Chain pillar design for U.S. longwall panels

Mining, Science and Technology, 2 (1985) 279-305 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

279

CHAIN PILLAR DESIGN FOR U. S. LONGWALL PANELS S.M. Hsiung and Syd S. Peng Department of Mining Engineering, College of Mineral and Energy Resources, West Virginia University, P.O. Box 6070, Morgan town, WV 26506- 6070 (U.S.A.) (Received December 1984; accepted February 9, 1985)

ABSTRACT A chain pillar design formula under weak roof conditions was developed by statistically analyzing the results from the three-dimensional finite-element parametric analyses. The parameters such as mechanical properties of the roof and floor strata, overburden depth, panel width and length, and coal strength were incorporated in the formula. Case studies were performed to

verify the effectiveness of the formula developed. A conversion formula which transfers a rectangular chain pillar into a square chain pillar of equal strength is proposed. The influence of high in-situ horizontal stresses, which are often encountered in the coalfield, on chain pillar stabifity is also discussed.

INTRODUCTION

chain pillars mean a relatively low coal recovery. Therefore, the proper design of longwall chain pillars is necessary in order that a maximum recovery can be achieved economically and safely. The traditional chain pillar designs by using either the ultimate strength concept or the progressive failure concept do not take the interaction among roof, pillar, and floor into consideration. Babcock et al. [3,4] and Peng and Johnson [5] indicated that a stronger roof-and-floor constraint results in a more stable coal pillar. Based on the theory of elasticity, if the ratio of the Young moduli for the roof and floor to that of the coal is 30, the strains in the coal would be 30 times those in the roof and floor provided that their Poisson ratios are equal. The net effect is that the roof

The main purpose of chain pillars is to protect panel entries from the influence of panel extraction so that entry functions such as transportation and ventilation can be safely mainted. Therefore, chain pillars must be designed to assure intact entries during the panel development. During retreating longwall mining the pillars must protect and support the headentry so that it will provide a usable tailentry for the next longwall panel [1]. Some operators have opted to leave sufficient rows of chain pillars between panels to avoid side abutment loads from the mined out panel. This, of course, is the simplest solution and requires a minimum of innovative engineering [2]. On the other hand, sufficient rows of

280 and floor restrict the horizontal expansion of the coal and give it an apparent strength that is much greater than the strength of the coal when unconfined. On the other hand, if the condition is reversed, the net effect will be that, instead of confining the coal seam, the roof and floor would actually pull the coal pillar apart [4,5]. A similar result has been reported by Peng and Hsiung [6] in which the finite-element method of stress analysis was used to simulate three roof conditions, the ratio of Young's modulus of the roof to that of the coal being equal to 1, 4, and 10, respectively. The analyses indicate that the stability of a chain pillar increases with the increase of the ratio. The fraction of the yield zone in a pillar next to the gob reduces from 50% to zero as the ratio increases. It is quite obvious, therefore, other parameters being invariant, that different sizes of chain pillar will be required for different roof conditions. The work presented here is: (1) to analyze the effects of roof and floor conditions on chain pillar stability; (2) to determine longwall panel size effect on pillar stability; (3) to develop and validate the chain pillar design formula which includes roof and floor properties, coal strength, seam depth, and panel size; (4) to evaluate the shape effect on pillar stability and to establish a conversion formula for a rectangular pillar to a square one such that the latter has the same strength as the former; and (5) to assess the effect of high in-situ horizontal stresses on pillar stability.

boundaries and the bottom boundary of each finite element model are roller-constrained. The longwall layout simulated by the finite-element model was a commonly used three-entry system. In order to simplify the problem, two rows of square chain pillars of equal size were used. The width of panel entries and crosscuts were 20 ft. (6.1 m) for the general analysis. Three different entry widths, 12 ft. (3.6 m), 15 ft. (4.6 m), and 20 ft. (6.1 m), were adopted to evaluate their effect on pillar stability. The panel length was 4000 ft. (1219 m). The pillar sizes simulated were 50 ft. (15.2 m), 75 ft. (22.9 m), 100 ft. (30.5 m), and 125 ft. (38.1 m); the panel widths were 220 ft. (67.1 m), 460 ft. (140.2 m), 580 ft. (176.8 m), and 700 ft. (213.4 m). Because of symmetry, only one quarter of the longwall panel was used. The typical three-entry longwall panel and its corresponding finiteelement model are shown in Fig. 1. All the crosscuts in the coal seam 460 ft. (140.2 m) away from the area of major concern, having little effect on the area [7], were neglected in order not to create an excessive number of elements. The entries and crosscuts were simulated by the removal of elements at specific locations. Caving behind the face was modeled by the deactivation of elements in

Face i A Panel

I i i

,~.• • ~

.;

...,..,

• Gob . • • . , . •

.~ " ' .h .

