IJCG-Majdi-Hassani-Nasiri's Published Paper

Prediction of the height of destressed zone above the mined panel roof in longwallcoal mining

Abbas Majdi a,⁎, Ferri P. Hassani b, Mehdi Yousef Nasiri c

a School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iranb Department of Mining and Materials Engineering, Faculty of Engineering, McGill University, Montreal, Canadac Khavar Tunnel Consulting Engineering Inc., Tehran, Iran

a b s t r a c ta r t i c l e i n f o

Article history:Received 27 January 2012Received in revised form 7 April 2012Accepted 7 April 2012Available online 18 April 2012

Keywords:Longwall miningHeight of destressed zoneMathematical modelCaving zoneFracturing zone

Longwall mining is one of the most widely used underground mining methods most suitable in relatively flat-lying, thick, and uniform coalbeds. Due to extraction of the coal seam, the panel roof strata above the minedzone will be destressed and then the roof loads will be redistributed and transferred to the front abutmentand neighboring solid sections with higher load bearing capacity where the adjacent access tunnels andthe corresponding barrier pillars are located. The height of destressed zone (HDZ), in this paper is taken asequivalent to the combined height of the caving and fracturing zones above the mined panel roof induceddue to longwall mining. The height of destressed zone plays a vital role in accurate determination of theamount of loads being transferred towards front abutment and panel sides. The paper describes the mecha-nism of development of the height of this zone. Finally, five new simple, yet conclusive, mathematical ap-proaches to estimate the height of destressed zone are presented. The results of the methods proposed arecompared with each other and with the comparable methods. The methods proposed are further comparedand verified with in-situ measurements reported in the literatures. The comparative results confirm theagreement that exist among the methods and those with the in-situ measurements as well. Finally themethods have shown that, in short term, the height of destressed zone ranges from 6.5 to 24 times the extrac-tion coal seam height; while, in long term, the height of destressed zone ranges from 11.5 to 46.5 times theextraction coal seam height. Therefore, beyond this height the overburden pressure will be transferred to-wards the front abutment, the adjacent access tunnels, the intervening barrier pillars as well as the panelrib-sides.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Longwall mining is one of the most widely used methods in un-derground coal extraction. One of the most important advantages ofthis method is the automated form of underground coal mining char-acterized by high efficiency. The main objective of coal mining is toeconomically extract coal and safely remove them from the ground.Hence, the mining efficiency solely depends on the coal seams overallconditions. In this method, due to the extraction of coal seams withina considerable panel width, after advancing the hydraulic jacks orpowered roof supports, the immediate roof of the mined panel isunsupported and hence is allowed to collapse and cave in some dis-tance behind the hydraulic jacks or in the goaf area. The downwardmovement of the roof strata then gradually extends upwards andwill cause the disturbed roof strata to become destressed. Thus, theoverburden pressure above the destressed zone will be redirected

towards the front abutment and the two adjacent neighboring solidsections where the gate roads (access tunnels serving the coal face),the intervening barrier pillar and the adjacent un-mined solid sec-tions are located. The upward extension of destressed zone (HDZ) de-pends on a variety of parameters such as: depth, thickness of theextracted coal seams, panel width, the number and the relative thick-ness and the strength of the panel roof strata and the correspondingcoefficient of expansion.

Nowadays, the prime concerns of many coal mining researchersare to find the appropriate approaches to appraise the panel roof stra-ta behavior during and after panel extraction. Professional mining en-gineers who are dealing with the longwall mining design need toeffectively determine the height of destressed zone above the panelroof that induced due to longwall mining. The height of destressedzone (HDZ), in this paper, is considered to be equivalent to the com-bined height of the caving and the fracturing zones that exist abovethe mined panel roof. To suitably evaluate the amount of transferra-ble loads to the adjacent tunnels as well as the intervening barrier pil-lars, the height of destressed zone must be estimated accordinglywhich is the main objective of this paper.

International Journal of Coal Geology 98 (2012) 62–72

⁎ Corresponding author. Tel.: +98 514 398 2215.E-mail addresses: [email protected] (A. Majdi), [email protected] (F.P. Hassani).

0166-5162/$ – see front matter © 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.coal.2012.04.005

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2. Existing views of mined panel roof caving and fracturing appraisal

Longwall mining is a highly productive underground coal miningtechnique whose basic principles have been traced to the latter partof the 17th century to Shropshire and other counties in England(Anon, 1995). When a longwall panel is extracted then the immediateroof strata are allowed to move downward. Due to the roof strata'sdownward movements the original natural in-situ stress regime andthe hydraulic conductivity will be changed. Hence the roof stratawill collapse and fall into the extracted panel space. Depending upon the volume expansion of the fractured rocks, the movementswill gradually influence the rock layers above the immediate roofstrata. The roof strata will behave differently, depending upon manyfactors including: strength, thickness and the number of roof rocklayers and the thickness of the overburden in all, in one hand, andthe extracted coal seam height, the panel width and the panel length,on the other hand. The behavior of the panel roof strata and the pro-cess of the gradual upward movement have been of prime concernand hence investigated by many researchers to account for the ob-served movement as well. The following outlines various literatures,in particular, those by Chekan and Listak (1993); Chuen (1979);Denkhausi (1964); Dinsdale (1935); Eavenson (1923); Hasenfus etal. (1998); Kenny (1969); Luo (1997); National Coal Board (NCB)(1975); Palchik (1989); Peng (1992); Peng and Chiang (1984);Richard et al. (1990); Ropski and Lama (1973); Singh and Kendorski(1981); Styler (1984); Wiggill (1963); Zhou (1991); andmany otherswhose work will be referred later in this paper, wherever they apply.

