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Numerical modelling as an aid to the determination of the stress distribution in the goaf due to longwall coal mining
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.30, No.7, pp. 1403-1409, 1993
0148-9062/93 $6.00 + 0.00 Pergamon Press Ltd
Printed in Great Britain
Numerical Modelling as an Aid to the Determination of the Stress Distribution in the Goaf Due to Longwall Coal Mining tI. G. T. THIN "I'R. J. PINE :~R. TRUEMAN To dat~ it has not been possible to take accurate in-situ measurements of the stress rise in the goal as a result of longwall mining, date to the difficulty in maintaining contact between in-situ equipment and data loggers. For this reason, research into stress distributions within the goal,, loaded by overlying strata, has been _addressed through numerical modelling, with a strain stiffening constitutive law for the goal. The modelling results have been compared with existing methods and significant differences noted.
INTRODUCTION Prior to longwall panel extraction, barrier pillars are delineated, which can tie up large reserves of valuable coal. When the coal is extracted, the immediate roof, behind the advancing face, will collapse and bulk to form the goaf. The goaf will carry some part of the abutment pressure, the remainder being carried by pillars. To design the pillars, an understanding of the stress development in the goaf is required. The research has the potential of reducing dimensions of barrier pillars, thus increasing minable coal, while still maintaining a safe underground environment. Three zones of disturbance may be defined in response to longwall mining. These are the caved zone (goat'), fractured zone and continuous deformation zone. The caved zone, which is the immediate roof before excavation, ranges in thickness depending on the bulking factor [1]. In this zone the strata collapses to the mine floor, and is broken into irregular shapes with various sizes. Due to the mechanics of failure the collapsing material increases in bulk volume. Above this caved zone lies the fractured zone. The strata here is broken into blocks by predominantly vertical and horizontal cracks associated with bed separation. The blocks in each broken stratum are connected either fully or partially across near vertical fractures. The thickness of the fractured zone ranges from about 28 to 42 times the mining thickness, t [1]. The final (uppermost) zone is where continuous deformation occurs. The strata deforms without causing major cracks, as in the fractured zone. The strata behaves essentially as a continuous medium. "l'Cambome School of Mines, Pool, Redruth, Cornwall TR15 3SE. UK. :l:Division of Geomechanics, CSIRO Australia, PO Box 883, Kenmore, Queensland 4069, Australia.
Continuous Deformation Zone
_ ~ ~ F f ~ c t u r e d
Zone
Figure 1. Three zones of disturbance due to longwall mining [1 ] Results and observations from the numerical modelling indicate the main parameters that are of importance when determining goaf pressure. Authors of previous work have obtained results without taking into consideration the effect of all these parameters, and hence require a number of different simplifying assumptions to be applied to their models. The results from present research have attempted to eliminate as many assumptions as possible, but still to determine the distance at which cover load is reached as a comparable end result. EXISTING E S T I M A T I O N S OF T t I E STRESS D I S T R I B U T I O N IN T I I E G O A F It is generally assumed that the vertical stress builds up gradually in the goaf, until cover load is reached at a distance proportional to seam depth from solid abutments. Several different authors have attempted to analyse this mechanism. Wilson [2], wanting to deduce the stress in the ribside as an aid to pillar design, proposed that the vertical stress in the goaf increases linearly, from zero at the rib to the
1403
1404
ROCK MECHANICS IN THE 1990s
original overburden pressure at some point within the goat'. He estimated that the distance required for the goaf to return to cover load was typically 0.3 times the seam depth (0.3 H). This estimation resulted from research into the width of the pressure arch (a zone of de-stressed strata) on a large number of roadways. In longwall workings, the most important pressure arch is longitudinal, with one abutment in the coal in advance of the face and another in the goaf some distance behind the face. Longwall roadway conditions are generally good for some distance back from the face, beyond this distance the roadway begins to disintegrate. The point where disintegration commences and moves forward with the face, is an indication of the position of the back abutment. The distance between the position of the back abutment and the face will approximate the width of the longitudinal pressure arch. In Wilson's investigations, the pressure arch widths lay in a band between 0.2 H and 0.3 H. He adopted the value of 0.3 H giving the greater pillar stress, leading to the design of larger (safer) pillars. King and Whittaker [3] and C'hoi and McCain [4] proposed another technique which was based on the concept of a shear angle to determine goaf loading. It was suggested that the shear angle might be equal to the angle of draw used in subsidence analysis. Smart and Haley [5] questioned the accepted distance of 0.3 H from abutments, at which full overburden pressure is reached in the goaf. Using roof strata tilt theory and assuming the broken material of the goaf behaved like a very large stone-built pack next to the goaf, they concluded that cover load would be reached at a distance of 0.12 times depth. Unlike other authors, Smart and Haley attempted to take into consideration directly the material properties of the goal Trueman [6] attempted to extend the work of Smart and Haley by obtaining more realistic values of goal compaction, with distance from solid abutments, through numerical modelling. In addition, the stress-strain relationship of the stone-built pack was modified to make it more representative of the goaf material. Trueman proposed that the goaf behaves as a strain stiffening material, with exponential and asymptotic load deformation characteristics which are dependent on the bulking factor of the immediate roof. The material which makes up the goaf is derived from the immediate roof, but its broken state means it must be modelled differently. The goaf is a strain stiffening material and the modulus of deformation will increase with compaction. Trueman [7] attempted to use material properties, that have been quantified by several authors [810], for use in his numerical models. Results were in marked contrast to the observed behaviour in the goaf [7]. However, this was not surprising since there was little justification given by the authors who postulated the initial properties. A severe limitation existed with the particular numerical model that Trueman used. There was no facility in the finite element (IRE) package to simulate a strain stiffening material. Trueman used a manual