I[Z]QE]D[Z]E FINITE-ELEMENT MODELING Three-dimensional finite-element parametric stress analyses were employed. The elements used in the analysis were hexahedral. Each of the elements represent an isotropic and homogeneous region. The boundaries of the modeled longwall structure were far from the area of interest in order to minimize t h e influence of the boundaries. All four side

sl

Fig. 1. Plan view of finite-elementmodel.

281

the roof of the gob and subsequent activation of gob elements. Most of the finite elements were laid out so that their edges coincided with the pillar edges and bedding planes, except for the area of major concern, where finer elements were used. A step-down approach was also employed, that is, the longwall panel was simulated and modeled in three dimensions in larger elements to obtain a first-order solution which then provided the boundary conditions for detailed analysis of smaller regions in smaller elements or certain structural elements. An idealized seven-layer geologic model was used in the analysis (Fig. 2). The thickness of coal seam simulated was 8 ft. (2.4 m). The material properties used for the finite-element models are listed in Table 1. To represent the in-situ condition, a reduction factor of 1 / 5 was applied to the strength obtained in the laboratory. No reduction was made to the Young's moduli and Poisson's ratios. The material properties and thicknesses of the first and second layer above the coal seam and the material property of the floor were varied. The height of the model from the bottom of the coal seam was 787 ft. (239.9 m). Additional stress was applied to the top surfaces of the finite-element models in order to simulate the remaining overburden on top of the model. Although the stress field that exists at

any underground site is a complex combination of stresses produced by gravitation, tectonics, and material property variations, only the stress produced by gravitation is considered in the development of the chain pillar design formula; the vertical stress is dependent on the overburden depth and the density of the overlying strata, and the horizontal stress is a function of Poisson's ratio of the material and the vertical stress. The effect of high horizontal stress fields on pillar stability will be discussed in a separate section. Each of the layers in Fig. 2 was assumed to be isotropic, homogeneous, and perfectly elastic. The N A S T R A N computer program [8] was used. In order to simulate the extent of roof 6aving over the gob and the possible fracturing and yielding in the roof strata and coal pillars, a modified Coulomb criterion was adopted as follows: (1)

o 1 >~ o c + q % ,

or

(2)

O3~< - - T0,

w h e r e o I and 0 3 are maximum and minimum principal stresses, respectively, oc is the compressive strength, q is the triaxial stress factor, and TO is the uniaxial tensile strength. When the condition specified by eqn. (1) or

TABLE 1 Physical and mechanical properties of the geologic strata Material

Coal

Young's modulus, psi (MPa)

Poisson's ratio

5.105

0.2

(3.45-103 ) Sandstone Shale Clay shale

5.106 (3.45.104 ) 2.10 6 (1.38-104 ) 2.7.106 (1.80-104 )

Uniaxial compressive strength Lab, Model, Lab, psi (MPa) psi (MPa) psi (MPa) 4500

(31) 0.17 0.25 0.3

18070 (124.6) 14800 (102.1) 16500 (113.8)

Density, lbs/in 3 ( M N / m 3)

Model, psi (MPa)

900 (6.2) 3614 (24.9) 2960

170 (1,17) 80O

(0.23) 16o

5

(5.52) 230

(1.1) 46

3.8

(20.4) 3300 (22.8)

(1.59) 50O (3.45)

(0.32) 100

34

(0.69)

4

0.0579

(0.0157) 0.09375 (0.0254) 0.0972 (0.0264) 0.09375 (0.0254)

282

1/10, 1/20, for the Young's modulus were used. The Poisson's ratio for all of the fractured elements was assumed to be 0.05. The gob elements were formed by three types of material. Their Young's moduli ranged from 1/100 to 1 / 5 7 of those of the intact rock [7,9,10]. The material properties for gob materials are listed in Table 2.

General Overburden

787-

~assive Clay Shale

INFLUENCE OF GEOLOGIC AND GEOMETRIC PARAMETERS ON THE SIZE OF THE YIELD ZONE IN CHAIN PILLARS

78' i

I

--Shale

O o 58" Z Vary >

oIxl < Z

2'

a.

8-

_o W

-.I kU

Vary

0 o

Vary

-10"

;

•

,

.'

,...

•

"

~

-.'." •

•. : :

. .

° .

. .

• .

.. .

•

"

." •

"~

. .

.

Massive Sandstone "

ii

:

• ~ • ._. .. : . . .

° •

"-

" " •.

-695 Fig. 2. Idealized geologic model used.

