsequent to development and up to the maingate belt intersection with the retreating longwall face.

In terms of any coal mine roadway,it is necessary to take into consideration that it is not just a roof fall that would be considered an unsatisfactory outcome as practical mining considerations require that the roof be maintained with a satisfactory level of stability during longwall retreat so as to minimise any potential negative impact on longwall production,knowing that productivity and safety can be adversely affected by excessive roof convergence trapping equipment(e.g.stage loader)or deteriorating roof conditions necessitating the installation of remedial roof support.

It also needs to be recognised that with respect to belt roads,the installation of remedial support about the belt is difficult,will inevitably cause production stoppages and is essentially unacceptable,unlike a tailgate where a low or moderate level of remedial support in isolated areas (while of course never desirable) would be likely to have a lesser impact on safety and/or productivity.Therefore,a more conservative approach to belt road roof support design(as compared to a tailgate where there is also the option of standing support) is understandable and warranted.

However,once again in terms of practical mining considerations,it is important to appreciate that an overly conservative roof support design may result in the belt road roof“hanging up”in the goaf inbye of the longwall supports causing ventilation problems.Ground support design associated with coal mine roadways is far different from a civil construction associated with tunnelling and has unique challenges.

The next part in the development of the model is to start with a simple concept,to which one can subsequently add the layers of complexity if or as required.In this instance(and with experience)the initial assessment was made that the level of support required to maintain satisfactory roadway conditions throughout the mining cycle,would primarily be a function of 1) some measure or index that relates to the structural integrity/lateral strength of the immediate roof and 2) the horizontal stress acting across the roof as a result of roadway formation then subsequently the belt road horizontal stress concentration effect associated with longwall retreat (i.e.σR-MGB).

With respect to the CMRR (and therefore the primary bolted interval)the above concept or model for the belt road intersection with the retreating longwall face is illustrated by way of Fig.17.The Ground Support (GRSUP) Rating is a measure of the bolt and longer tendon roof support capacity (kN) per square metre of roof normalised to the primary bolted interval(boxed in red).The interested reader is referred to Colwell and Frith [11] where the calculation of GRSUP is fully detailed.It is also very important to note that it will be the data analysis that will verify or disprove the concept/model (as a part of the Scientific Method) and not the other way around.

It should be noted that σR-MGB is also calculated specifically with respect to the primary bolted interval and therefore the Young’s Modulus (E,GPa) and Poisson’s Ratio (ν) of the rock units associated with bolted interval are required as the in situ stress measurements are typically conducted in roof units above the bolted interval or below the coal seam.

It is recognised that σR-MGB is an approximation and not an“exact” calculation and therefore while its units are MPa (as used within an analytical model),within an empirical model σR-MGB is an index that is utilised to “capture an effect”,which in this instance is the stress notching effect about the belt road intersection with the retreating longwall face.Ultimately it is the strength of the various statistical relationships that will determine how useful these indices are.

The type of statistical technique which is used to analyse a database will primarily depend on whether the outcome(referred to as the dependent variable)is continuous or categorical.In relation to ALTS,ADRS and ADFRS,extensive use is made of logistic regression(where the outcome is categorical),multiple linear regression,linear regression as well as mean and standard deviation.

As previously discussed,the installation of remedial support about the belt is essentially unacceptable and therefore in developing an empirical method for maingate belt road roof support design only those cases with a satisfactory outcome were utilised,i.e.there were no production delays or safety concerns attributable to roof instability or ventilation issues and certainly no roof falls or remedial roof support measures required.

Fig.17.Maingate belt road empirical model.

For MGB roof support design,the desired outcome is to quantify the level of support (GRSUP) to maintain satisfactory roof conditions and is therefore a continuous outcome,with potentially the CMRR and σR-MGB as the significant predictors of that outcome.Therefore,in this instance the most appropriate statistical technique to use is multiple linear regression.

The maingate belt road database comprises 58 satisfactory cases representing 33 longwall operations where the CMRR ranges from 25 to 77 and the cover depth ranges from 100 to 510 m.Fig.18 plots GRSUP against the CMRR and σR-MGB and while a strong relationship exists between simply GRSUP and CMRR (i.e.R2=0.73),with the inclusion of σR-MGB the correlation increases significantly and is an extraordinarily high 0.89.The GRSUP vs.CMRR relationships for varying stress levels acting across the roof(i.e.σR-MGB) fit seamlessly within the upper and lower boundaries.The maximum σR-MGB associated with the maingate belt road database is approximately 45 MPa.

The real test of any rock mass classification index(or any of the indices)when used as a part of a ground support design technique is the strength of the correlations.In simple (and practical) terms,theR2of 0.89 associated Fig.18 essentially means that 89% of the reason why Australian collieries select the required level of belt road roof support is a function of the CMRR and σR-MGB.In relation to the 11% not accounted for directly by the relationship,this would include a number factors other than the purely geotechnical considerations;a perfect example being the variability in the quality and timing of bolt and cable installation across the industry.

It is accepted that in statistics“correlation does not necessarily prove causation”,in other words one shouldn’t deduce a causeand-effect relationship between variables solely on the basis of an observed association or correlation between them.However,the mathematical science of statistical analysis associated with the ALTS and ADFRS databases is a legitimate and crucial part of the overall observational process to help prove or disprove the hypothesis being totally consistent with the use of clinical trials employed by the medical profession (refer Fig.1).

AnR2value of 0.89 for a geotechnical database is an exceptional outcome and almost certainly confirms that the mechanics of the problem under analysis have been fully incorporated into the inputs,namely the CMRR and horizontal stress acting.It is noted that it is not only the ALTS database that returns such a high statistical correlation between CMRR,horizontal stress magnitude and required ground support;the ADFRS database for wide roadways(Colwell and Frith[8])which represents an entirely different database to that of ALTS,returns similar correlations.