iterativc technique to derive initial solutions to the problem. He found that the distance to return to cover load was not purely a function of seam depth as was generally accepted. It was apparent from the results that the distance at which the cover load is reached in the goaf was affected by the seam thickness, or more importantly, the total height of caving. This is influenced by the seam thickness and immediate roof bulking factor. He also found that the goaf could in some cases develop a vertical stress in excess of cover load, but noted that this could have been a numerical / modelling error. Salamon [11] attempted to determine the stress distribution in the goaf analytically using a laminated model of stacked linear elastic plates, in conjunction with a non-linear compaction characteristic for the caved rocks, to describe the behaviour of the rock mass. The model of the rock mass was characterised by two parameters, Young's modulus and an effective lamination thickness. The goaf material was characterised by an effective 'modulus' and the coal seam by an elastic modulus. This allowed the goaf to be modelled as a non-linear strain stiffening material. Summers and Jeffery [12] developed a numerical modelling technique for the prediction of subsurface strata deformation following the extraction of coal by longwall mining. The goaf was represented as a compressible granular fill material. The model was developed primarily for use in the identification of factors that might influence the risk of water flow onto longwall faces and in the quantification of that risk. A factor that appears common to all previous work, is that the longwall panel (which is usually isolated), and subsequent goal have been examined through a transverse cross section parallel to the advancing face. Modelling in this direction will not consider stress distributions local to the face, unlike modelling in a longitudinal direction. T H E USE OF NUMERICAL M O D E L L I N G TO DETERMINE T I l E STRESS DISTRIBUTION IN T H E GOAF Due to difficulties involved with in.situ monitoring, it is clear that numerical modelling offers a possible alternative to determining goaf / pitlar stress distributions, especially with increasing model sophistication. However, all models should be validated, where possible, by available in-situ measurements, such as goaf stress and convergence, subsidence and pillar loading. A successful numerical model must be able to describe the development and behaviour of all factors associated with the extraction of a coal seam and subsequent strata changes. This is usually limited to the available material properties and modelling method. The current research concentrated on stress development in the goaf through modelling, taking into account strata changes resulting from seam extraction. All modelling assumed an isolated panel under hydrostatic stress conditions, on a longitudinal section through the cemre,
ROCK MECHANICS IN THE 1990s without roadways, and used the finite difference code FLAC [13], (Figure 2). First Weighting Interval Modelled Longitudinal Section / /
n2wall
Face
Final
1405
used, which were determined by a combination of precedent, published values and judgement. Limited sensitivity analyses for some of the more critical values is planned for the current research. More comprehensive sensitivity analysis can not be justified until good in-situ data is available (see later). Table 1. Input parameters for H_.AC numerical modelling.
Face Host rock p vy vz G~ E~ Ey
SUeighting \ . b ~Intervals Pc.riocl.i. u ce n t ~.
Coal seam 2550 kg/m3 0.25 0.3 4380 MPa 16700 MPa 8900 MPa
p vy v, G,,r F~ Es
1452 0.25 0.3 1670 6700 3340
kg/m3
MPa MPa MPa
Figure 2. Layout for Iongwall panel modelling Goaf The main stages in the modelling, in order of increasing complexity, were the variation of goaf stiffness and thickness, according to bulking factor, the inclusion of bed separation and vertical joints in the fractured zone and the effects of progressive excavation. Since 1991, researchers at the Camborne School of Mines have used an experimental double yield model (DY) incorporated in the FLAC program, version 2.27. This has recently been made generally available in the release of version 3.0, but is still considered experimental. The DY model was intended to represent a material in which there may be significant irreversible compaction in addition to shear yielding. Such materials include hydraulically-placed backfill or a lightly-cemented granular material. The rock material that makes up the goaf can be considered as a type of backfill. The failure criterion consists of two yield surfaces, one that is mainly active for shear straining, and another that is mainly active during volumetric straining. Both surfaces yield in threedimensional terms, with the out-of-plane stress taken as a principal stress. The shear yield surface corresponds to a Mohr-Coulomb failure criterion, in which only the major and minor principal stresses are active in the formulation. Using the DY model to represent the goaf is considered to be much more realistic than the two dimensional, essentially elastic FE package used by Trueman [6]. The DY model parameters used in the modelling are included in Table 1. The values were based on the goaf strain stiffening relationship proposed by Trueman [6]: = 1/3 (1 - exp ( - (o/2.874)) °'757) where
(1)
e = vertical strain in goal o = vertical stress in goaf
Since coal strata and adjacent host rock are of a sedimentary nature. It was decided that the rock mass would be modelled using the transversely isotropic model available in FLAC. Table 1 shows the parameter values
Bed separations / vertical fractures
K G c p
13583 MPa 273 MPa 0.001 MPa 1700 kg/m3
~b
25.2 °
T Lo(28t) Lo(42t) Lp
0 MPa 128 m 156 m 25 m
P vy, v~
= = = = = = = = =
K. K.
100 MPa/m 100 MPa/m
2°
K,,K~ e
T Lo, Lp
Bulk density Poisson's ratio Shear, Young's, Bulk moduli Shear, Normal stiffnesses Cohesion Dilation angle Friction angle Tensile strength First, periodic weighting intervals
Goaf stiffness and thickness Initial modelling involved simulating a completely mined out panel, with barrier pillars at either end, the goaf being instantly generated through the DY model. The undisturbed strata above the goaf arched between the pillars, resulting in low stresses in the centre of the goaf. It was clear that in order to model the behaviour of the goaf as realistically as possible, it was necessary to incorporate the mechanisms of broken rock creation and compaction. The next model involved a mechanism similar to the assumption made by Wilson [2]. The overlying undisturbed beds "cantilever" from the abutment over the goaf from which they receive vertical support. This support increases progressively away from the abutment, until full cover load is achieved.