Eavenson (1923) believed that the inner-burden shear failure dur-ing multiple seam extraction in longwall mining extends to the groundsurface. Dinsdale (1935) proved that the height of destressed zone(dome) is directly proportional to the depth of cover and to the excava-tion width and inversely proportional to the horizontal reaction. Wiggill(1963) depicts the concept of a composite destressed zone (dome) andtrough theory, where the movement trough does not start from theface but from higher up at the dome boundary. According to Denkhaus(1964), in treating the problem a distinction should be made betweensufficiently cohesive rock and insufficiently cohesive rock. For a domewith sufficient cohesion, the maximum height is equal to 50% of thedepth of cover above excavation. If the rock is insufficiently cohesive,then the maximum height is 63% of the depth of cover above excavation.Kenny (1969) discussed a method of quantifying the description of thecaving zone by means of simple observations and measurements alongwith the relevance of the manner of caving to roof control. Ropski andLama (1973) used the terms of primary and secondary regions of cavingwhile working coal seams by longwall mining. The latter authors showedthat regions of primary and secondary caving extend to a height of 3–3·5times the thickness of the coal seam extracted.

Chuen (1979); National Coal Board (NCB) (1975); and Peng andChiang (1984) proposed empirical approaches to estimate the heightof caving and fracturing zones induced by longwall coal mining basedon the large experiences gained from the British coal mines where themethod of longwall mining was originated as well as the USA. Singhand Kendorski (1981)have found that there are three distinct zones(caved zone, fracture zone and continuous deformation zone) of dis-turbance in the overburden strata in response to longwall mining.Singh and Kendorski (1981)further suggested that the height of cav-ing is dependent on the extracted coal seam thickness as well as thestrength and stratigraphy of the roof strata, generally extending up-wards 3 to 6 times the thickness of the mined coalbed. Karmis et al.(1983) have indicated that the height of the caved zone can be 12times the underlying coal seam thickness. According to Styler (1984)measurements of inter-burden deformations above 6 longwall faces, 5in the United Kingdom, and 1 in the U.S.A. showed that the caving heightabove a longwall face is equal to 8 to 12 times the extraction seamheight,with a zone of fractured rock extending to approximately 50 times the ex-traction height above the seam.

Peng and Chiang (1984) differentiated four zones in the overbur-den when a wide enough longwall coal panel is mined; Caved Zone:the immediate roof caves irregularly, filling the void. The strata losetheir continuity and bedding planes disappear. Fractured Zone: Locat-ed over the caved zone, its main feature is the loss of continuity andbreaking or yielding of materials but some bedding planes may re-main. Continuous Deformation Zone: In which strata bend downwardswithout breaking. Only occasional tension cracks can be observed. SoilZone: The surface layer, whose behavior is very site-dependent. Accord-ing to Peng and Chiang (1984) the first two zones can be consideredplastified, that is, their forming materials yield and hence they can besimulated by means of an elasto-plastic constitutive model. Fawcett etal. (1986) based on their personal communication with Farmer (1980)quoted an alternative formula which is based on the panel width ratherthan the extraction thickness, predicts greater fracture heights at typicalwidths between 100 and 200 m.

Palchik (1989) has found that there are three distinct zones(caved zone, fracture zone and continuous deformation zone) of dis-turbance in the overburden strata in response to longwall mining.According to Palchik (1989) the thickness of the fractured zone variesgreatly from 20 to 100 times the seam thickness. The zone above thefractured zone is the continuous deformation zone where there areno major fractures. The extent of the zones of rock movement overlongwall mining may vary significantly.

According to Richard et al. (1990) as the mine roof is allowed tocollapse, there is an area of caving and severe fracturing which occursdirectly above the mined coal seam. This area extends upwards 30–60times the coal seam thickness, depending on the mechanical qualitiesof overlying rock strata. Strata sag above the caved area. A “zone ofcontinuous deformation” may extend to approximately 50 ft of theground surface, depending on the geomechanical properties of over-burden layers. This zone is characterized by intermittent fracturing, bed-ding plane separation, and some sliding of beds across each other. A nearsurface zone comprising the upper 50 ft of overburden may show in-creased fracturing or permeability because of compression and tension.Richard et al. (1990) further quoted an interesting study included subsi-dence monitoring, time domain reflectometry, static water level obser-vations, and hydraulic conductivity in test wells, pre-mining and post-mining coring, and seismic surveys conducted in Virginia coal mineswhich was reported by Hasenfus et al. (1998); four distinct zones wereidentified in the panel roof rock strata due to coal seam extraction:Zone 1, the gob zone, just above themined panel and extending upwards4 to 6 times themined seam thickness, Zone 2, the highly fractured zone,above zone 1 and extending to about 30 times the seam thickness is atransitional, highly-fractured zone with massive block-type caving andvertical fracturing. Zone 3, the composite beam, extending from abovethe highly fractured zone towithin 50 ft of the surface, exhibits little ver-tical fracturing and occasional horizontal slippages between strata. Zone4, the surface zone, comprises the uppermost 50 ft. Strata in this zone aresusceptible to fracturing and movements.

Zhou (1991) believes that the height of caving and fracturingzones follow a geometric function of the height of mining based onextensive field measurements and then modified the empirical equa-tion that was given by Peng and Chiang (1984). According to Peng(1992) the combined height of caved and fractured zones is in gener-al 20 to 30 times the extraction height, being bigger for hard strataand vice versa.

Booth and Spande (1992) suggest that due to longwall mining, dif-ferent forms of deformation at various levels within the overburdenwill induce hydraulic changes accordingly. The latter authors believethat there are three different zones of deformation above longwallpanel: the first zone is intensely fractured and tends to dewater intothe mined panel itself and extends typically up to 20–60 times themined thickness; the second zone is the intermediate levels of theoverburden which subside more coherently and commonly remaina confining layer, and the third zone is the shallow, near surface

63A. Majdi et al. / International Journal of Coal Geology 98 (2012) 62–72

aquifers which deform more freely and exhibit fractured-controlledhydrologic responses to subsidence separate from the deeper drain-age effects.