(2) was satisfied, the individual element is considered to have fractured or yielded and the reduced elastic properties for the element are introduced. The finite-element model is then rerun; the stability of elements is again evaluated. The whole process is repeated, if necessary, until the final stable condition is reached. Depending on the extent of fracturing, t h r e e types of reduction factors, 1/2,

Once the chain pillar starts to yield, its supporting ability decreases. The width of the yield zone in the pillar is greatly controlled by the overburden depth, E i / E c, Em/Ec, Ef/Ec, coal and roof strength, pillar size, etc. Several terms used in this paper need to be defined first. The main roof is a thick roof stratum overlying the immediate roof and is not necessarily a strong stratum. The immediate roof which is immediately above the coal seam will be treated as a main roof if it is so thick that its volume after caving is sufficiently expanded, due to bulking effect, to fill the void created by coal extraction and that it offers immediate support to the overlying strata. The symbols E l , Ec, E l , and E m a r e Young's moduli of the floor, coal, immediate roof, and main roof, respectively. The symbols Hi, H m , and H c denote the thickness of the immediate roof, main roof, and coal seam, and E ~ / E c is defined as the ratio of the Young's modulus of the immediate roof to that of coal. Figures 3 and 4 show the effect of the Young's modulus of the main roof on vertical pillar stress as the face retreats. Panel 1 at the right side of both figures was extracted first, followed by panel 2. The ratios E i / E c --- 0 and H i / H c = 0 denote that there is no immediate roof between the main roof and the coal seam. For the c a s e E m / E c = 10 (Fig. 3), vertical pillar stress in the two rows of chain

283 TABLE 2 Gob materials properties for various models Material

Sandtone

Shale

Aa

Young's modulus, psi (MPa) 8.77.10 4 (6.05" 102) 6.25" 104 (4.31-102 ) 5- 104 (3.45" 102 )

Poisson's ratio 0.1 0.08 0.05

3.51.104 (2.42.102) 2.5.10 a (1.72-102 ) 2.10 4 (1.38' 102 )

0.1

8.77" 103 (0.605" 10 2) 6.25" 103 (0.431" 102) 5" 103 (0.345" 102)

0.1

0.08 0.05

0.08 0.05

Density, lbs/in 3 (MN/m 3) 0.0838 (0.0227) 0.0838 (0.0227) 0.0838 (0.0227)

Note

0.0838 (0.0227) 0.0838 (0.0227) 0.0838 (0.0227)

well packed gob

0.0838 (0.0227) 0.0838 (0.0227) 0.0838 (0.0227)

well packed gob

well packed gob packed gob loosely packed gob

packed gob loosely packed gob

packed gob loosely packed gob

a Properties of material A are assumed to be identical to those of coal.

pillars continues to increase even after the face of panel 2 has completely passed them. N o yield zone has developed in either the main roof or coal pillars. During and after the extraction of panel 1, m a x i m u m side abutment pressures in both rows of chain pillars are located at the side toward the active panel. After the extraction of panel 2 begins, maxim u m side abutment pressure in the chain pillar next to panel 1 gradually shifts from the side near the mined-out panel (i.e., panel 1) toward the other side (i.e., panel 2). The maxim u m side abutment pressure in the pillar near panel 2, however, remains at the same side even after the face is well past it. Relatively speaking, vertical stress in the pillar near panel 1 is always higher than that in the pillar near panel 2. For the case E m / E c = 1 (Fig. 4), a completely different type of pillar stress occurs. The pillar is no longer intact, instead a yield

zone starts to develop in the pillar, and gradually extends outward as the face advances. When the face is 70 ft. (21.3 m) outby, a total of 50% of the pillar has yielded. As the face moves further, a complete yielding of the pillar occurs. When the face is 910 ft. (277.4 m) away, 50% of the pillar near panel 2 has yielded (Fig. 4) and it yields completely when the face is 1390 ft. (423.7 m) outby. Figure 5 shows a stabilized yielding condition in the roof and coal pillars after the panel has been mined-out, for the case shown in Fig. 4. The direction of mining was toward the right side of the figure. Five consecutive chain pillars in both rows from the panel center were completely yielded. The next five chain pillars in the first row were also completely yielded. There was 50% yielding for the next four pillars in the second row away from the gob. A complete yielding of the roof above the first five chain pillars and adjoining entries

284 Ei/Ec Hi/Hc Em,/Ec Hm/Hc 0 0 10 5 --x--

Face of panel 1 is 7Oft outby

--

Face of panel 1 is 1 2 3 0 f t outby

o--

--o--

Face of panel 2 is

--

Face of panel 2 is 19Oft

"--

7Oft inby / ~ /|

3-

~0

.___../ ol ¢.tJ

2-

{tJ w lff)

)~..o

j o

_1 D. ._1

m I-w

1

Fig. 3. Effect of E m / E c on vertical pillar stress as the face retreats.