Fig.18.GRSUP vs.(CMRR and σR-MGB).

These statistical correlations provide further evidence of the link between the hypothesis being tested and real world experience.

5.Assessment of the CMRR using slender beam theory

In relation to the extraordinary high roof support correlations(typically between 0.8 and 0.9) associated with ALTS and ADFRS,why and how did this come about? It is either a statistical fluke that has “accidently” worked for several independent databases in Australia and overseas (which is not credible reasoning),or the manner by which the key parameters(UR,CMRR and horizontal stress) have been calculated in those databases are credible.

The weighting or relative impact of the two dominant factors(i.e.UCS and the average spacing of the bedding/laminae)in calculating the UR and CMRR is consistent with established beam theories,in that beam geometry (and its end-fixing conditions)dominate,as compared to the beam’s intact material properties(e.g.UCS),when calculating the beam’s axial load bearing capacity.Utilising information from the ADFRS database,the following example is provided to illustrate.

With respect the 201 ADFRS roof units,the average UCS is approximately 35 MPa with 94%having an averageFSeff<500 mm and approximately 75% theFSeff<100 mm.The average Modulus(E,GPa):UCS (MPa) ratio is 0.26 and therefore for a UCS of 35 MPa an averageEof 9.1 GPa would be returned.The ADFRS database also revealed that the average 1st Pass roadway width employed is 5.1 m,which also reflects the average gateroad and mains drivage width.

Colwell and Frith [24] detail the process by which the Axial Load Bearing Capacity (MPa) of a column/beam (length,L) with increasing thickness (d) is calculated moving from long (slender)columns/beams that fail due to buckling through intermediate to short(stumpy) columns/beams which will fail in simple compressive failure;that is when the load (MN)/area (m2) of the column/beam exceeds the allowable stress.Column/beams of intermediate slenderness exhibit a combined failure mode involving both yielding and large lateral deflections.

As previously discussed,the end-fixing condition of the beam will have a significant impact on its load bearing capacity.With respect to coal mine roof beams Galvin [2] states,“In most cases of practical interest,values ofKof about 0.6–0.8 can be expected to apply”.However due to the possible/probable presence of subvertical jointing Colwell and Frith [24] suggest aKof 1 is more appropriate.

Utilising the average values detailed in the preceding paragraphs,Fig.19 is produced which displays both Axial Load Bearing Capacity(MPa)and UR for a variableFSeffup to 2000 mm.For simplicity the yield strength is taken to be equal to the UCS(being brittle failure).Utilising a constant UCS of 35 MPa;the UCS Rating is also a constant of 12.5 such that the variation in the UR is solely due to the variation in the Discontinuity Rating based onFSeff.

Fig.19 confirms that up to approximately 500 mm,it is the change in the beam thickness that dominates the Axial Load Bearing Capacity (MPa) of the beam and that the change in the UR (in this case solely due the increase in the Discontinuity Rating)is consistent with the change in the beam’s axial strength.

In an attempt to assess the impact of both a change in the UCS and beam thickness on the beam’s Axial Load Bearing Capacity(MPa)Fig.20 has been produced.In this instance the typical range of 5 to 80 MPa for coal mine roof strata has been utilised.The reasonable assumption has been made that as theFSeffincreases the more “massive” the unit becomes and accordingly its UCS and E would typically increase.It is fully recognised that there will be rock types that have material properties,such as that depicted in Fig.4,that are not consistent with this assumption;however,the material properties listed on Fig.20 are considered to be a reasonable approximation so as to simply assess and demonstrate the relative impact of UCS and beam thickness on the beam’s axial strength.TheFSeffof 8.7 mm is back-calculation associated with a highly broken unit where the RQD=0 resulting in the minimum Discontinuity Rating of 18.

Fig.19.Axial Load Bearing Capacity (MPa) and UR vs.Effective Fracture Spacing(mm) with a constant UCS=35 MPa and E=9.1 GPa.

Fig.20.Axial Load Bearing Capacity (MPa) and UR vs.Effective Fracture Spacing(mm) utilising variable UCS and E with a constant E (GPa):UCS (MPa) ratio=0.26.

The change in UR is now almost entirely consistent with resultant Axial Load Bearing Capacity(MPa)of the beam and mechanistically explains why the extraordinary high ground support correlations associated with ALTS and ADFRS are not a “statistical fluke”.Therefore the statement by Galvin[2]that,“the CMRR does not take account of behaviour mechanisms” is both simplistic and incorrect and illustrates how a superficial and biased review of a rock mass classification system,similar to that described by Barton and Bieniawski [31] with respect to RMR and Q (with their references to Palmstrom and Broch [32] and Pells and Bertuzzi [33]),leads to “misconceptions” that unfortunately influence others and require (as Barton and Bieniawski [31] state) “Setting records straight”.

Therefore,it is logically concluded that the CMRR is not simply a numerical rock mass “index”,but a rock/roof mass classification system that is founded in the first principles of structural engineering and so can be used with a high degree of confidence by the underground coal industry in assessing the structural competence of the bolted mine roof interval for roof support design purposes.

Furthermore,remembering that the CMRR was developed to adequately provide for the layered geology and geologic structures typical of underground coal mines,as a “model” the CMRR is consistent with the structural component of the ACIRL physical model(Fig.2);while the ALTS and ADFRS models are then consistent with the ACIRL physical model as a whole simulating the typical structural and stress conditions associated with the vast bulk of Australian collieries.