1406
ROCK MECHANICS IN THE 1990s
The new model was tested; completely mining out a panel with the goaf instantly generated. This time, only one barrier pillar was used so that the goal in effect, was loaded by the eantilevering beam (Figure 3 and 3a). Simulations were carried out with seams at various depths and of thicknesses (t). The results of the stress distribution in the goaf, are shown in Table 2. It is evident that the thicker the seam, the greater the distance at which cover load is reached first, because a thicker seam produces a thicker, more deformable g o a l The results also show that cover load was achieved at shorter spans from the abutment with the deeper seams. The greater overburden load available results more quickly in a stiffer goaf response, because of the strain stiffening nature of the goal This trend is opposite to that given by distance to cover load equal to 0.3 H, as used conventionally. Trueman [6] also gave results comparable to the current modelling results. i c¢
Overlying Strata (interfacing representing bed separation)
r,
Coal Seam ¢
@
~x
Table 2. Distanoea into the $oaf at which cover load is reached.
Depth to seam (m)
200
400
600
800
1.5
240
216
180
168
3.0
315
288
228
210
Seam thickness (m)
Effect of fractured zone above the goaf Incorporating the fractured zone (a direct response of seam extraction) was the next stage of modelling. As the seam is extracted, bed separation propagates within the fractured zone, together with the generation of vertical and sub vertical fractures. First, however, it was decided to model horizontal bed separation only. This was simulated through the use of an interface, with the lower and upper limits of zone thickness (28t to 420. The goaf was generated instantly after the panel was mined out and loaded by the cantilevering beds (Figure 4). The modelling involved seams at various depths and of various thicknesses (t). For comparison, a model was also included without bed separation.
el>
Direction of Mining
Roller Boundary Bed Separation
Figure 3. Datum model
Fracture Zone Thickness Pillar
Overlying Strata Cantilevering Over Goaf
c~
Mining Direction
(b
-
>
6x
I
I
Instant Goaf
~
6x
Figure 4. Instant goaf with bed separation Pillar
[
Instant Goaf
¢
Figure 3a. Instant goaf, loaded by cantilevefing beam
Table 3 shows the distances that cover load is reached first. It is obvious that without the bed separation, the "beam" above the goaf is at its stiffest and large spanning distances are required before vertical stress is generated in the goat'. With bed separation, the thickest beam (420 is stiffer than the thinnest (28t) resulting in greater spans, but less than those of the intact beam.
ROCK MECHANICS IN THE 1990s Table 3. Distances into the goaf at which cover load is reached, without the fractured zone and with the lower and upper limits of the fractured zone.
Depth to seam (m)
200
400
600
Block Generated by first Weighting Interval
,U
800
Seam thickness 1.5m Without fractured zone Fractured zone 28t Fractured zone 42t
1407
Pillar 246 200 219
213 171 189
195 158 175
174 138 156
330 231 260
240 207 218
225 183 205
210 165 189
Direction of Mining
~o
>
Coal Seam
Seam thickness 3.0m Without fractured zone Fractured zone 28t Fractured zone 42t
Figure 5. Gradual extraction with first weighting interval Subsequent Periodic Weighting Intervals, Modelled as a Single Block
Effect of grad, al panel extraction ,
The previous models gave some confidence in the me of interfaces and the DY model, but were clearly some way short of a good simulation. Ultimately the modelling was developed to include the progressive creation of the goaf with the accompanying horizontal bed separation and vertical fracturing in phase with the excavation geometry. The modelling of the gradual extraction of the panel incorporated first and subsequent (periodic) weighting intervals [1]. The first phase is controlled by the maximum span of the overlying beds before significant caving commences. With such a span, the maximum roof pressure measured at the face area is called the first weighting and the span is known as the first weighting interval, Lo. Second phase commences immediately after the first weighting and extends to the completion of the excavated panel. During this period, roof pressure at the face area increases and decreases cyclically due to the breakage of the immediate roof, this is termed the periodic roof weighting. The maximum pressure occurring in each period is the periodic roof weighting pressure, and the distance between two consecutive peak roof weightings is called the periodic roof weighting interval, Lp. Bed separation and vertical fractures are predominant in this zone. Sub vertical fractures are also present, the intensity dependent on strata conditions. It was decide first to model the first weighting interval, again dependent on immediate roof strata, and a subsequent single block which included a number of periodic weighting intervals (Figure 5 and 5a). This approach was adopted to limit modelling time. This was considered to be a reasonable starting point, since the actual intensity of sub vertical fractures was unknown. A more detailed and extensive fracture pattern was considered later.
q q q
',
Pillar
6x
:
:
,,
i
* i ¢
I * i
'
~
; i i
;
l
Goaf
~
Figure 5a. Gradual extraction with periodic weighting interval Again the modelling involved seams at various depths and of varying thicknesses. The overlying strata continued to cantilever over the goaf, and since the fractured zone was then in blocks as opposed to a beam, a relatively sharp contraflexure section developed. Results of distances to reach cover load first, are shown in Table 4. With gradual panel extraction, the blocks generated by first and periodic weighting intervals, do not allow large spanning distances and are freer to move downward and more rapidly load the g o a l Table 4. Distances to cover load in the goal which has been generated gradually.