was also shown. Roof yielding also occurred in the second entry for the next four pillars. Comparing Fig. 3 with Fig. 4, it is apparent that the higher the Young's modulus is for the main roof, the smaller is the yield zone in the coal and the stronger is the coal pillar. The Young's modulus of the immediate roof has the same effect as that of the main roof on the yield zone in the coal around a longwall panel. Figure 6 shows that the yield

zone in the pillar diminishes when E ~ / E c increases from 1 to 4. The yield zone in front of the face in this case, however, does not change. Figure 7 shows the effect of the Young's modulus of the floor on the yield zone in the pillar. The yield zone in the second and third pillars behind the face disappears as E f / E c increases from 1 to 4. In conclusion, the relative magnitude of the

285 4-

Ei/Ec Hi/He Em/Ec Hm/Hc 0

/

0

1

5

0

--,--Face --x--

--o--Face --o--

3"

of panel 1 is 7Oft outby

Face of panel 1 is 87Oft outby of panel1 is 99Oft outby

Face of panel 1 is 1350ft outby

--V--Face

of panel1 is 1710ft outby

2' i

E

/ panel 2 ]

pillar

Fig. 4. Effect of Em/E c on vertical pillar stress during the mining progress.

Young's moduli of the roof and floor with respect to that of coal has a great influence on chain pillar stability. The pillar is more stable when E i / E o , Em/Eo, and E f / E c are larger and the reverse is true when the ratios become smaller. The influence of pillar size on the yield

zone in the coal is different from those of the Young's moduli of the roof and floor. Figures 8 and 9 show the effects of pillar sizes on reducing the yield zone in the pillar and the panel for two different roof conditions. In Fig. 8, the width of the yield zone in the pillars surrounding the gob area cannot be

286

~ ~Yield [77/ImYield

Centerline of the panel

zone in pillar zone in roof

Gob

EVEC Hi/Hc Em/Ec Hm/Hc 0 0 1 5

I

11 I-I D D D ~ B I-I I-I I-1 I-I f-I I-1 I-I I-I 1-11-] 1-11-] I-1

D~DDN.N I

Fig. 5. Yield zone in the roof and pillar after the panel has been mined out.

t Gob

[al. Ei/Ec = 1 Ei/Ec Hi/Hc Ern/Ec Hrn/Hc lal 1 1.25 1 5 Ibl 4 1.25 1 5

III

II II

~--;2!!!2::re:aTr°°f~ [b].

Ei/Ec= 4

III II Panel

reduced by simply increasing the pillar size. However, by increasing the pillar size from 100 ft. (30.5 m, Fig. 9a) to 125 ft. (38.1 m, Fig. 9b), the fraction of the yield zone in each pillar behind the face is reduced from 50 to 40%; this, of course, in turn enhances the supporting ability of the pillar. Although the pillar size does not have a direct effect on the width of the yield zone surrounding the gob area, it does prevent the yield zone from developing in the other side of the pillar. As shown in Fig. 9, when the pillar size decreases from 100 ft. (30.5 m) to 75 ft. (22.9 m), no specific change in the width of the yield zone on the gob side occurs. However, the yield zone also occurs in the first row of chain pillars on the middle entry side and the fraction of yield zone increases sharply from 25 to 67% on the first row of chain pillars. There are also yield

Fig. 6. Effect of Young's modulus of the immediate roof on the yield zone in the coal.

287

iF I[-1 Gob Panel

Ei/Ec Hi/Hc Em/Ec Hm/Hc /I 1 1.25 1 5 /~

la]. Ef/Ec= 1

Panel

[al. Pillar size, 75ft(22.9ml

i Jl I

i-ll-1

Gob

~]--Yield zone in main [] --Yield zone in coal

roof

Panel

Ib}. Ef/Ec=4 Fig. 7. Effect of Young's modulus of the floor on the yield zone in the coal.

•

~Yield

[]---Yield

] zone in zone in

immediate roof

coal

I b]. Pillar size,

~~M

Gob

[al. Pillar

Panel

size, lOOft

130.5ml

7f/YL 17//72 l

Gob Ei/Ec Em/Ec Hi/Hc Hm/Hc o 1 0 5

lOOft

1 )

Panel

130.5m1

Fig. 9. Effect of pillar size on the yield zone in the pillar and panel.

zones in the roofs of the middle entry and crosscuts. It is apparent that pillars of inadequate size cannot provide enough protection to prevent excessive interaction between the panel and its entries so that yielding in the entry roof occurs.

STABILITY OF CHAIN PILLARS

~

Panel

[bl. Pillar size, 125ft 138.1m] Fig. 8. Effect of pillar size on the yield zone in the pillar and panel.