6.Dissenting views and oversights based on numerical modelling

Despite nearly 40 years of intensive research and proving work in this subject area,there remain dissenting views that slender beam/column behaviour and buckling of roof strata and riblines(due to axial loading) is not a dominant behavioural mechanism(e.g.Gale [34] and Heritage [35]).Furthermore,numerical models(as utilised by the underground coal industry) continue to ignore this basic behavioural mechanism.As a part of the Scientific Method it is important to review such views and understand why slender beam behaviour is being ignored by the “numerical modelling fraternity” as this may disprove the hypothesis.

Gale [34] forms his views in relation to roof and ribline deformation predominantly based on desktop numerical modelling studies founded on his understanding of the underground coal geotechnical environment,while Heritage [36] utilises numerical modelling (i.e.FLAC 2D) to “validate” the inferred failure mechanisms for the rib deformation related to the three monitoring sites associated with her project.

Best reported that the basic tool of the structural analyst is the mathematical theory of elasticity [37].He went on to state that based on the assumption of continuum behaviour this theory establishes a set of differential equations that describe the load–deflection (stress–strain) behaviour of a typical elemental region within the body.A given problem is solved by obtaining a solution for the differential equations that also satisfies the boundary conditions of the problem.The theory of elasticity provides the fundamental relationships that form the basis of numerical methods of solution.

However,the theory of elasticity is restricted to materials in which the load–deflection behaviour is linearly elastic and as rock yields and displays both linear and non-linear behaviour,the theory of plasticity needs to be incorporated within the analyses of rock behaviour,Hill[38].The inclusion of plastic behaviour as well as taking into account the discontinuities within the rock mass(which introduce additional boundary conditions over those existing in a corresponding continuum) significantly increase the difficulty of realistically modelling rock behaviour using numerical methods.

Over the last 40 years these issues have presented researchers with an ever-evolving challenge to select(or calibrate)the mathematical routine that best represents the expected physical behaviour of the rock mass.In contrast to ACIRL’s physical model(Fig.2);numerical modelling researchers for reasons of either numerical code limitations or computing processing power have been typically considering geometries (or setting up their models)which contain structural elements that,by their very nature,cannot buckle and must therefore fail in shear or the models simply do not contain the necessary mathematical routines to representatively incorporate buckling (e.g.Wu [39]).

Recently,Abousleiman et al.[40]and Esterhuizen et al.[41]discussed coal mine roof deformation mechanics and roof support design as a part of parametric studies using numerical models.Abousleiman et al.[40] utilised the discrete element method(DEM)approach in Itasca’s Universal Distinct Element Code(UDEC v.6.0),while Esterhuizen et al.[41] utilised Itasca’s FLAC3DV5.1 finite difference software package.

Both studies emphasise the need for calibration prior to utilising the proposed models for design purposes.In relation to numerical methods,Abousleiman et al.[40] state,“When using such an approach,calibration to existing empirical relationships is imperative to ensure that numerical model results are realistic.”,while Esterhuizen et al.[41] indicate that their roof stability rating(RSR) is,“biased towards coal mine operations in the eastern U.S.”,where field studies had been conducted to calibrate their model.

Esterhuizen et al.[41]utilised numerical modelling(as a part of their parametric studies) in conjunction with statistics of the heights of reported roof falls in U.S.coal mines to develop an equation to predict the height of detached roof.Their RSR is then calculated from the ratio of the load-carrying capacity of the support system relative to the dead weight of the detached roof.

Essentially their roof support design approach is a complicated version of suspension design,which was confirmed by Dr.Esterhuizen when answering the lead author’s question subsequent to his webinar presentation to the Bowen Basin Underground Geotechnical Society (BBUGS) conducted on Thursday 22nd April 2021.In addition,upon further questioning,Dr.Esterhuizen confirmed that their “model” for roof support design doesn’t contain any mathematical code to deal with slender beam behaviour including Euler Buckling and that mine-site monitoring is essential for calibration purposes prior to using their design approach.

The UDEC model utilised by Abousleiman et al.[40]also doesn’t contain any mathematical code associated with buckling,however in their study a strain softening ubiquitous joint(SUBI)model was selected to account for closely-spaced bedding planes between explicitly modelled discontinuities.In their conclusions,Abousleiman et al.[40]state,“Surprisingly,in-situ stress,explicit DFN type,and explicit joint strength had minor influences on overall stability of the entry and the magnitude of stable roof deflection.”,where the DFN is the discrete fracture network.

Given the UDEC model doesn’t contain any mathematical code associated with buckling,Abousleiman et al.[41]findings are actually not surprising at all and totally consistent with the inappropriate use of these techniques to model the dominant behavioural mechanism associated with coal mine roof strata;being slender beam behaviour.

Therefore,the issue of buckling (due to axial loading) as a failure mechanism about the mine opening/roadway has essentially been ignored by the numerical modelling fraternity;however,Gale[34] and Heritage [35] take this to a whole new level.While Gale[34] accepts that it is common to see coal ribs which are “apparently” buckled (refer Figs.8,9 and 10),for Gale [34] this is somehow caused by deeper conjugate shear failure applying a lateral force to the outer ribline to make it“look like buckling”.An extract from Gale [34] is presented in Fig.21 to assist with the following discussion.

As illustrated within Fig.21,Gale[34]states with respect to the roof;“only thin plies would fail,as a result of pure Euler buckling for normal stress conditions” and therefore is clearly suggesting that thin roof plies are the “exception rather than the norm” with respect to Australian underground coal mines such that Euler Buckling is no more than a “secondary consideration”.

This is simply incorrect and as previously discussed is in direct conflict with decades(and an overwhelming level)of observational evidence from a wide range of researchers and practitioners in the field.