Chekan and Listak (1993) mentioned three distinct zones of dis-turbance in the overburden strata in response to longwall mining;the caving zone, which is the immediate roof before it caves, rangesin thickness from 2 to 20 times the height of excavation. The cavingzone can actually be further divided into three sub-zones: the com-plete caving zone is a zone that the strata fall onto the mine floor.This zone is generally 3 to 6 times the mining height dependingupon the bulking factor. The partial caving zone is a zone which ex-tends from the top of complete caving zone, that is, from 6 to 12times the mining height. The upper limit of the caving zone occupiesa distance of 12 to 20 times the mining height. The fracturing zonewhich is located above the caved zone whose thickness ranges from20 to 50 times the mining height. The continuous deformation zonewhich is sometimes called the sagging zone is located between thefracturing zone and the ground surface. Indeed, according to Chekanand Listak (1993), the combined height of the caved and fracturingzones reaches to about 50 times of the extracted coal seams. Luo(1997) mentioned that the greatest potential for shearing occurs incoalbeds lying within 12 times the extracted coal seam height or inthe partial caving zone where the strata have significant degree ofbending, leading to intense fracturing or displacement.

A surface subsidence and extensometer monitoring research pro-gram undertaken above longwall panels 4 and 5 at Clarence Collieryin Australia was reported by Mills and O'Grady (1998). The latter au-thors aimed to investigate the behavior of the overburden strata duringlongwall extraction on two faces of differentwidths. Themonitoring in-dicated that a dome shaped zone of large downward movement ex-tends up into the overburden strata to a height equal to about 1.0 to1.1 times the panel width (Mills and O'Grady, 1998).

According to Jeffrey and Zhang (2001) hydraulic fracturing was usedat Moonee Colliery in Australia, to induce caving as part of the routineoperation of this longwall mine. The weak roof coal sequence typicallycaves immediately behind the supports leaving the 30 to 35 m thick con-glomerate section bridging the 100 m wide longwall panel (Jeffrey andZhang, 2001).

Apart from the above remarkable referred literatures, an interestingmicroseismic monitoring study was carried out at the Gordonstone orKestrel Coal Mine, in Australia (Kelly et al., 1998; Kelly et al., 2002;Luo et al., 1998) to investigate the ground caving processes, the patternof the caving and the extent of ground failure induced by undergroundlongwall mining. The failure extended to a height of about 120 m abovethe extracted coal seam as was observed and commenced about 15 mahead of the face. Kelly et al. (2002) believe that despite the impressivegrowth in Australia's longwall production, many longwall mines haveexperiencedmajor geotechnical problems. The later authors further ex-press that these types of problems are not just confined to Australia andare common in many countries, restricting the production potential ofmodern longwall faces.

Palchik (2002a) during his in-situ investigation over abandonedsubsurface coal mines in Donetsk, Ukraine reported the height ofthe caved zone in porous weak rock mass over shallow, abandonedunderground workings (up to 80 m) that were detected by drillingand linked with laboratory measurements of the physical characteris-tics of the rock mass overlying the underground openings. Palchik(2002a) has found that the height of the caved zone could reach 4to 11 times the thickness of the underlying coal seam where overbur-den rocks are weak and porous. The fractured zones caused by long-wall mining were further studied by Palchik (2003) using verticalwells drilled from the ground surface down to active undergroundworkings in the overburden of the Torezko-Snezhnyanskaya area.The latter author found that the maximum heights of the zone of inter-connected fractures and separate horizontal fractures may reach 19–41and 53–92 times the thickness of the coal seam, respectively.

According to Karacan et al. (2005) the permeability of the cavedzone in the longwall gob is not easily predictable since it mostly de-pends on the type of rock units, the extent of their fragmentationand packing in the void space, and caving height. Therefore, it is natu-ral to assume that this permeability valuemay vary widely for differentlocations and for different roof rocks when they cave. Karacan et al.(2007) believe that longwall mining is a high-volume coal extractionmethod which creates large-scale disturbances around the longwallface and in the overlying strata. They believe that occurrence of suchan extensive area of mining induced stress relief and resultant rockdamage changes the gas flow-related properties in the overlying (andin some cases the underlying) strata, particularly the permeability.

According to Karacan and Goodman (2009); Kendorski (1993);and Singh and Kendorski (1981) evaluated the disturbance of rockstrata resulting from mining beneath surface water and waste im-poundments. The latter authors in their analysis, describe a cavedzone that extends from the mining level to 3–6 times the seam thick-ness, a fractured zone that extends from the mining level to 30–58times the seam thickness, an aquiclude zone where there is no changein permeability that extends from 30 times the seam thickness to50 ft below ground surface, and a surface cracking zone that is 50 ftthick.

RafiqulIslam et al. (2009) employed a two-dimensional boundaryelement modeling to analyze the deformation and failure behavior ofrock elements for a multi-slice longwall mining in Bangladesh, withspecial reference to the Barapukuria coal mine. The results showthat fracture propagation would be about 240 m upward for single-slice (height 3 m) mining extraction (up to 80 times the extractedcoal seam). From the contours ofmean stressmagnitudes, it is observedthat the high range of fracture propagation increased upward for multi-slice extraction of coal (RafiqulIslam et al., 2009). Singh and Singh(2010) illustrated a numerical modeling based integrated approachfor predicting the progressive caving behavior of strata and optimumcapacity requirement of powered support for longwall working in agiven geo-mining and strata condition.

Zhang et al. (2011) reported that in order to deal with the appar-ent conflict between water protection and high production in under-ground mining, an aquifer protection mining technique was trialedin panel number 51201 in the Shangwan colliery, the ShendongCoalfield, China. Overburden failure, water level of the unconsolidat-ed aquifer, surface cracks, and ground subsidence were monitored ina series of boreholes using borescope, and also by observations innearby water well and by surface surveys. The observation indicatedthat the height of the caved zone was in the range of 5 to 6 times themining height, while the height of the fractured zone is about 10 to11 times the mining height (Zhang et al., 2011).