In the section above, it was discussed how the development of yield zone in the chain pillar will be affected by the geologic and geometric parameters. One basic problem emerged, that is, how the stability of a chain pillar with some yield zone can be evaluated or how the stability of a chain pillar under a specific geologic and geometric conditions will

288 be different from that of others? In order to find the answers, the parameter stability factor is introduced. Stability

factor

of chain

EVEc Hi/Hc Em/E¢ Hrn/Hc 0 0 1 5

pillar

The stability factor is defined as that ratio of the allowable uniaxial bearing capacity of the pillar to the integrated equivalent uniaxial stress (equivalent loading) over the pillar, which can be expressed as follows

sf-

f A,OCC dA'

(3)

AOecd A 0

where Sf is the stability factor, Occ is the uniaxial compressive strength of the coal, A is the cross-sectional area of the pillar, A' is the cross-sectional area of the intact portion of the pillar, and Oe~ is the equivalent uniaxial stress in the pillar. The equivalent uniaxial stress is equal to the magnitude of the maxim u m principal stress minus the stress due to the confining effect, i.e. oec = ol - qo3

(4)

Equation (4) can be used to determine Oec for both the intact zone and the yield zone of the pillar. According to eqn. (3), it was assumed that the uniaxial compressive strength for the yield zone is equal to zero, that is, the yield portion of the pillar can only support load b y confining effect. The advantages of eqn. (3) are that: (1) it allows the yield zone to be considered, and (2) the allowable bearing capacity of the pillar decreases as the yield zone increases. The stability factor basically decreases as the yield zone increases and will be equal to zero if the whole pillar yields. W h e n the stability factor is equal to or larger than one, the pillar is considered stable; otherwise, it is unstable. Figure 10 illustrates the variations of safety factor of the pillar elements due to mining activity for a typical finite-element model.

-1

'-~

' -a

-2

'

-~ '

xlO2m

-~',
DISTANCE TO FACE , d

Fig. 10. Variations of safety factor as a function of face distance for each element of a pillar.

The overburden depth, h, and the uniaxial compressive strength of coal assumed for the model were 1787 ft. (544.7 m) and 900 psi (6.2 Mpa), respectively. The pillar discussed here is the one next to the gob area. The stability factor in the figure was determined according to eqn. (3), except that the area A and A' were the cross-sectional areas of the element in question. Curves 1, 2, 3 and 4 represent the variations of stability factors for pillar elements 1, 2, 3, and 4, respectively. The face distance is measured from the centerline of the pillar in the direction parallel to the face line and the negative sign in the horizontal axis of the figure indicates that the pillar is on the gob side (or behind the face). The figure shows that the element which is close to the gob area is in most cases less stable than others. Elements I and 2 yield right after the face passes the pillar, whereas elements 3 and 4 remain stable until the face is 790 ft. (240.8 m) away. Curve 5 in the figure represents the stability factor of the pillar. It predicts insta-

289 m- 6 " .J .J

E

re

4.

2E2 .aoe, [ ] E l

[]D

p"32' em

0 |

o

-1 I

-2

I

-~

I

l

-~

-~

-3 _

i

i

'-1'o

42

- 4 x 102rn i ×102ft

DISTANCE TO FACE

Fig. 11. Stability of pillars as a function of face distance for a typical roof condition. bility when the pillar is about 120 ft. (36.6 m) behind the face. Figure 11 shows the stability comparison between the pillar in the headentry side (pillar 1) and that in the tailentry-to-be side (pillar 2). The model used here is exactly the same as that in Fig. 10. The figure clearly indicates that the stability of pillar 2 will not be affected significantly by the mining activity until far after pillar 1 has yielded entirely. Pillar 1 becomes unstable when the face is 120 ft. (36.6 m) outby, while pillar 2 becomes unstable when the face is 940 ft. (286.5 m) outby. Therefore, it is the pillar in the headentry side that demands immediate attention. As long as the stability of that pillar is secured, one does not have to worry about the instability problem for the pillar in the tailentry side. The study in the following sections, including the development of pillar design formula, will therefore concentrate on the pillar in the headentry side.

Effects of geological parameters

and

geometric

It has been found that the stress distribution and the development of a yield zone in the pillar is affected by the mechanical properties of the immediate roof and the main

roof, and especially the strength characteristics of the roof [11]. The "strong roof" restricts the development of the yield zone in the pillar to a minimum, even when the coal is relatively weak, while the "weak roof" stimulates the expansion of the yield zone in the pillar. Theoretically speaking, the strength of the roof is a relative number. It varies with the mining conditions such as longwall panel layout, face location, etc. The roof is considered strong when no yield zone develops due to the side abutment pressure created by mining activities. Other things being equal, the pillar under a weak roof is less stable than the one under a strong roof. In other words, a relatively large-sized pillar is needed when the roof becomes weak [11]. The discussion herein will focus on the pillar stability under the weak roof conditions since they are most critical. The parameters which affect the pillar stability will be discussed as follows. Figures 12, 13 and 14 illustrate the effects of Young's moduli of the immediate roof, main roof, and floor on the pillar stability, respectively. All of them show a decrease in pillar stability with decreasing Young's modulus. In other words, the higher the ratios of Ei/Ec, E m / E c and Ef/Ec, the more stable the pillar. The stability factor reflects the extent of the yield zone development in the

290 7'

n,-

~6 ..J D.

u..5' 0

I--

1. 2. 3.