One of the reasons why Gale [34]is dismissing buckling due to axial loading as a dominant roof failure mechanism would appear to be based on Gale and Fabjanczyk [42],where they take no account of the impact and effect of the bedding/laminae within a roof (stone/coal) unit which significantly reduces the effective beam thickness from that of the unit’s lithological thickness to the spacing between the bedding/laminae (refer Figs.3,4,5 and 11).

Gale and Fabjanczyk [42] found that numerical modelling of a generalised Goonyella Middle Seam roadway roof strata indicated that the top coal(immediate roof unit)acts as an independent unit within the roof section and that the stability of this unit can be analysed using the following criteria:(1) buckling failure of the coal top,(2) self-weight failure of the coal,(3) overstressing of the top coal due to a combination of deflection imposed from the strata above and the in situ stress within the coal and (4) ability of the top coal to confine the strata above.

Gale and Fabjanczyk[42]utilised numerical modelling to assess criteria ii to iv,while the potential for buckling failure was assessed separately on the basis of Euler failure criterion(i.e.the numerical model they used contained no mathematical code with respect to buckling and therefore the ability to simulate or assess slender beam behaviour).In relation to buckling failure they state,“Buckling failure of the coal roof is likely where its thickness reduces less than a nominal 0.5 m and the stresses are low 2 MPa.” and concluded,“..that shear failure of coal is the most likely failure mechanism,with buckling failure only likely with very thin coal beams at low stress levels.”

In relation to collieries operating in the Goonyella Middle Seam,Gale and Fabjanczyk [42] state,“the possibility exists to use low density (<1 bolt per square metre) roof bolting patterns within specific limitations of coal roof thickness and management of structured areas” and further indicate,“With a 2 m thick coal roof a high level of stability can be achieved in higher stress levels(200 m of cover)” and “A 4-bolt pattern is adequate for low stress conditions,however a 6-bolt pattern is more capable of controlling the strata under higher stress conditions.”

In subsequent years,similar recommendations based on numerical modelling studies have proved to be totally inadequate for certain mines operating in the Goonyella Middle Seam (e.g.Thomasson,[43]) and for safety reasons the use of 4 bolt patterns is clearly discouraged by the Queensland Department of Natural Resources and Mines(i.e.Mines Safety Bulletin No.148,23 January 2015,Version 1 [44]).

Fig.21.Extract from Gale [34].

As opposed to Hoek and Brown[3]and Galvin[2],the preceding discussion indicates that Gale and Fabjanczyk [42] have chosen to ignore the bedding/laminae within the coal unit when assessing the unit’s propensity for buckling.This is a clear example where oversimplification of the problem (presumably to suit one’s preferred method of analysis and its limitations) is simply unacceptable and potentially leads to disastrous results.

Therefore it is not appropriate in assessing the lateral load bearing capacity of a roof coal unit to simply use the lithological thickness and ignore the bedding/laminae within the coal unit when assessing the unit’s propensity for buckling.In addition (and as previously discussed),laminated roof units are extremely common to Australian collieries and therefore thin roof plies are overwhelming the norm and not the exception as Gale[34]mistakenly contends.

Fig.22 is a reproduction of Gale’s Fig.13 [34] (as illustrated within Fig.21),while including some noteworthy additions and changes.Firstly,the maximum limit for the axes has been changed.Roadway roof and ribline stress monitoring would suggest that in relation to the y-axis the typical maximum levels of horizontal stress that a belt road roof and vertical stress that a tailgate ribline would be subject to during longwall retreat is in the order of 50 MPa.The beam/column thickness or x-axis has been changed from 1.5 m to a practical upper limit of 500 mm as previously discussed.

To simulate the roof/stone units Gale[34]utilises a modulus(E)of 10 GPa for both a 5 m roof span (i.e.average roadway width associated with Australian collieries) and a 1 m distance between bolts.This is considered reasonable.For coal Gale [34] utilises anE=2 GPa(once again this is reasonable),however for some inexplicable reason a 1.5 m length.Given approximately 50%of the immediate roof associated with Australian longwall operations is coal,the question posed is why isn’t a 5 m roof span andE=2 GPa(for a coal roof) simulated? Furthermore,given the average development height in Australia is approximately 3 m why is this length not also simulated for coal? Fig.22 includes these simulations to provide more representative context of the types of beam/column geometries that are present in coal mine roof and ribs.

Based on the review of the ADFRS and ADRS databases,approximately 75%of the immediate roof and rib contains material where if delamination is allowed to occur then beam/column thicknesses of<100 mm will form which,based on Gale’s[34]own calculations,can readily buckle due to axial loading(i.e.Euler Buckling),as illustrated in Fig.22.

Fig.22.Critical buckling stress (MPa) vs.beam/column thickness.

Now let us deal visually (utilising previous studies) and mechanistically with Gale’s [34] statement,“It is common to see coal ribs,which are apparently buckled,however under close inspection it is often,although not always,the case that behind the buckled zone is a conjugate shear fracture,which has dilated and allowed aside loading on the coal ply.In this case the failure process is more complex”.

Visually:Fig.23 is from Gale [34] when discussing the concept of buckling failure of an isolated ply under axial loading.Fig.24 is a photo of a Crinum colliery blockside ribline subject to one longwall side abutment load.The similarities between Figs.23 and 24 are self-evident and the only substance behind the buckled section of ribline in Fig.24 being ‘thin air” as is behind the buckled zone illustrated in Fig.10 associated with Appin colliery.The wordlimit and space considerations associated with a technical paper,is the only reason that prevents many more similar photos from being presented.

Previous field investigations:As discussed earlier,all significant Australian studies into ribline behaviour (other than Fabjanczyk et al.[17])found buckling due to vertical loading to be a significant failure mechanism as opposed to what Gale[34]and Heritage[35]suggest.