In regards to the above referred views some existing empirical cri-teria that were used to estimate the height of caving/fracturing zoneare also reviewed and presented in Table 1. To estimate the heightof fractured zone above the mined panel induced due to longwallmining, in this paper, five mathematical models have been proposed,analyzed, interpreted, and compared with each other and with the re-sults obtained from the present comprehensive literature reviewwhich will be outlined in the following sections.

3. New mathematical modeling for determining the height ofdestressed zone

There are several approaches to determine the height of des-tressed zone above the mined panel roof in longwall mining; in-situmeasurement, laboratory physical simulation, numerical modeling,and mathematical modeling. Although in-situ measurements providehelpful and reliable results, due to the inherent complexity of deter-mining the height of the destressed zone using this approach, in par-ticular for deep coal mining, actual implementation of this proceduremight be considered cumbersome, lengthy, and costly. Laboratory

64 A. Majdi et al. / International Journal of Coal Geology 98 (2012) 62–72

physical simulation is not a popular approach owing to discordantlylimitations for model construction length of time and cost requiredto execute the experiment. The last two remaining approaches, how-ever, are the simplest, least costly and may yield very handy and reli-able result as well.

In this paper, the authors focus on the last method, that is, the math-ematical approach so that with regards to mechanism of panel roof frac-ture initiation and their extents, two general models are proposed;Geometry-independent roof fracture and Geometry-dependent rooffracture both of which will be outlined henceforth.

3.1. Geometry-independent roof fracture model

In this model, it is assumed that the width of destressed zone isequal to the extracted panel width. In other words, the tensile failureoccurs at two extreme ends of the panel perpendicular to the advanc-ing direction. On the basis of these assumptions the following twonew sub-models are proposed.

3.1.1. Sub-model-1In this sub-model, it is assumed that all panel roof strata have equal

thickness and the average volume expansion of broken caved inmaterialsand fractured rocks is a coefficient of the extracted seam height (Fig. 1a).The schematic diagram of the two access tunnels along with the corre-sponding barrier pillars indicated by “B.P.”, before mining the coal seamout is also shown in Fig. 1a. Next, it is presumed that the coal seam witha thickness of (hs = ho), has been removed from the ground and thepack supports have been erected at the panel ends as illustrated inFig. 1b. If the number of roof rock strata is assigned as n, then n=0 indi-cates the coal seam layer alone. Now, if the coal seam is extracted then thefirst roof layer is broken down. Theoretically, if there is no volume

expansion, then the volume of broken layer must fill the extractedspace equally. However, it is a proven fact that every solid material afterfracture expands. In this sub-model, the volume expansion factor istaken as a coefficient of the extracted seam height and represented by“d”. Thus, the height of broken materials is equal to (ho+d) and leftover space above the broken materials is equal to (ho−d) as shown inFig. 2a. Fig. 2b shows the sequential failure of the roof rock strata afterthe coal seam extraction by assuming that all the strata have equal thick-ness and each stratum is as thick as the coal seam. The sum of the frac-tured roof strata thickness indicates the height of destressed zone, Hc,above the extracted panel and can be expressed as follows:

Hc ¼ nþ 1ð Þhs−1=2n n−1ð Þð Þd ð1Þ

In order to prove the convergence of Eq. (1), it can be proved thatthe difference between any two consecutive terms in an arithmeticsequence is in a descending order, that is;

anþ1−an ¼ nþ 2ð Þho−1=2n nþ 1ð Þd− nþ 1ð Þho−1=2n n−1ð Þd½ �¼ ho−nd ð2Þ

Itmust be born inmind that in Eq. (2), the terms hs andn are variablesso thatwith an increase of n, its overall valuewill be decreased andhence,the Eq. (2) represents a convergence series. For determining the limitingvalue of n, it can be expressed as follows:

n ¼ hs=d ð3Þ

Table 1Fracture/caving height prediction empirical formulas extracted from the existingliteratures.

Fracture/cavingheightpredictionformulas

Overburdenrockconditions

Rock propertyconstants

Remarks References

a b c

Hc,f=100hs/[(a.hs+b)±c]

Hard rock 0.640 16.00 8.20 Modifiedfrom Pengand Chiang(1984)

YingxinZhou(1991)

Medium hard 1.433 19.00 7.20Soft rock 1.890 32.00 4.90Weathered 2.134 63.00 3.90

Hf=a.w−b – 0.83 11.00 – – Fawcett etal. (1986)

Hc=(hs−Ss)/(b−1)

If the loweststrata sagging

– – – – Peng andChiang(1984)Hc=hs/b−1 If the strata

break and fallwithout anysagging

– – –

Hf=56(hs)1/2 Generalformula

– – – 0.0≤hs≤3.5 Singh andKendorski(1981)

Hf=100hs/(a.hs

+b)Weakoverburden

3100 5.00 – – Chuen(1979)

Mediumoverburden

1.6 3.60 –

Strongoverburden

1.2 2.00 –

Hf=105 NCBminimumcover

– – – hs≤1.7 NCB, PI/1968/8 (revised1971)

Hf=43hs+a 32.00 – – 1.7≤hs≤4.0

Where in equation proposed by Peng and Chiang (1984), Hc is the caving height, b isthe bulking factor, Ss is the sagging of the lowest uncaved strata and Smax is themaximum allowable sagging. If the strata break and fall without any sagging, then,Ss=Smax=0. In the remaining equations given in Table 1, W is the panel width, Hc,for Hf is the fractured height or minimum cover as appropriate, hs is the extracted thick-ness and all quantities are in meters.

a)

b)

Ground Surface

Ground Surface

Fig. 1. Schematic cross-sectional view of a longwall with the corresponding adjacentaccess tunnels and barrier pillars: a) before coal seam extraction, b) after coal seam ex-traction and pack supports erection for the Arithmetic model.