Depth to seam (m)
200
400
600
800
246 173 161
213 131 131
195 125 119
174 116 101
330 197 187
240 167 149
225 161 137
210 149 119
Seam thickness 1.5m Without fractured zone Fracture zone 28t Fracture zone 42t Seam thickness 3.Ore Without fractured zone Fracture zone 28t Fracture zone 42t
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ROCK MECHANICS IN THE 1990s
Final model
This final stage in modelling was similar to the previous stage but differing in two ways. Barrier pillars, at either end of the panel were included, together with the modelling of each individual periodic weighting interval, creating an extensive fracture pattern in the fracture zone. This simulation needed a large model that required over thirty hours of computing time on a 30486-DX PC. The results showed increasing and decreasing stress in the goaf due to the cyclical breakage of the fractured zone and gradual goaf development. The cyclical process corresponded to actual mining cycles; panel extraction, advancing supports, immediate roof collapsing forming the goal, generating the fractured zone, for the entire panel length. Because of the size of model and computing time required, a complete parametric study was not carried out. Some results are shown in Figure 6. Mo~el ¢ o m ~ , oep~ 4oo m ,,~eaZl~1,5 m, ~ w e r I,,,oad1Q MPa
Thick beam (42t)
50
100
_ ,:~7...
150
200
:r,
250
300
The FLAC finite difference model described includes most of these requirements in two dimensions, but gives a data limited understanding [14], due to lack of in-situ measurement and monitoring. So far, only single separation planes have been included in the models. It is considered that the most important zone is below the separation plane. Provided the effective strength and stiffness parameters are approximately correct in this zone, the resulting goaf pressure distributions should be correct (or nearly so). Further work is planned to model the zone both as an anisotropic continuum and with additional separation planes. Clearly local geology will affect the choice of a suitable type of model. The modelled stress distributions are qualitatively different from previous assumptions. In particular the distance to full cover load developing within the goal has been shown to be sensitive to many factors. These include the height and nature of the fractured zone, the height, bulking factor and compressibility of the caved zone and the generation of fractures with the progression of the face line. As also found by Trueman [6], the conventional direct linear relationship between depth to seam and distance to cover load was not substantiated. The strain stiffening behaviour of the goaf is very important in this regard. Model validation requires a combination of direct and indirect in-situ measurements. Depending on the actual extraction this could or should include in-situ stress, induced stresses in pillars, height of fracturing / softening above goaf, subsidence profiles, roadway damage observations and measured goal pressures. Some of these types of measurement are available but many are still needed. There is a need Ibr a comprehensive measurement program at one location.
Figure 6. Model comparisons of different goaf pressure profiles In this Figure, pressure profiles are plotted for the 1.5 m thick seams with 28t and 42t thick fracture zones (previous simplified model) and for the final model. The effects of cyclical excavation are more pronounced in the latter. Although distances to first cover load are similar, the pressure profiles show significant differences. In contrast to the Wilson model, the profiles are non-linear. DISCUSSION AND C O N C L U S I O N The design of longwall panel and pillar layouts will be aided by a better understanding of the relative pillar and goaf load distributions, in particular the pressure profile in the goaf. Numerical modelling, in conjunction with comprehensive in.situ measurements provides a good approach. A useful model must include strain stiffening behaviour of goaf, rock mass strength and deformation anisotropy and the development of fractures with progressive excavation. Ultimately the modelling must be in true three dimensions (four including the progression of the face).
Acknowledgment- The lead author is supported financially by the UK Science and Engineering Research Council.
REFERENCES 1. Peng S.S. and Chaing tt.S. Longwa/I Mining, p. 17-73. John Wiley & Sons, Inc., New York (1984). 2. Wilson A.H. The stability of underground workings in the soft rocks of coal measures. Unpublished Ph.D Thesis, Univ. Nottingham (1980). 3. King H3. and Whittaker B.N. A review of current knowledge on roadway behaviour. Proc. Syrup. on Roadway Strata Control Inst. Mi~ Met. 73-87 (1971). 4. Choi D.S. and McCain D.L. Design of longwall systems. Trans. Soc. Min. Eng, AIME, 7,68, 1761-1764 (1980). 5. Smart B.G.D. and Haley S.M. Further developments of the establishment of stress development in a caved waste. Min. ScL Technol. 5, 121-130 (1987). 6. Trueman R. A finite element analysis for the establishment of stress development in a coal mine caved waste. Min. Sci. Technol. 10, 247-251 (1990). 7. Trueman R. An evaluation of strata support techniques in
ROCK MECHANICS IN THE 1990s dual life gateroads. Unpublished Ph.D. Thesis. Univ. Wales, Cardiff (1988). 8. Peng S.S. Coal mine ground control, p. 281-294. John Wiley and Sons Inc., New York. (1978). 9. Hsuing S.M. and Peng S.S. Chain pillar design for US Longwall panels. Min. Sci. Technol. 2, 297-305 (1985). 10. Price M.A. The prediction of powered support behaviour on longwall coal faces. Unpublished Ph.D. Thesis. Univ. Wales, Cardiff (1981).