Heritage[35]states,“Tensile cracking can occur through the rib dilation caused from deeper shear failure pushing out the near rib–this can often appear as buckling style failure” and provides Fig.25 to partially illustrate her“theory”of a stress driven rib failure mechanism.

Therefore,Heritages’interpretation of a stress driven rib failure mechanism has the failure starting 2 to 3 m inside the ribline and working its way out to the ribline such that it only “looks” like buckling due to axial loading [35].It is worth noting that this in direct contrast to what her Strata Control Operation Pty Ltd (SCT)colleagues found some 28 years earlier as illustrated in Fig.6 where failure commences in the outer rib and progresses further into the rib/pillar.

In monitoring the rib failure mechanism of buckling,O’Beirne et al.[16]found that plates or slabs formed at the ribside are subjected to vertical loading and sometimes “pushing” from behind.They indicate that this pushing can be caused by other buckling plates (refer Figs.6 and 10) or simply due to overall expansion(i.e.Poisson’s effect).Therefore,their finding is diametrically opposed to that of Gale[34]and Heritage[35]in that the observed and monitored ribline buckling is more often than not driven by vertical loading rather than “pushing” from behind.Colwell([15,21]) came to the same conclusion.

Fig.23.Concept of axial loading and buckling (after [34]).

Fig.24.Crinum colliery blockside ribline buckling (after [21]).

Fig.25.Formation of buckling/tensile failure (after [35]).

Mechanistically:The mechanistic basis for Euler Buckling associated with a coal mine ribline has been previously discussed via the Angus Place colliery ribline extensometry monitoring as illustrated by Fig.14.Based on that extensometry data what is also clear is that there is no “pushing” of the outer rib from behind as Gale [34] suggests is the primary cause.Similar ribline behaviour to that at Angus Place was found at the other ADRS project instrumentation sites.

So why is there such disparity of opinion between Gale[34]and most other researchers (other than his SCT colleagues e.g.Fabjanczyk et al.[17],Gale and Fabjanczyk [42] and now Heritage[35])? The inevitable reason is simple and is to be found in the words of Heritage [36] when providing an update for ACARP Project C25057 where she states,“Rock failure modelling using FLAC 2D was conducted to validate the inferred failure mechanisms for the rib deformation at each site.”

In other words,a numerical model with absolutely no mathematical code associated with buckling has been used to “validate”the ribline failure mechanisms,as Gale [34] did in his desktop study when “defining” coal mine roadway roof failure mechanisms.Therefore,in hindsight it was inevitable that buckling(due to axial loading) would not be identified as a failure mechanism and indeed should have been obvious in foresight based on any reasonable literature review.

Furthermore,utilising numerical modelling (or any model for that matter which is not set up to simulate the structural nature of the “body” under investigation);to “validate” the observed and monitored underground behaviour is at total odds and ignores/misrepresents the Scientific Method.In contrast the ACIRL physical model (Fig.2) was set up to accurately reflect or simulate the structural (i.e.laminated) nature of the roof and floor subject to horizontal stress and the interpretation was then made based on the observations.It is also important to note that the ACIRL physical model provided a clear indication of what the dominant or typical failure mechanism is with respect to coal mine roof and floor strata subjected to elevated horizontal stress conditions.

Not surprisingly there is the constant “theme” associated with such numerical modelling research that all ground support design needs to be “tailored” to the site-specific mechanisms for roof/rib deformation;thereby suggesting that the roof/rib deformation mechanisms are somehow vastly different from colliery to colliery and elaborate/costly instrumentation/monitoring is required at each colliery to then be “validated” by a numerical model before“optimal” ground support design can be undertaken.

Tarrant [45] suggests that researchers utilise numerical modelling to develop a “better understanding” of roadway behaviour.Tarrant [45] points out that,“Use of such tools is limited by the simplifications required however when used in conjunction with field measurement and observation,the model findings can be tested and a level of confidence in the results defined.”

The use of numerical modelling in the manner described by Tarrant [45] (as well as Fabjanczyk et al.[17],Gale and Fabjanczyk[42],Gale [34],Heritage [35],Abousleiman et al.[40] and Esterhuizen et al.[41]) only provides a calibrated (via field measurements) model to then be used for site-specific prediction or design.With some imagination one could virtually calibrate any“model” to do that!

In addition,calibrating a numerical model to a limited number of sites does not provide an underground coal industry with a widely applicable and therefore accepted design tool for roadway ground support design.None of the project’s/study’s associated with Fabjanczyk et al.[17],Gale and Fabjanczyk [42],Tarrant[45],Gale [34],Heritage [35],Abousleiman et al.[40] and Esterhuizen et al.[41]have provided an underground coal industry with a readily useable ground support design methodology.

In relation to the Australian research mentioned above;each project only contained between one to three field/monitoring sites.In relation to the three monitoring sites associated with ACARP Project C25057 and in comparison to previous rib related research,Heritage[35]states,“To provide a point of difference from the previous studies,this review focuses on measurement of rib deformation,with reference to assessment of the mechanisms of deformation.” and yet as previously described;with respect to the ADRS project (Colwell [21]) of the 26 collieries that participated in the project seven also participated as instrumentation sites involving 33 ribline monitoring locations incorporating roof and rib extensometry as well as stress cells.

The above comparison in terms of data collection and experimentation would appear to be one of reasons that numerical modellers can come to such erroneous conclusions.As Esterhuizen et al.[41] state,“Monitoring rock mass response and support performance in the field is costly and time consuming.In this research,numerical models were used to supplement field data with information about support system performance under geologic and stress conditions beyond those that were measured in the field.”