Hence, the limiting equation to be used for determining the heightof destressed zone can be given in the following form:

Hc ¼ hs hs þ 3dð Þ=2d ð4Þ

It is obvious that if expansion factors of the panel roof strata areknown then Eq. (3) can be used to determine the number of roof stratathat must be fractured until the extracted panel space is completelyfilled. Thus, Eqs. (1) or (4) is considered as an arithmetic series whichcan be used to estimate the combined height of fractured and cavedzone or simply the height of destressed zone (HDZ) above the extractedpanel.

3.1.2. Sub-model-2In this model, it is assumed that an increase in volume of broken

panel roof rock strata is a function of the free space in mined panelarea. Hence, if the thickness offirst roof stratum is equal to the extractedseamheight then the height of broken layerwill be increased by a factorof “α”, that is, the height of free space will be decreased accordingly(Fig. 3a). Therefore, the leftover space will be equal to [ho(1−a)]. Ifthe second stratum above extracted panel caves in, then the freespace will be equal to [ho(1−a)2] as illustrated in Fig. 3b. Summingup the terms shown in Fig. 3b yields:

Hc ¼ nhs−ahs n−3ð Þ−ahs 1−að Þ n−5ð Þ−ahs 1−að Þ2 n−7ð Þ−…

þ ahs 1−að Þn−1 ð5Þ

Eq. (5) represents a geometric series whose limiting value can becomputed as follows:

Hc ¼hs 1þ að Þ

að6Þ

By employing Eq. (6), the height of destressed zone above theminedpanel roof can be estimated.

3.2. Geometry-dependent roof fracture

3.2.1. Sub-model-1In this sub-model, it is assumed that the roof failure depends on the

geometry of the panel roof situation and follows a vertical parabolicfunction as has been illustrated in Fig. 4a. Thus by considering the mid-point of the panel roof as the origin of the coordinate system thenwhere the vertical axis intersects themaxima of the parabola representsthe height of fracture zone. Since the parabolic equation can be written

y ¼ ax2 þ bxþ c ð7Þ

Then, by employing the boundary conditions, that is, (0, Hc), (Lw/2, 0),(−Lw/2, 0) and solving Eq. (7) Hc can be determined which representsthe height of destressed zone as shown in Fig. 4b. Hence,

y ¼ 4Hc=L2w

� �x2 þ Hc ð8Þ

a)

b)

Ground Surface

Ground Surface

Fig. 2. Schematic cross-sectional view of a longwall: a) after the first panel roof stratumfailure due to the coal seam extraction, b) due to a gradual increase of the height offracture zone above the extracted panel for the Arithmetic model.

a)

b)

Ground Surface

Ground Surface

Fig. 3. Schematic cross-sectional view of a longwall: a) after the first panel roof stratumfailure due to coal seam extraction, b) due to a gradual increase of the height of fracturezone above the extracted panel for the Geometric model.


Taking the expansion factor of the broken materials into consider-ation and on this account cross-sectional area of the caved in rocks willbe “α” times the area of the parabolic shape shown in Fig. 4b. Thus, theEq. (8) can be further simplified and presented as follows:

Hc ¼ 1:5hs=α ð9Þ

By using Eq. (9) the height of destressed zone above the extractedpanel can be estimated.

3.2.2. Sub-model-2In this model, it is assumed that the shape of destressed zone is

similar to half a vertical ellipse as depicted in Fig. 5a and b. Similarto the parabolic model, it is presumed that the cross-sectional areaof the fractured materials is “α” times the cross-sectional area of thecaved zone. Thus the height of destressed zone can be estimated bythe following formula

Hc ¼ 1:273hs=α ð10Þ

3.2.3. Sub-model-3In this sum-model, it is assumed that the shape of destressed zone

resembles to a triangle as depicted in Fig. 6a. Employing the boundaryconditions (Fig. 6b) similar to the elliptical model and assuming thecross-sectional area of the fractured materials is “α” times the cross-

sectional area of the caved zone then the height of destressed zonecan be estimated by the following equation:

Hc ¼ 2hs=α ð11Þ

By employing the Eq. (11), the height of destressed zone above themined panel roof can easily be estimated.

4. Discussion and comparative analysis of the results

In this section, comparative analyses of the results obtained fromthe five new approaches are given for estimation of the height of des-tressed zone (HDZ). The results are further compared with the onlycomparable formula given by Peng and Chiang (1984). In this paper,variations of the height of destressed zone versus the extracted coalseam height are illustrated in Figs. 7–14. Figs. 15 to 22 illustrate thenon-linear variations of the height of destressed zone with the minedpanel roof rock expansion factors.

Triangular, Parabolic, Elliptical, and Geometric models as well asPeng and Chiang's model illustrate a linear relation between HDZand parameters such as; the expansion factor and the extracted coalseam height. Hence, in these models, the ratio of (Hc/hs) is alwaysconstant, no matter what the coal seam extraction seam height is.While, the Arithmetic model represents a nonlinear relation betweenHDZ and the parameters such as; the expansion factor and the extractedcoal seamheight. Therefore, in the case of Arithmeticmodel, the ratio of

a)

OLw

Hc

hs

b)Ground Surface

Fig. 4. a) Schematic cross-sectional view of a longwall with the corresponding adjacent access tunnels, barrier pillars after coal seam extraction and pack supports erection withparabolic roof failure concept, b) Theoretical Parabolic panel roof failure with a prescribed boundary conditions.

a)

hs

Lw = 2a

Hc =

b

b)Ground Surface

Fig. 5. a) Schematic cross-sectional view of a longwall with the corresponding adjacent access tunnels, barrier pillars after coal seam extraction and pack supports erection withelliptical roof failure concept, b) Theoretical elliptical panel roof failure with prescribed boundary conditions.


(Hc/hs) is not constant; rather it is a linear function of both the expan-sion factor and the extracted coal seamheight. In this paper, the averageexpansion factor of the panel roof rock strata, in all, is taken in the rangeof 5% to 80% for the extracted coal seam thickness ranging from 1.0 to4.5 m.