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11. Salamon M.D.G. Displacements and stresses induced by Iongwall mining in coal. 7th Int. Congress Rock Mech., ISRM, Aachen, Germany, 2, 1199-1202 (1991). 12. Summers J.W. and Jeffery R.I. Numerical prediction of strata deformation associated with Iongwall mining. Trans. Instn. Min. Metall. Sect A, 101, 63-74 Jan-April (1992). 13. FLAC manual (vet 3.01). ltasca Consulting Group, Inc. Minnesota. 55414 USA (1987). 14. Starfield A.M and Cundall P.A. Towards a methodology for rock mechanics modelling. Int. J. Rock Mech. Min. ScL & Geomech. Abstr. 25, No. 3, 99-106 (1988)
0148-9062/93 $6.00 + 0.00 Pergamon Press Ltd
Printed in Great Britain
Numerical Modelling as an Aid to the Determination of the Stress Distribution in the Goaf Due to Longwall Coal Mining tI. G. T. THIN "I'R. J. PINE :~R. TRUEMAN To dat~ it has not been possible to take accurate in-situ measurements of the stress rise in the goal as a result of longwall mining, date to the difficulty in maintaining contact between in-situ equipment and data loggers. For this reason, research into stress distributions within the goal,, loaded by overlying strata, has been _addressed through numerical modelling, with a strain stiffening constitutive law for the goal. The modelling results have been compared with existing methods and significant differences noted.
INTRODUCTION Prior to longwall panel extraction, barrier pillars are delineated, which can tie up large reserves of valuable coal. When the coal is extracted, the immediate roof, behind the advancing face, will collapse and bulk to form the goaf. The goaf will carry some part of the abutment pressure, the remainder being carried by pillars. To design the pillars, an understanding of the stress development in the goaf is required. The research has the potential of reducing dimensions of barrier pillars, thus increasing minable coal, while still maintaining a safe underground environment. Three zones of disturbance may be defined in response to longwall mining. These are the caved zone (goat'), fractured zone and continuous deformation zone. The caved zone, which is the immediate roof before excavation, ranges in thickness depending on the bulking factor [1]. In this zone the strata collapses to the mine floor, and is broken into irregular shapes with various sizes. Due to the mechanics of failure the collapsing material increases in bulk volume. Above this caved zone lies the fractured zone. The strata here is broken into blocks by predominantly vertical and horizontal cracks associated with bed separation. The blocks in each broken stratum are connected either fully or partially across near vertical fractures. The thickness of the fractured zone ranges from about 28 to 42 times the mining thickness, t [1]. The final (uppermost) zone is where continuous deformation occurs. The strata deforms without causing major cracks, as in the fractured zone. The strata behaves essentially as a continuous medium. "l'Cambome School of Mines, Pool, Redruth, Cornwall TR15 3SE. UK. :l:Division of Geomechanics, CSIRO Australia, PO Box 883, Kenmore, Queensland 4069, Australia.
Continuous Deformation Zone
_ ~ ~ F f ~ c t u r e d
Zone
Figure 1. Three zones of disturbance due to longwall mining [1 ] Results and observations from the numerical modelling indicate the main parameters that are of importance when determining goaf pressure. Authors of previous work have obtained results without taking into consideration the effect of all these parameters, and hence require a number of different simplifying assumptions to be applied to their models. The results from present research have attempted to eliminate as many assumptions as possible, but still to determine the distance at which cover load is reached as a comparable end result. EXISTING E S T I M A T I O N S OF T t I E STRESS D I S T R I B U T I O N IN T I I E G O A F It is generally assumed that the vertical stress builds up gradually in the goaf, until cover load is reached at a distance proportional to seam depth from solid abutments. Several different authors have attempted to analyse this mechanism. Wilson [2], wanting to deduce the stress in the ribside as an aid to pillar design, proposed that the vertical stress in the goaf increases linearly, from zero at the rib to the
1403
1404
ROCK MECHANICS IN THE 1990s
original overburden pressure at some point within the goat'. He estimated that the distance required for the goaf to return to cover load was typically 0.3 times the seam depth (0.3 H). This estimation resulted from research into the width of the pressure arch (a zone of de-stressed strata) on a large number of roadways. In longwall workings, the most important pressure arch is longitudinal, with one abutment in the coal in advance of the face and another in the goaf some distance behind the face. Longwall roadway conditions are generally good for some distance back from the face, beyond this distance the roadway begins to disintegrate. The point where disintegration commences and moves forward with the face, is an indication of the position of the back abutment. The distance between the position of the back abutment and the face will approximate the width of the longitudinal pressure arch. In Wilson's investigations, the pressure arch widths lay in a band between 0.2 H and 0.3 H. He adopted the value of 0.3 H giving the greater pillar stress, leading to the design of larger (safer) pillars. King and Whittaker [3] and C'hoi and McCain [4] proposed another technique which was based on the concept of a shear angle to determine goaf loading. It was suggested that the shear angle might be equal to the angle of draw used in subsidence analysis. Smart and Haley [5] questioned the accepted distance of 0.3 H from abutments, at which full overburden pressure is reached in the goaf. Using roof strata tilt theory and assuming the broken material of the goaf behaved like a very large stone-built pack next to the goaf, they concluded that cover load would be reached at a distance of 0.12 times depth. Unlike other authors, Smart and Haley attempted to take into consideration directly the material properties of the goal Trueman [6] attempted to extend the work of Smart and Haley by obtaining more realistic values of goal compaction, with distance from solid abutments, through numerical modelling. In addition, the stress-strain relationship of the stone-built pack was modified to make it more representative of the goaf material. Trueman proposed that the goaf behaves as a strain stiffening material, with exponential and asymptotic load deformation characteristics which are dependent on the bulking factor of the immediate roof. The material which makes up the goaf is derived from the immediate roof, but its broken state means it must be modelled differently. The goaf is a strain stiffening material and the modulus of deformation will increase with compaction. Trueman [7] attempted to use material properties, that have been quantified by several authors [810], for use in his numerical models. Results were in marked contrast to the observed behaviour in the goaf [7]. However, this was not surprising since there was little justification given by the authors who postulated the initial properties. A severe limitation existed with the particular numerical model that Trueman used. There was no facility in the finite element (IRE) package to simulate a strain stiffening material. Trueman used a manual