~4.

Ei/Ec Hi/Hc Em/Ec Hm/Hc 10 1.25 4 5 4 1.25 4 5 1 1.25 4 5

>I-

~2' CO ¢~1 , I !

o

-1 !

-~

!

.~,

-2

Js

I

-~

-3

!

I

-lO

DIST'ANCE TO FACE Fig. 12. Effect of E i on pillar stability for

Em/E

I-z uJ

1. 2.

•

LU -tLU

Ei/Ec H i / H c E m / E c 0 0 10 0 0 4

xlO2m -12 × 102ft

1 = 4.

pillar under different roof and floor conditions quite well. Besides the Young's modulus of the immediate roof, main roof, and floor, the thickness of the main roof also has certain effects on the pillar stability when the face is nearby, but the influence will gradually disappear when the face moves farther away (Fig. 15). Figures 16, 17 and 18 show the effects of

uJ Q 03 8 . >-

'

the overburden depth, pillar size (Wp), and Panel width (Pw) on pillar stability, respectively. The pillar will become less stable as the coal seam gets deeper, the pillar size becomes smaller, and the panel width becomes larger, provided other variables are kept constant. Figures 10-18 clearly show that the pillar becomes less stable as the face moves away. But is there a critical distance between the

Hm/Hc 5 5

1 5

6'

"r" I.Z rv-

...i __.4O. l.I.

O

-|

3

I..; 0r}

0

t

-3

-2

-1 I

I

xlO~m

i

-1i

-2 DISTANCE

TO FACE

Fig. 13. Effect of E m on pillar stability for

Ei/E

I = O.

×102ft

291 4.

1. 2. 3.

Ef/Ec 10 4 1

r,

-I xl02m

-0.5 !

o

-:3

-i

=

×102 ft

DISTANCE TO FACE

Fig. 14. Effect of Ef on pillar stability.

pillar and the face beyond which the mining activity at the face will no longer affect the stability of the pillar? This question may be explained by the model shown in Fig. 5. Let's assume that in Fig. 5, the face still continued

8"

to advance to the right. The gob side pillars and the second-row pillars which are more than 790 ft. (240.8 m) and 1340 ft. (413.6 m), respectively, behind the face yielded completely and the next four pillars in the second

Ei/Ec Em/Ec Hm/Hc h 10 10 3.75 ] 1B 10 10 5 ~2400ft

1A

\ 6" e,--

o o

"<4. .J

2.

2A 2B -0.5 I

DISTANCE TO FACE

Fig. 15. Effect of H m on pillar stability.

-1 xlO2m I

xlO2ft

292 6"

Ei/Ec Hi/Hc Em/Em Hm/Hc h 1. 4 1.25 10 3.75 2,400 ft 1,787 ft • . . 5

4"

rr

>- 3" ...I

2-

-1

-0.5 !

0 DISTANCE

!

×lO}ft

-3

-2 TO FACE

×102m

I

Fig. 16. Effect of overburden depth on pillar stability.

3"

tr --I .J

1. 2. 3. 4.

E- 2 . U.

O o

i-

Ei/Ec Hi/Hc Em/Ec Hm/Hc Wp 1 1.25 1 5 lOOft 1 1.25 1 5 75ft 0 0 1 5 lOOft 0 0 1 5 125ft

p-

4

-I

2

-1

-0.5

0

j

I

DISTANCE TO FACE

Fig. 17. Effect of pillar size on pillar stability.

-i

xl02m

I

×102ft

293

,.

2;o. 7001t

nO I-

"<5 >-

I.J m

4o

-1 ×102m

-0.5

-1

-2

-3

× 102ft

DISTANCE TO FACE

Fig. 18. Effect of panel width on pillar stability.

row 910 ft. (277.4 In) behind the face, had 50% of the yield zone developed in each pillar. This indicates that the influence of the face location will not diminish even when the face is very far away. The face distance, therefore, should be considered as an important factor when it comes to pillar design. This finding is in agreement with Lu's argument [121.