As it can be seen from Figs. 7 to 14, the Arithmetic model is theonly one that reflects a non-linear relation between the height of des-tressed zone and the extracted coal seam thickness. This model alsoprovides the maximum height of destressed zone for most of thecases. One of the most important results of the proposed formulas isthat; the highest height of destressed zone is attained when the ex-pansion factor is the least. It is obvious that the least expansion factoris attainable with time as the goaf materials are compressed. If an av-erage of 10% expansion factor for the panel roof rock strata is taken torepresent the short-term condition of the fractured rocks for all thecases, then the following results are obtained; the Triangular modelyields Hc=20hs; the Parabolic model yields Hc=15hs; the Ellipticalmodel yields Hc=12.7hs; and the Geometric model yields Hc=11hs.However, the Arithmetic model is extremely sensitive to the extractionheight and yields Hc=6.5hs when hs=1 m, and plus 2.5hs for each halfa meter of increase in the thickness of the extracted coal seam, that is, ifthe value of hs=1.5 m, 2 m, 2.5 m, 3 m, 3.5 m, 4 m, and 4.5 m, then thecorresponding height of destressed zones are; 9, 11.5, 14, 16.5, 19, 21.5,and 24 times the extracted coal seam thickness, respectively. Indeed,

according to the Arithmetic model, for the short-term condition, themaximum height of destressed zone for a 4.5 m of coal seam to beextracted is equal to 24hs. It is interesting to notice that Peng andChiang's formula also have been used in all the cases for comparisonpurposes. As it can be seen from Figs. 7 to 14, Peng and Chiang's Modelyields the height of destressed zone equal to 10 times the extractedcoal seam thickness for the short-term condition. In other words, Pengand Chiang's model can be considered as a special case of the Arithmeticmodel proposed in this paper. Thus, the results of the five differentmath-ematical models presented in this paper, have proven that the height ofdestressed zone (HDZ) induced due to longwall mining is in the range of6.5 to 24 times the extracted coal seam thickness for the short termpanelroof fractured rock condition. In fact, the Arithmetic results representboth the lower and the upper limits for all the five models proposed inthis paper. Indeed, the other four models can be considered as specialcases of the Arithmetic model as well. The authors strongly believe thatthe long-term height of the destressed zone could be much more thanthose considered for the short term condition. Hence, in this paper, anaverage of 5% expansion factor has been taken to represent the long-term condition of the goaf materials and the fractured zone locatedabove the gob-side. On this basis, the long-term results of the modelsare almost twice as much as the height that is induced in the shortterm. That is, if an average of 5%expansion factor for the panel roofrock strata is taken to represent the long-term condition of the fractured

a)

Hc

hs Lw

b)Ground Surface

Fig. 6. a) Schematic cross-sectional view of a longwall with the corresponding adjacent access tunnels, barrier pillars after coal seam extraction and pack supports erection withTriangle roof failure concept, b) Theoretical Triangle panel roof failure with prescribed boundary conditions.

Fig. 7. Relationship between the height of destressed zone and the extracted coal seamheight for the panel roof rocks' average expansion factor of 10%.



rocks for all the cases, then the following results are obtained; the Trian-gular model yields Hc=40hs; the Parabolic model yields Hc=30hs; theElliptical model yields Hc=25.5hs; and the Geometric model yieldsHc=21hs. Peng and Chiang's model, for long term condition, yieldsHc=20hs, versus the value ranging from 20 to 30 times the extractedcoal seam thickness, as shown in Table 2. However, the lower and theupper limits for all five models can be represented by the Arithmeticmodel which ranges from 11.5 to 46.5 times the thickness of the extrac-tion seam height, respectively. Beyond this height the overburden pres-sure will be transferred towards the front abutment, the adjacent accesstunnels, the intervening barrier pillars as well as the panel rib-sides.Hence, no matter at what depth the longwall is located, the completeoverburden pressure will not be inserted on the broken rocks locatedsome distance behind the hydraulic jacks in the gob-side. In fact, the dif-ference between the longwall depth and the critical height of destressedzone must be considered for the calculations of the stress transfer to-wards the front abutment and the adjacent rib-sides. The long-term re-sults of the five new models presented in this paper are shown inTable 2 and are further comparedwith those obtained from the literaturereview. The authors gathered two series of information both ofwhich areprovided in Table 2; one series is based on the empirical inferring, whichshow the combined height of caving and fractured zone (height of des-tressed zone) in the range of 2 to 105 times the extracted coal seamthickness. Whereas, the second series is obtained from the in-situ mea-surements which show the height of destressed zone is in the range of

4 to 92 times the extracted coal seam thickness. The lower and upperlimits of both series of information are significantly far from each otherwhich may show the inherent complexity of the actual geological situa-tion of the mining sites. Though all the five models' results, for the longterm condition, are in the range of 11.5 to 46.5 times the extracted coalseam thickness, it seems that the Arithmetic model embraces the lowerand upper limits which better represent the in-situ conditions comparedwith the other fourmodels and all other existing empirical approaches asshown in Table 2. According to Table 2, the long-term results of themodels proposed in this paper are in a close agreement with the in-situ measurements and with those proposed empirically by researchersas well. Depending upon the depth of longwall mining and the panelwidth or the length of longwall, the height of destressed zone, mayhave a direct influence on the corresponding ground surface subsidencewhich is out of the scope of this paper. Finally, the authors believe thatfurther universal in-situ measurements are required to firmly expressthe integrity and applicability of the existing empirical approaches aswell as the models proposed in this paper.

5. Conclusions

Five new mathematical approaches were proposed to model theheight of destressed zone based on the assumptions of being independentand/or dependent on the geometry of the mined panel roof rock strata.


Fig. 10. Relationship between the height of destressed zone and the extracted coalseam height for the panel roof rocks' average expansion factor of 40%.