iterativc technique to derive initial solutions to the problem. He found that the distance to return to cover load was not purely a function of seam depth as was generally accepted. It was apparent from the results that the distance at which the cover load is reached in the goaf was affected by the seam thickness, or more importantly, the total height of caving. This is influenced by the seam thickness and immediate roof bulking factor. He also found that the goaf could in some cases develop a vertical stress in excess of cover load, but noted that this could have been a numerical / modelling error. Salamon [11] attempted to determine the stress distribution in the goaf analytically using a laminated model of stacked linear elastic plates, in conjunction with a non-linear compaction characteristic for the caved rocks, to describe the behaviour of the rock mass. The model of the rock mass was characterised by two parameters, Young's modulus and an effective lamination thickness. The goaf material was characterised by an effective 'modulus' and the coal seam by an elastic modulus. This allowed the goaf to be modelled as a non-linear strain stiffening material. Summers and Jeffery [12] developed a numerical modelling technique for the prediction of subsurface strata deformation following the extraction of coal by longwall mining. The goaf was represented as a compressible granular fill material. The model was developed primarily for use in the identification of factors that might influence the risk of water flow onto longwall faces and in the quantification of that risk. A factor that appears common to all previous work, is that the longwall panel (which is usually isolated), and subsequent goal have been examined through a transverse cross section parallel to the advancing face. Modelling in this direction will not consider stress distributions local to the face, unlike modelling in a longitudinal direction. T H E USE OF NUMERICAL M O D E L L I N G TO DETERMINE T I l E STRESS DISTRIBUTION IN T H E GOAF Due to difficulties involved with in.situ monitoring, it is clear that numerical modelling offers a possible alternative to determining goaf / pitlar stress distributions, especially with increasing model sophistication. However, all models should be validated, where possible, by available in-situ measurements, such as goaf stress and convergence, subsidence and pillar loading. A successful numerical model must be able to describe the development and behaviour of all factors associated with the extraction of a coal seam and subsequent strata changes. This is usually limited to the available material properties and modelling method. The current research concentrated on stress development in the goaf through modelling, taking into account strata changes resulting from seam extraction. All modelling assumed an isolated panel under hydrostatic stress conditions, on a longitudinal section through the cemre,
ROCK MECHANICS IN THE 1990s without roadways, and used the finite difference code FLAC [13], (Figure 2). First Weighting Interval Modelled Longitudinal Section / /
n2wall
Face
Final
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used, which were determined by a combination of precedent, published values and judgement. Limited sensitivity analyses for some of the more critical values is planned for the current research. More comprehensive sensitivity analysis can not be justified until good in-situ data is available (see later). Table 1. Input parameters for H_.AC numerical modelling.
Face Host rock p vy vz G~ E~ Ey
SUeighting \ . b ~Intervals Pc.riocl.i. u ce n t ~.
Coal seam 2550 kg/m3 0.25 0.3 4380 MPa 16700 MPa 8900 MPa
p vy v, G,,r F~ Es
1452 0.25 0.3 1670 6700 3340
kg/m3
MPa MPa MPa
Figure 2. Layout for Iongwall panel modelling Goaf The main stages in the modelling, in order of increasing complexity, were the variation of goaf stiffness and thickness, according to bulking factor, the inclusion of bed separation and vertical joints in the fractured zone and the effects of progressive excavation. Since 1991, researchers at the Camborne School of Mines have used an experimental double yield model (DY) incorporated in the FLAC program, version 2.27. This has recently been made generally available in the release of version 3.0, but is still considered experimental. The DY model was intended to represent a material in which there may be significant irreversible compaction in addition to shear yielding. Such materials include hydraulically-placed backfill or a lightly-cemented granular material. The rock material that makes up the goaf can be considered as a type of backfill. The failure criterion consists of two yield surfaces, one that is mainly active for shear straining, and another that is mainly active during volumetric straining. Both surfaces yield in threedimensional terms, with the out-of-plane stress taken as a principal stress. The shear yield surface corresponds to a Mohr-Coulomb failure criterion, in which only the major and minor principal stresses are active in the formulation. Using the DY model to represent the goaf is considered to be much more realistic than the two dimensional, essentially elastic FE package used by Trueman [6]. The DY model parameters used in the modelling are included in Table 1. The values were based on the goaf strain stiffening relationship proposed by Trueman [6]: = 1/3 (1 - exp ( - (o/2.874)) °'757) where
(1)
e = vertical strain in goal o = vertical stress in goaf
Since coal strata and adjacent host rock are of a sedimentary nature. It was decided that the rock mass would be modelled using the transversely isotropic model available in FLAC. Table 1 shows the parameter values
Bed separations / vertical fractures
K G c p
13583 MPa 273 MPa 0.001 MPa 1700 kg/m3
~b
25.2 °
T Lo(28t) Lo(42t) Lp
0 MPa 128 m 156 m 25 m
P vy, v~
= = = = = = = = =
K. K.
100 MPa/m 100 MPa/m
2°
K,,K~ e
T Lo, Lp
Bulk density Poisson's ratio Shear, Young's, Bulk moduli Shear, Normal stiffnesses Cohesion Dilation angle Friction angle Tensile strength First, periodic weighting intervals
Goaf stiffness and thickness Initial modelling involved simulating a completely mined out panel, with barrier pillars at either end, the goaf being instantly generated through the DY model. The undisturbed strata above the goaf arched between the pillars, resulting in low stresses in the centre of the goaf. It was clear that in order to model the behaviour of the goaf as realistically as possible, it was necessary to incorporate the mechanisms of broken rock creation and compaction. The next model involved a mechanism similar to the assumption made by Wilson [2]. The overlying undisturbed beds "cantilever" from the abutment over the goaf from which they receive vertical support. This support increases progressively away from the abutment, until full cover load is achieved.