Effects of entry width Three models were established to evaluate the entry which effect on pillar stability. The coal seam was assumed to be 1787 ft. (544.7 m) deep. The ratios for E i / E c , E m / E c , and E f / E c were 10, 4, and 4, respectively. The panel width and pillar width were 700 ft. (213.4 m) and 50 ft. (15.2 m), respectively. Three different entry widths, 12 ft. (3.66 m), 15 ft. (4.57 m), and 20 ft. (6.1 m), were simulated. By comparing the pillar stability for each entry width, no significant change was found. The difference in stability factors for the first pillar behind the face for the 12 ft, (3.66 m)- and 20 ft. (6.1 m)-cases is only

1.8% while it is less than 1% for the third pillar behind the face. Therefore, the entry width is excluded from the pillar design formula.

Effects of second-panel mining The pillar deteriorates as mining proceeds and will deteriorate further during the second-panel mining. Figure 19 illustrates the pillar deterioration due to first- and secondpanel mining. Three models are shown in the figure. Pillar A is close to the gob of the first panel and pillar B is next to the active panel (second panel). The uniaxial compressive strength, overburden depth, and pillar size assumed for all models were 900 psi (6.2 Mpa), 1787 ft. (544.7 m), and 100 ft. (30.5 m), respectively. Figure 19 shows that pillars A and B for models 1 and 2 remain stable even after the face of the second panel is well past them. However, for model 3 with E m / E c = 4, both pillars become unstable after the face of the second panel passes them about 87 ft. (26.5 m). The major function of the chain pillars is to

294

[z ..J ..A 13. tl.

]

4,

[]

2rid [ ] [ ] Pa.e,

1st [ ] [ ]

~][-~] pane'~][~ /

Ei/Ec Hi/HcErn/Ec Hm/Hc h 12". 40 1.05 110 :} 1,787ft 3.

4

1.25

4

5

o

~.3-

o

I.-

>I- 2.

_3_ Ill O3

3A

1 .

.

.

X

\

.

-4j.__ . . . .

\

~

3B ~A

-1 O

'-2 [1st

I

-4 panel]

I

-2

-6

I

-3 -8 11'0 '-1'2 DISTANCETO FACE

/['

0 I 0

I__~.~

-1 l

L -4 [2nd panel]

I

-2! ×102m -~, ,,1o2.

Fig. 19. Effect of second p a n e l mining on pillar stability.

protect the roofs in the headentry and tailentry. After the function has been fulfilled, the chain pillars no longer need to remain stable. As a matter of fact, they are encouraged to yield or totally collapse after the face of the second panel passes. Therefore, the pillar size for model 3 is the optimum while the chain pillar for either model 1 or model 2 is considered to be oversized. Since the pillar stability will be affected only when the face is fairly close to or past the pillar, the pillar surviving from the first panel extraction will remain stable at least until the face of the second panel is past. Therefore, in pillar design practice the effect of second-panel mining does not have to be taken into consideration. The development of pillar design criterion in the next section will be based on this concept.

DEVELOPMENT FORMULA

OF

PILLAR

DESIGN

Strength characteristics used in the finiteelement study were assumed to be one fifth of the laboratory ones. Therefore, for the convenience of comparing directly with the laboratory strength, the equivalent uniaxial stress in the following discussion will be five times the one calculated from model study. As discussed, the stability factor defined in eqn. (3) is the ratio of the uniaxial bearing capacity of the pillar to the actual load that the pillar sustains; the bearing capacity, however, varies depending on the extent of the yield zone in the pillar. It decreases as the yield zone increases which means that the uniaxial compressive strength for the entire

295 pillar is reduced relatively. Should the stability factor be used for design purposes, one must first determine the extent of the yield zone, which of course is a difficult task. One alternative to avoid this problem is to introduce another parameter called “equivalent uniaxial compressive strength,” Do, which is defined as the minimum uniaxial compressive strength required for a specifically sized pillar under a typical roof condition to remain stable, and can be expressed as follows a

M=

a cc

(5)

Sf

Combining we obtain a

cc=

the above equation

J sod A’ A’

zz

with eqn. (3)

Sf

(6)

DM sA

%cd

A

If there is no yield zone developed pillar, then

in the

acc = and (JM will be equal to the average equivalent uniaxial stress (average loading) over the pillar. Otherwise, eqn. (6) suggests that as long as the stability factor is the same, a pillar with a yield zone can be transformed into (or replaced by) a pillar which has no yield zone but sustains proportionally higher loading. Through the transformation of eqn. (6), the bearing capacity (or uniaxial compressive strength, relatively speaking) of the pillar becomes invariant and forms a perfect basis for evaluating pillar stability. Furthermore, the yield zone in the pillar will no longer be a problem as far as pillar design is concerned. The introduction of “equivalent (minimum) uniaxial compressive strength,” aM, not only makes the development of the pillar design formula much easier but also simplifies the formula greatly. Another aspect has to be addressed here.