The resultswere analyzed and comparedwith both in-situmeasurementsand those proposed empirically by researchers, obtained from a compre-hensive literature review. An average of 5% expansion factor has beentaken to represent the long-term condition of the goaf materials as well

as the roof fractured rocks. Beyond this height the overburden pressurewill be transferred towards the front abutment, the adjacent access tun-nels, the intervening barrier pillars and the panel rib-sides. Hence, nomatter at what depth the longwall is located, the complete overburdenpressurewill not be inserted on the broken rocks located some distance



Fig. 15. Relationship between the height of destressed zone and the panel roof rocks'average expansion factor for an extracted coal seam thickness of 1 m.


Fig. 18. Relationship between the height of destressed zone and the panel roof rocks'average expansion factor for an extracted coal seam thickness of 2.5 m.



behind the hydraulic jacks in the goaf area. In fact, the difference be-tween the longwall depth and the critical height of destressed zone(HDZ) must be considered for the calculations of the stress transfer

towards front abutment and the adjacent rib-sides. On this basis, thelong-term results of the models are proven to be in a close agreementwith the in-situ measurements and with those proposed empiricallyby researchers as shown in Table 2. Though the present models are in-dependent of the strength properties of the mined roof rock strata,they yield very promising and reliable results.





Table 2The results of in-situ measurements and those proposed empirically by researchers in-cluding the results of the five newmathematical models proposed in the present paper.

Height ofcaving zone(×hs)

Height of fractureor destressed zone(×hs)

Reference Method ofappraisal

3–3.5 – Ropski and Lama (1973) Empirical– 50–105 NCB, PI/1968/8 (revised 1971) Empirical– 5–12 Chuen (1979), for weak rock Empirical– 13–31 Chuen (1979), for strong rock Empirical3–6 26–56 Singh and Kendorski (1981) Empirical12 – Karmis et al. (1983) Empirical8–12 50 Styler (1984) In-situ– 20–30 Peng and Chiang (1984) Empirical– 71–105 Fawcett et al. (1986) Empirical4–6 30 Hasenfus et al. (1998) In-situ– 20–100, 19–92 Palchik (1989, 2003a) In-situ– 30–60 Richard et al. (1990) Empirical– 2–3 Zhou (1991), for soft rock Empirical– 5–6 Zhou (1991), for hard rock Empirical– 20–60 Booth and Spande (1992) Empirical2–20 20–50 Chekan and Listak (1993) Empirical– 12 Luo (1997) Empirical– 1–1.1 WP,

WP=160 m,200 m

Mills and O'Grady (1998) In-situ

– 30–35 m, hs=?,(WP=100 m)

Jeffrey and Zhang (2001) In-situ

– 40, 120 m,hs=3 m

Kelly et al. (2002) In-situ

4–11 – Palchik (2002a) In-situ3–6 30–58 [Singh and Kendorski (1981) and

Kendorski (1993), from Karacanand Goodman (2009)]

Empirical

– 80, hs=3 m RafiqulIslam et al. (2009) In-situ5–6 10–11 Zhang et al. (2011) In-situ– 40 Present paper (Triangular model) Theoretical– 30 Present paper (Parabolic model) Theoretical– 25.4 Present paper (Elliptical model) Theoretical– 22 Present paper (Geometric model) Theoretical– 13–48 Present paper (Arithmetic model) Theoretical


Acknowledgments

Acknowledgement is due to the School of Mining Engineering, Col-lege of Engineering, University of Tehran, Tehran, Iran for providing thesabbatical opportunity to the first author to complete this researchwork at the Department of Mining and Materials Engineering, Facultyof Engineering, McGill University, Montreal, Canada. The first authoralso acknowledges that this work could not be completed without re-search support provided by the Department of Mining andMaterials En-gineering, Faculty of Engineering, McGill University, Montreal, Canada.The views expressed in this paper are those of the authors and not nec-essarily of the institutes they work for.

References

Anon, 1995. Longwall Mining, Office of Coal, Nuclear, Electric and Alternate Fuels,20585. U.S. Department of Energy, Washington, DC, pp. 9–10.

Booth, C.J., Spande, E.D., 1992. Potentiometric and aquifer property changes above sub-siding Longwall mine panels, Illinois basin coalfield. Journal of Groundwater 30(3), 362–368.

Chekan, G., Listak, J., 1993. Design practices for multiple-seam longwall mines. Infor-mation Circular 9360. U. S. Bureau of Mines, Pittsburgh, PA. 35 pp.

Chuen, L.T., 1979. Practice and knowledge of coal mining under water bodies. 10thWorld Mining Congress, Istanbul.

Denkhaus, H.G., 1964. Critical review of strata movement theories and their applicationto practical problems. Journal of the Southern African Institute of Mining and Met-allurgy 64 (8), 310–332.

Dinsdale, J.R., 1935. Ground pressure and pressure profiles around mining excavation.Colliery Engineering 12, 406–409.

Eavenson, H., 1923. Mining an upper bituminous seam after a lower seam has beenextracted. Transaction of AIME 69, 398–405.

Fawcett, R.J., Hibberd, S., Singh, R.N., 1986. Analytic calculations of hydraulic conductiv-ities above longwall coal face. Int. J. Mine Water, International Mine Water Associ-ations, pp. 45–60.

Hasenfus, G.J., Johnson, K.L., Su, D.W.H., 1998. A hydrogeomechanical study of overbur-den aquifer response to longwall mining. In: Peng Syd, S. (Ed.), Proceedings of the7th International Conference on Ground Control in Mining. Morgantown: WestVirginia University, COMER, Department of Mining Engineering, pp. 149–162.

Jeffrey, R.G., Zhang, X., 2001. Hydraulic fracturing to induce caving: fracture model de-velopment and comparison to field data. The 38th U.S. Symposium on Rock Me-chanics (USRMS), Washington D.C., Paper No. 01-0251, No. of Pages 10.