There is commonly a very heavy reliance on numerical simulation for understanding as opposed to real-world observations and the benefits to our understanding when formulating an industry wide database of information(specific to the problem)incorporating a significant (rather than limited) number of monitoring sites with this being an inherent requirement of the empirical/mechanistic approach,whether that be in terms of a resultant/recommended ground support rating or factor of safety.

Furthermore,such extensive and comprehensive databases of information were essential in developing the highly successful and widely used ALTS 2009 gateroad(chain pillar and roof support)design methodology,the rib support design methodology ADRS and ADFRS for wide roadway roof support design.

These empirical/mechanistic models/design techniques clearly prove that ground support design models and methodologies can be developed for an entire industry and readily utilised by the mine-site geotechnical engineer.As Emery,Canbulat and Zhang[46]state,“ALTS 2009 and associated software package,has grown to be the prevalent technique for chain pillar and gateroad ground(roof and rib) support design at most operating longwall mines in Australia.This is largely because the outputs from ALTS 2009 most accurately reflect the design requirements to provide serviceable gateroads associated with longwall extraction.”

The success of these empirical/mechanistic design techniques can’t simply be a “fluke” i.e.there must be a reason! In the same way as there must be a reason why after 30 years of pouring many millions of dollars in relation to numerical modelling research for ground support design in Australia nothing has been produced that the mine-site geotechnical engineer can use.

In relation to numerical modelling the reasons are two-fold:(1)these models are not set up to deal with slender beam/column behaviour and even if they were,there is no mathematical code in relation buckling and (2) numerical modelling is primarily a stress analysis tool and its application to roadway ground support design is a dubious extension of its purpose/use and in terms of its historical application in the Australian underground coal industry;is simply flawed.

The fundamental reason for the success of ALTS 2009,ADRS and ADFRS is that slender beam/column behaviour and the associated deformation process of delamination (or de-coupling),bucking(due to axial loading) and ensuing shear failure (on which these models are based)is not only common to all collieries but is in fact the dominant behavioural mechanism associated with coal mine roadway roof/rib/floor deformation.

Whilst the world today incorporates the use of computers in our everyday lives to the extent that they are indispensable to our way of life,the one notable exception to this MUST be the continued application of the Scientific Method as it was originally envisaged many years ago.Testing hypotheses in the real rather than virtual world,guarantees that any theories that may emanate best reflect the real world when used in addressing and solving real-life problems.

Testing hypotheses via the use of numerical codes with their inherent simplifications and limitations is inevitably a backwards step and should be fully discouraged.At the end of the day,the primary engineering skill is that of “judgement” which is borne of experience.When making such judgements,professional engineers need to decide whether they will prioritise real-world experience that has been judiciously analysed to determine cause-and-effect,or outputs from numerical codes.The contents of the paper should leave the reader in no doubt as to the opinions of the authors on this fundamental issue.

Therefore,it is assessed that the review of the “dissenting views” (which is requirement of the Scientific Method) strongly reinforces the hypothesis put forward in this paper.

7.Roof reinforcement mechanisms

As stated in the introduction,the Scientific Method can be applied to almost all fields of study as a logical,rational,problem-solving method and provides a way of examining the world that allows us to reach conclusions about how it works and that these conclusions can be tested.So,can the hypothesis put forward in this paper be further tested in relation to roof reinforcement mechanisms?

In terms of roof reinforcement,primary bolts and longer tensioned cables are fundamentally different for a variety of technical reasons.The mechanical advantage aspect of AMCMRR clearly suggests that all roof support should be placed at or near the centre of the roadway to take advantage of the maximum mechanical advantage,however this aspect of the AMCMRR model can only be effectively employed if in fact there is “beam behaviour” and to form a beam within a coal mine roof (so that it can behave as a beam across the full width of the roadway)will only come about through “pattern bolting.”

The authors’view this as the role of the primary bolts.A reasonable spread of bolts is required at a regular spacing to assist in building a “reinforced” beam;that is the primary bolts are close enough to each other and the riblines to effectively interact to form such a beam.Slender beam behaviour tells us that the end-fixing condition is as important as “nodes” along the beam i.e.the outer bolts are just as important as the inner bolts.However,the questions have always been,“how do the primary bolts reinforce the roof mass and how is the beam formed?”

Fig.11 clearly demonstrates that immediately about the bolt a thicker beam can be created by pinning “the slabs together by means of short rockbolts” as suggested by Hoek and Brown [3].However,Fig.11 also clearly reveals that this effect does not radiate across the entire roadway,because if it did,underground roadway roof would only need one bolt/m and that is not a reality.Fig.11 also demonstrates why AMCMRR assesses the potential for instability not simply across the entire roadway width in relation to the reinforced roof beam but also between bolts and in particular between the two centre bolts,which is generally the greatest span between bolts or between the outer bolts and the ribline.

In examining the interaction of rock bolts with the rock mass and the role that they play in modifying rock mass behaviour about an opening,typically the rock mechanics researchers’ concept is that the ground support reinforces the broken (i.e.post failure)rock by offering additional confinement and in so doing improves its residual strength (i.e.about the bolt) thereby minimising further stress redistribution and restricting the extent and severity of failure.Based on these concepts the rock reinforcement or confinement provided by the rock bolts manifests itself in two ways:i.e.Axial and Shear Restraint.

Fully resin-grouted rock bolts are loaded by movement or failure within the rock matrix.Fig.26 illustrates failure or separation of bedding which in turn mobilises forces within the bolt and thereby provides axial restraint and transfers load via mechanical interlock between the bolt,resin &rock.