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ROCK MECHANICS IN THE 1990s
The new model was tested; completely mining out a panel with the goaf instantly generated. This time, only one barrier pillar was used so that the goal in effect, was loaded by the eantilevering beam (Figure 3 and 3a). Simulations were carried out with seams at various depths and of thicknesses (t). The results of the stress distribution in the goaf, are shown in Table 2. It is evident that the thicker the seam, the greater the distance at which cover load is reached first, because a thicker seam produces a thicker, more deformable g o a l The results also show that cover load was achieved at shorter spans from the abutment with the deeper seams. The greater overburden load available results more quickly in a stiffer goaf response, because of the strain stiffening nature of the goal This trend is opposite to that given by distance to cover load equal to 0.3 H, as used conventionally. Trueman [6] also gave results comparable to the current modelling results. i c¢
Overlying Strata (interfacing representing bed separation)
r,
Coal Seam ¢
@
~x
Table 2. Distanoea into the $oaf at which cover load is reached.
Depth to seam (m)
200
400
600
800
1.5
240
216
180
168
3.0
315
288
228
210
Seam thickness (m)
Effect of fractured zone above the goaf Incorporating the fractured zone (a direct response of seam extraction) was the next stage of modelling. As the seam is extracted, bed separation propagates within the fractured zone, together with the generation of vertical and sub vertical fractures. First, however, it was decided to model horizontal bed separation only. This was simulated through the use of an interface, with the lower and upper limits of zone thickness (28t to 420. The goaf was generated instantly after the panel was mined out and loaded by the cantilevering beds (Figure 4). The modelling involved seams at various depths and of various thicknesses (t). For comparison, a model was also included without bed separation.
el>
Direction of Mining
Roller Boundary Bed Separation
Figure 3. Datum model
Fracture Zone Thickness Pillar
Overlying Strata Cantilevering Over Goaf
c~
Mining Direction
(b
-
>
6x
I
I
Instant Goaf
~
6x
Figure 4. Instant goaf with bed separation Pillar
[
Instant Goaf
¢
Figure 3a. Instant goaf, loaded by cantilevefing beam
Table 3 shows the distances that cover load is reached first. It is obvious that without the bed separation, the "beam" above the goaf is at its stiffest and large spanning distances are required before vertical stress is generated in the goat'. With bed separation, the thickest beam (420 is stiffer than the thinnest (28t) resulting in greater spans, but less than those of the intact beam.
ROCK MECHANICS IN THE 1990s Table 3. Distances into the goaf at which cover load is reached, without the fractured zone and with the lower and upper limits of the fractured zone.
Depth to seam (m)
200
400
600
Block Generated by first Weighting Interval
,U
800
Seam thickness 1.5m Without fractured zone Fractured zone 28t Fractured zone 42t
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Pillar 246 200 219
213 171 189
195 158 175
174 138 156
330 231 260
240 207 218
225 183 205
210 165 189
Direction of Mining
~o
>
Coal Seam
Seam thickness 3.0m Without fractured zone Fractured zone 28t Fractured zone 42t
Figure 5. Gradual extraction with first weighting interval Subsequent Periodic Weighting Intervals, Modelled as a Single Block
Effect of grad, al panel extraction ,
The previous models gave some confidence in the me of interfaces and the DY model, but were clearly some way short of a good simulation. Ultimately the modelling was developed to include the progressive creation of the goaf with the accompanying horizontal bed separation and vertical fracturing in phase with the excavation geometry. The modelling of the gradual extraction of the panel incorporated first and subsequent (periodic) weighting intervals [1]. The first phase is controlled by the maximum span of the overlying beds before significant caving commences. With such a span, the maximum roof pressure measured at the face area is called the first weighting and the span is known as the first weighting interval, Lo. Second phase commences immediately after the first weighting and extends to the completion of the excavated panel. During this period, roof pressure at the face area increases and decreases cyclically due to the breakage of the immediate roof, this is termed the periodic roof weighting. The maximum pressure occurring in each period is the periodic roof weighting pressure, and the distance between two consecutive peak roof weightings is called the periodic roof weighting interval, Lp. Bed separation and vertical fractures are predominant in this zone. Sub vertical fractures are also present, the intensity dependent on strata conditions. It was decide first to model the first weighting interval, again dependent on immediate roof strata, and a subsequent single block which included a number of periodic weighting intervals (Figure 5 and 5a). This approach was adopted to limit modelling time. This was considered to be a reasonable starting point, since the actual intensity of sub vertical fractures was unknown. A more detailed and extensive fracture pattern was considered later.
q q q
',
Pillar
6x
:
:
,,
i
* i ¢
I * i
'
~
; i i
;
l
Goaf
~
Figure 5a. Gradual extraction with periodic weighting interval Again the modelling involved seams at various depths and of varying thicknesses. The overlying strata continued to cantilever over the goaf, and since the fractured zone was then in blocks as opposed to a beam, a relatively sharp contraflexure section developed. Results of distances to reach cover load first, are shown in Table 4. With gradual panel extraction, the blocks generated by first and periodic weighting intervals, do not allow large spanning distances and are freer to move downward and more rapidly load the g o a l Table 4. Distances to cover load in the goal which has been generated gradually.