Karacan, C.Ö., Diamond, W.P., Esterhuizen, G.S., Schatzel, S.J., 2005. Numerical analysisof the impact of longwall panel width on methane emissions and performance ofgob gas vent holes. Proc. Int. Coalbed Methane Symposium, Paper 0505, Tuscaloosa,AL. 18–19 May. 28 pages.

Karacan, C.Ö., Esterhuizen, G.S., Schatzel, S.J., Diamond, W.P., 2007. Reservoirsimulation-based modeling for characterizing longwall methane emissions andgob gas vent hole production. International of Journal of Coal Geology 71 (2–3),225–245.

Karacan, C.Ö., Goodman, G., 2009. Hydraulic conductivity changes and influencing fac-tors in longwall overburden determined by slug tests in gob gas ventholes. Interna-tional Journal of Rock Mechanics and Mining Sciences Abstract 46 (7), 1162–1174.

Karmis, M., Triplett, T., Haycocks, C., Goodman, G., 1983. Mining subsidence and its pre-diction in an Appalachian coalfield. Rock Mechanics: Theory, Experiment, Practice.Proc. 24th US Symp. Rock Mechanics, 20–23 June 1983, Texas A&M University.Balkema, Rotterdam, pp. 665–675.

Kelly, M., Gale, W., Hatherly, P., Balusul, R., Luo, J.X., 1998. Combining modern assess-ment methods to improve understanding of longwall geomechanics. COAL98Conf. Wollongong 18–20 February, pp. 523–535.

Kelly, M., Luo, X., Craig, S., 2002. Integrating tools for longwall geomechanics assess-ment. Journal of Rock Mechanics and Mining Sciences Abstract 39, 661–676.

Kendorski, F.S., 1993. Effect of high-extraction coal mining on surface and ground wa-ters. Proc 12th Conf. Ground Control in Mining, Morgantown, West Virginia Uni-versity, Morgantown.

Kenny, P., 1969. The caving of the waste on longwall faces. International Journal ofRock Mechanics and Mining Sciences abstract 6 (6), 541–555.

Luo, J., (1997). Gateroad design in overlying multi-seam mines, M.Sc. Thesis in Miningand Minerals Engineering, Faculty of the Virginia Polytechnic Institute and StateUniversity, Blacksburg, Virginia, USA.

Luo, X., Hatherly, P., McKavanagh, B., 1998. Microseismic monitoring of longwall cavingprocesses at Gordonstone Mine, Australia. In: Lin, Y. (Ed.), Advances in Rock Me-chanics. World Scientific Publishing Co. Pte Ltd, pp. 67–79.

Mills, K., O'Grady, P., 1998. Impact of longwall width on overburden behavior. In: Aziz, N.(Ed.), Coal 98: Coal Operators' Conference, University of Wollongong & the AustralasianInstitute of Mining and Metallurgy, pp. 147–155.

National Coal Board (NCB), 1975. Subsidence Engineers Handbook. Production Depart-ment, London, U.K. 49 pp.

Peng, S., Chiang, H., 1984. Longwall Mining. John Wiley & Sons, Inc., New York, NY.708 pp.

Peng, S.S., 1992. Surface Subsidence Engineering. The Society for Mining, Metallurgyand Exploration.

Palchik, V., 1989. Analytical and empirical prognosis of rock foliation in rock masses.Journal of Coal Ukraine 7, 45–46.

Palchik, V., 2002. Influence of physical characteristics of weak rock mass on height ofcaved zone over abandoned subsurface coal mines. Journal of Environmental Geology42 (1), 92–101.

Palchik, V., 2003. Formation of fractured zones in overburden due to longwall mining.Journal of Environmental Geology 44 (1), 28–38.

RafiqulIslam, Md., Hayashi, D., Kamruzzaman, A.B.M., 2009. Finite element modeling ofstress distributions and problems for multi-slice longwall mining in Bangladesh,with special reference to the Barapukuria coal mine. International Journal of CoalGeology 78 (2), 91–109.

Richard, R., Randolph, J., Zipper, D., 1990. High extractionmining, subsidence, andVirginia'swater resources, chapter 4. Subsidence Effects on Water Resources. Virginia Centerfor Coal & Energy Research. Virginia Polytechnic Institute and state University, Virginia,pp. 17–20.

Ropski, S.T., Lama, R.D., 1973. Subsidence in the near-vicinity of a longwall face. Inter-national Journal of Rock Mechanics and Mining Sciences abstract 10 (2), 105–106Available online 18 February 2003.

Singh, M.M., Kendorski, F.S., 1981. Strata disturbance prediction for mining beneathsurface water and waste impoundments. Proc. 1st Conference on Ground Controlin Mining, 76–89., Uni. West Virginia, July 1981.

Singh, G.S.P., Singh, U.K., 2010. Prediction of caving behavior of strata and optimum ratingof hydraulic powered support for longwall workings. International Journal of Rock Me-chanics and Mining Sciences Abstract 47 (1), 1–16.

Styler, N., 1984. Prediction of inter-strata movements above longwall faces. The 25thU.S. Symposium on Rock Mechanics (USRMS), June 25–27, Evanston, IL, PaperNo. 84-0651. 8 pages.

Zhang, D., Fan, G., Ma, L., Wang, X., 2011. Aquifer protection during longwall mining ofshallow coal seams: a case study in the Shendong Coalfield of China. Internationalof Journal of Coal Geology 86 (2–3), 190–196.

Zhou, Y., 1991. Evaluating the impact of multi-seam mining on recoverable coal re-serves in an adjacent seam. Virginia Division of Mineral Resources, Commonwealthof Virginia, Department of Mines, Minerals and Energy, Publication, 104.

Wiggill, R.B., 1963. The effects of different supportmethods on strata behavior around stop-ping excavations. Journal of the Southern African Institute of Mining andMetallurgy 63,391–426.


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