Fig.27 demonstrates both that of shear restraint and the benefits of maintaining surface to surface contact along a discontinuity.Seedsman[47]contends that shear along bedding is the precursor in relation to roof failure and that bolts should be designed in the context of resisting shear.Seedsman [47] reported that a fully grouted bolt installed across an open discontinuity has a shear resistance initially controlled by the compressive strength of the rock and for typical coal measure strata that would be in the order of 5 to 10 tonnes.However,if the bolt is installed across a closed discontinuity the shear resistance is controlled by the strength of the bolt and the friction angle of the discontinuity and can be as high as 20 tonnes in the same rock.

The basic concept of providing maximum reinforcement at the point of failure (or to resist failure),was a dominant factor in the Australian coal industry’s now exclusive use of fully resingrouted roof bolts as opposed to point-anchored mechanical bolts.It is the comparative stiffness of the two systems that sets them apart in relation to their effectiveness in reinforcement of the rock.

However,based on the authors’ contention that slender beam behaviour or buckling (due to axial loading) is typically the dominant behavioural mechanism occurring within the immediate coal mine roof measures,there is another reinforcement mechanism whereby the bolts essentially act as “moveable nodes” within a buckling beam system.

From first principles the critical load (referred to as the Euler Buckling Load) for a beam/column pinned at both ends at which buckling can occur is given by:

whereEandLare as previously defined andIis the least moment of inertia of the beam.

The values ofn,define the buckling mode shapes,with the first three modes of buckling illustrated in Fig.28.However,sinceP1

Fig.26.Axial restraint.

Fig.27.Shear restraint.

Fig.28.First three modes of buckling behaviour.

Unless the primary bolts are securely anchored into a “fixed”rock layer (or strong bed) they will effectively “float” within the bolted interval and become “moveable nodes”.Even when anchored into a supposed stable rock layer there will inevitably be some vertical movement.The nature of the anchor,quality of installation,the stiffness of the bolt and the level of pre-load applied to the bolt will all affect the associatedKvalue (refer Table 1) and therefore the effective length of the beam (overall and between bolts/nodes).

The ALTS and AMCMRR research demonstrated that for fully encapsulated bolts(as typically installed in Australia and accepting a certain level of variability in the quality of installation between pits and operators),the significant predictors of the bolts’effectiveness in terms of roof reinforcement are individually (1) the length of the bolts,(2)the capacity of the bolts(i.e.Typical Ultimate Tensile Strength,kN),and(3)the bolting density as well as when these are combined into the overall Primary Roof Support (PRSUP) Rating.The research of Mark et al.[9] essentially reached the same conclusions.Therefore,anything that can be done to make the bolt a more fixed or less moveable node in a buckling system will promote roof stability or at minimum allow a rock unit achieve its maximum lateral load bearing capacity;i.e.no matter how many bolts or cables are installed one can’t make the“rock stronger than the rock”!

Colwell suggests that the introduction of bolts and tendons to the rock mass is in many ways similar to the introduction of a drug to the human system to treat an illness[15].The medical scientists may or may not understand exactly how the drug interacts with the human body but what is certain is two different human beings will react to the drug in two different ways.Sometimes this will not even be noticeable and on other occasions there is a dramatic difference in the reaction that can affect issues such as required dosage and treatment regime(i.e.not only quantity but also timing and sequence).

Furthermore,many drugs when introduced into the human system actually trigger the body’s own immune system to fight the ailment or disease.As reported in the Sydney Daily Telegraph Tuesday,March 6,2007;Professor Ian Frazer (2006 Australian of the Year) was working on a “SUPER Vaccine” to treat the flu virus and other debilitating conditions such as Hepatitis C.Professor Frazer states,“It is a drug that changes the immune response to the virus,it works by turning up the volume control on part of the immune system so there is a stronger immune response–not specific to any one virus but across all the viruses.”

The“moveable nodes”model does not rely on failure of the rock mass to trigger a response but simply“turns up the volume”on the roof unit’s own ability to resist buckling.It is considered that the“moveable nodes” model provides a far more rational explanation as to how the bolts interact across the roof and why pattern bolting proved to be a great success in terms of roadway roof reinforcement.

The reinforcement mechanism or concept of beam building (as discussed by Mark [10]) associated with the installation of roof bolts has long been recognised in the underground coal mining industry.While numerous researchers (e.g.Hoek and Brown [3],Peng[48],Gale et al.[49]and Seedsman et al.[50])have discussed the various mechanisms by which the bolts act to “create thicker beams” (e.g.by maintaining friction on bedding planes etc.),AMCMRR was the first such study that in a practical way attempted to quantify the beam building effect and then incorporate this effect within an analytical model.

However,as this discussion indicates,the introduction of roof bolts does not actually “create thicker beams” across the entire roadway width as that is not likely with the standard Australian primary roof support pattern of 6 (1.8 or 2.1 m) bolts/m and certainly not with the four bolt patterns predominantly associated with the ARBS U.S.database.Mechanistically what is occurring is that the bolts are modifying the effective length of the beam(overall and between bolts/nodes).The problem faced by the authors in the development of AMCMRR is that it is not possible (as previously discussed) to accurately quantify the exact startingKvalue or end-fixing condition of the roof beams prior to or subsequent to the bolts being installed.

However,what is known is that the lateral load bearing capacity of the roof beam will be a function of its end-fixing condition,the nodes along the beam,its actual geometry(i.e.length–Land thickness–d) and its modulus.While the effective length of the beam over which buckling occurs (i.e.Leff=KL) is affected by the endfixing condition and the nodes along the beam,its thickness is not! In relation to beam’s thickness within an individual rock unit there is a reasonable starting point and that is (as previously defined) the Effective Fracture Spacing (FSeff,mm).