Depth to seam (m)
200
400
600
800
246 173 161
213 131 131
195 125 119
174 116 101
330 197 187
240 167 149
225 161 137
210 149 119
Seam thickness 1.5m Without fractured zone Fracture zone 28t Fracture zone 42t Seam thickness 3.Ore Without fractured zone Fracture zone 28t Fracture zone 42t
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ROCK MECHANICS IN THE 1990s
Final model
This final stage in modelling was similar to the previous stage but differing in two ways. Barrier pillars, at either end of the panel were included, together with the modelling of each individual periodic weighting interval, creating an extensive fracture pattern in the fracture zone. This simulation needed a large model that required over thirty hours of computing time on a 30486-DX PC. The results showed increasing and decreasing stress in the goaf due to the cyclical breakage of the fractured zone and gradual goaf development. The cyclical process corresponded to actual mining cycles; panel extraction, advancing supports, immediate roof collapsing forming the goal, generating the fractured zone, for the entire panel length. Because of the size of model and computing time required, a complete parametric study was not carried out. Some results are shown in Figure 6. Mo~el ¢ o m ~ , oep~ 4oo m ,,~eaZl~1,5 m, ~ w e r I,,,oad1Q MPa
Thick beam (42t)
50
100
_ ,:~7...
150
200
:r,
250
300
The FLAC finite difference model described includes most of these requirements in two dimensions, but gives a data limited understanding [14], due to lack of in-situ measurement and monitoring. So far, only single separation planes have been included in the models. It is considered that the most important zone is below the separation plane. Provided the effective strength and stiffness parameters are approximately correct in this zone, the resulting goaf pressure distributions should be correct (or nearly so). Further work is planned to model the zone both as an anisotropic continuum and with additional separation planes. Clearly local geology will affect the choice of a suitable type of model. The modelled stress distributions are qualitatively different from previous assumptions. In particular the distance to full cover load developing within the goal has been shown to be sensitive to many factors. These include the height and nature of the fractured zone, the height, bulking factor and compressibility of the caved zone and the generation of fractures with the progression of the face line. As also found by Trueman [6], the conventional direct linear relationship between depth to seam and distance to cover load was not substantiated. The strain stiffening behaviour of the goaf is very important in this regard. Model validation requires a combination of direct and indirect in-situ measurements. Depending on the actual extraction this could or should include in-situ stress, induced stresses in pillars, height of fracturing / softening above goaf, subsidence profiles, roadway damage observations and measured goal pressures. Some of these types of measurement are available but many are still needed. There is a need Ibr a comprehensive measurement program at one location.
Figure 6. Model comparisons of different goaf pressure profiles In this Figure, pressure profiles are plotted for the 1.5 m thick seams with 28t and 42t thick fracture zones (previous simplified model) and for the final model. The effects of cyclical excavation are more pronounced in the latter. Although distances to first cover load are similar, the pressure profiles show significant differences. In contrast to the Wilson model, the profiles are non-linear. DISCUSSION AND C O N C L U S I O N The design of longwall panel and pillar layouts will be aided by a better understanding of the relative pillar and goaf load distributions, in particular the pressure profile in the goaf. Numerical modelling, in conjunction with comprehensive in.situ measurements provides a good approach. A useful model must include strain stiffening behaviour of goaf, rock mass strength and deformation anisotropy and the development of fractures with progressive excavation. Ultimately the modelling must be in true three dimensions (four including the progression of the face).
Acknowledgment- The lead author is supported financially by the UK Science and Engineering Research Council.
REFERENCES 1. Peng S.S. and Chaing tt.S. Longwa/I Mining, p. 17-73. John Wiley & Sons, Inc., New York (1984). 2. Wilson A.H. The stability of underground workings in the soft rocks of coal measures. Unpublished Ph.D Thesis, Univ. Nottingham (1980). 3. King H3. and Whittaker B.N. A review of current knowledge on roadway behaviour. Proc. Syrup. on Roadway Strata Control Inst. Mi~ Met. 73-87 (1971). 4. Choi D.S. and McCain D.L. Design of longwall systems. Trans. Soc. Min. Eng, AIME, 7,68, 1761-1764 (1980). 5. Smart B.G.D. and Haley S.M. Further developments of the establishment of stress development in a caved waste. Min. ScL Technol. 5, 121-130 (1987). 6. Trueman R. A finite element analysis for the establishment of stress development in a coal mine caved waste. Min. Sci. Technol. 10, 247-251 (1990). 7. Trueman R. An evaluation of strata support techniques in
ROCK MECHANICS IN THE 1990s dual life gateroads. Unpublished Ph.D. Thesis. Univ. Wales, Cardiff (1988). 8. Peng S.S. Coal mine ground control, p. 281-294. John Wiley and Sons Inc., New York. (1978). 9. Hsuing S.M. and Peng S.S. Chain pillar design for US Longwall panels. Min. Sci. Technol. 2, 297-305 (1985). 10. Price M.A. The prediction of powered support behaviour on longwall coal faces. Unpublished Ph.D. Thesis. Univ. Wales, Cardiff (1981).
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11. Salamon M.D.G. Displacements and stresses induced by Iongwall mining in coal. 7th Int. Congress Rock Mech., ISRM, Aachen, Germany, 2, 1199-1202 (1991). 12. Summers J.W. and Jeffery R.I. Numerical prediction of strata deformation associated with Iongwall mining. Trans. Instn. Min. Metall. Sect A, 101, 63-74 Jan-April (1992). 13. FLAC manual (vet 3.01). ltasca Consulting Group, Inc. Minnesota. 55414 USA (1987). 14. Starfield A.M and Cundall P.A. Towards a methodology for rock mechanics modelling. Int. J. Rock Mech. Min. ScL & Geomech. Abstr. 25, No. 3, 99-106 (1988)