So,using the concept of beam building one can use the starting beam thickness(i.e.FSeff)and a measure of the roof support(in this instance PRSUP)to evaluate the“effective”Reinforced Beam Thickness (RBT,mm) and thereby the increased lateral load bearing capacity of the reinforced roof unit.Colwell and Frith [24] explain this process which resulted in the relationship detailed in Fig.29.Essentially while recognising that the concept of beam building is not entirely mechanistically correct,it can still be effectively utilised (via practical engineering simplification) to obtain the same end result i.e.the lateral load bearing capacity of the reinforced roof unit.

The process by which the RBT andFSeffrelationship was determined is in many ways similar to the process by which the empirically derived Hoek-Brown Failure Criterion for rock was developed(refer Hoek and Brown[3]).Once again it is important to note that irrespective of the resultant RBT,the beam’s lateral load bearing capacity will be limited by the material’s strength and the unit’s lithological thickness,i.e.one can’t make the “rock stronger than the rock” or the RBT >the unit’s actual thickness.

In its adaptation from the RMR one of the most important concepts incorporated into the CMRR is that of the Strong Bed Adjustment (SBADJ).Many years of experience with roof bolting (in Australia and U.S.) has found that the overall structural competence of mine roof is very often determined by the quality of the most competent bed (i.e.rock unit) within the bolted interval.

The original SBADJ concept was primarily to do with the reinforcement mechanism of “suspension”.As Mark and Molinda [4]explain,“experience in many U.S.coalfields has clearly established that roof stability is greatly enhanced when the roof bolts anchor in a strong layer.This effect is most evident in the Illinois Basin,where roof falls are almost unknown when the bolts anchor in a limestone that is at least 0.6 m thick.The strong bed effect has also been recognized in Alabama and central Appalachia.Indeed,even the Code of Federal Regulations implies a strong bed effect when it states at 30 CFR 75.204(f)(1)that“roof bolts that provide support by suspending the roof from overlying stronger strata shall be long enough to anchor at least 12 in.into the stronger strata.”

In Australia there are also several examples;notably Moonee,Elouera and Grasstree collieries,and a few other mines where there is a lessor impact.So while there are relatively few collieries in Australia where the SBADJ has been or is a significant issue or component of the CMRR,it is apparent from the analyses(and field investigations) that at those collieries where the SBADJ is a significant component of the CMRR,if for any reason anchorage within the strong bed is compromised(e.g.due to gloving,water,installation difficulties)or the strong bed is absent within the bolted interval (for example due to a thickening of weaker strata beneath the strong bed or the strong bed “lenses out”) then roof performance can be significantly and adversely effected particularly during longwall retreat.Conversely where solid anchorage within the strong bed is maintained,then “bagging” of the roof is not observed and significant deformation/delamination is not measured.

If the bolts are solidly anchored into a strong bed they essentially become “less moveable” and “more fixed” nodes within the weaker roof below the strong bed.The relative decrease in the K value would result in greater stability for the weaker material beneath the strong bed as the effective beam lengths (i.e.across the roadway or between tendons) within the weaker units would be reduced.Mechanistically this explains why the SBADJ reinforcement mechanism has such a significant impact on roof behaviour,and therefore has very little to do (if at all) with suspension and furthermore is totally consistent with the hypothesis put forward.

Fig.29.Relationship between RBT, FSeff and primary roof support levels (PRSUP).

8.Conclusions

From the “apple hitting Sir Isaac Newton on the head”,engineering methods have been developed in the past based on observing the real world,attempting to derive mathematical equations and algorithms that allow those observations to be replicated in terms of cause and effect,and testing predictions back in the real world.It is commonly known as The Scientific Method.

Unfortunately,in the field of coal mine strata control it is now evident that some cause-and-effect research is being founded in mathematical models with selective observations or measurements being used to justify the findings.This is an exact reversal of the process that has served mankind well for centuries and if allowed to proliferate must inevitably lead to a lessening rather than improvement in our fundamental understanding of the real world.

The irrefutable evidence for this warning is the recent dismissal of buckling (due to axial loading) as the dominant behavioural mechanism in coal mine roadway roof and ribs by reference to numerical modelling simulations.This goes directly against physical modelling findings,many observational reports and around 40 years of empirical/mechanistic research studies within the Australian coal industry which are founded in the principles of slender beam/column behaviour and have returned very high statistical correlations between cause and effect.

The substantial real-world observational and measured evidence as discussed in this paper demonstrates the hypothesis i.e.that horizontal and vertical stress driven slender beam and column behaviour (which includes unstable Euler Buckling) are respectively the dominant (but not only) roadway roof and ribline behavioural mechanism that (if not controlled) can lead to excessive deformation,failure and eventual collapse and therefore must be representatively accounted for in any credible empirical,analytical,or numerical approach to coal mine roof/rib stability assessment and associated ground support design.

Therefore,the challenge to the numerical modelling fraternity is clear;if they wish to continue using this approach in a credible manner with respect to ground support design associated with underground coal mines then they have to find a way of incorporating slender beam/column behaviour and the necessary mathematical code associated with Euler Buckling and if they do,they are to be congratulated in undertaking what would essentially be an “academic” exercise.

There are three basic questions that an engineer should ask in applying a design technique;“is the technique credible in terms of the application for which it is being used?”,“what are the practical benefits that the technique offers in terms of safety,productivity and cost-effectiveness?” and lastly,“what benefits,if any,would the technique provide over other methods already available?” The reality in Australia is that even if a numerical model incorporating slender beam/column behaviour and Euler Buckling were developed,it would still require the very costly process of being calibrated on a site-by-site basis and offer the pits no better(and in all likelihood less) than what ALTS 2009,AMCMRR,ADFRS and ADRS already provide.