Originally, the chain pillar simulated in the finite-element model was usually divided into either four or sixteen elements and the element size was either 100 ft. X 25 ft. (30.5 m x 7.6 m) or 25 ft. X 25 ft. (7.6 m X 7.6 m) which was rather large. It has been known that lower stresses are induced in larger element sizes. Most likely, the stability factors discussed previously will be higher than they should actually be. In order to obtain a more accurate number, a step-down approach for the chain pillars was employed; that is, the whole panel was modeled with larger elements to obtain a first-order solution, which then provided the boundary conditions for detailed analysis of smaller regions with smaller elements. The element size chosen for the stepdown analysis was 5 ft. X 5 ft. (1.5 m X 1.5 m) which was considered to be more representative. According to Bieniawski 1131, the critical specimen size for testing the coal strength was about 5 ft. (1.5 m). It was found that the stability factor of the pillar determined from the original analysis was 1.6 times that from the step-down analysis regardless of the element sizes-either 100 ft. x 25 ft. (30.5 m x 7.6 m) or 25 ft. X 25 ft. (7.6 m x 7.6 m)-and the distance between the pillar and the face. Equation (5) therefore should be readjusted as follows

(7)

aM = 1.6? f

In order to develop the design formula for the chain pillar, multivariate analysis for the data obtained from finite-element analysis was employed. A general mathematical model which expresses the pillar size as a function of the relevant parameters, can be expressed as Wp = f ( E/E,

2 Em/EC 3 H,/‘Hc

h, aM, d, p,)

3 Ef,/E, 3 (8)

where d is the distance between the face and the pillar, and W, is the pillar size.

296 The best fit for the above model is log Wp = - 4 . 6 8 6 × 1 0 - 3 E i / E c - 4.04 × l O - 3 E m / E c - 3.33 × 10 2 log(Ef/Ec )

- 0 . 0 7 8 9 log o M + 0.5144 log h + 0.0494 log d + 0.1941 log P,v

(9)

R 2 for eqn. (9) is 0.9995. The parameter H m / H c is only weakly correlated with Wp. Therefore, it is not included in the formula. According to eqn. (5), the pillar is stable when its stability factor is equal to or larger than one, that is, when its uniaxial compressive strength is equal to or larger than the equivalent uniaxial compressive strength, O~c >~ o M. Thereore, to obtain the optimum pillar size, o M in eqn. (9) can be replaced by Occ. Since the pillars in the middle of the panel are always the ones with the lowest stability, they should be so designed that they will remain stable after the panel is completely mined-out. Therefore, the maximum distance between the pillar and the face is equal to one half the panel length, Lp/2. Replacing d in eqn. (9) by Lp/2, the pillar design formula is then completed and can be expressed as follows log Wp = - 4 . 6 7 6 × 10 3Ei/E c - 4.04 × l O - 3 E m / E c - 3.33 × 10 -2 l o g ( E f / E c )

- 0.0789 log Occ + 0.5144 log h +0.0494 log(Lp/2) +0.1941 log Pw

(10)

where Wp, h, Lp, Pw are in ft. and %c in psi. Or, log Wp = - 4 . 6 8 6 × 10 3Ei/E o - 4.04 × l O - 3 E m / E c - 3.33 × 10 -2 l o g ( E f / E c )

formulae based on either the ultimate strength of the progressive failure theory, the major advantages of eqn. (10) are: - - i t is in a much simpler form; - - t h e yield zone in the pillar has been included implicitly; - - t h e mechanical properties of the roof and floor strata have been taken into consideration; - - m o s t importantly, it is easy to use. The derivations for the traditional design formulae and their comparison are discussed elsewhere [11]. For the convenience of application, a monogram (Fig. 20) can be constructed based on eqn. (10). As an example of using the figure, the pillar size Wp = 61 ft. (18.6 m) results from the following conditions (following the dotted line abcdefgh): Oco

1000

Em/E c

10

Ei/E c

0

Panellength Overburden depth Ef/E c

psi

5000

ft. (1524 m)

500

ft. (152.4 m)

1

Panelwidth

400

ft. (121.9 m)

Pillar width

61

ft. (18.6 m)

If the roof properties are not known, it is recommended that E i / E c and E m / E c should be assigned as small as possible to achieve a safe design. It is suggested that E i / E c and E m / E c are assumed to be zero. Since the parameter Ef/Eo in the formula is in a logarithm form, it cannot be zero. Therefore, it is assumed to be one.

- 0 . 0 7 8 9 log Ooc+ 0.5144 log h +0.0494 log(Lp/2) +0.1941 log P w - 0.2955

(10a)

where Wp, h, Lp, ew are in m and Occ is in MPa. Compared with the traditional pillar design

EFFECTS OF PILLAR SHAPE ON PILLAR STABILITY The chain pillar design formula (eqn. 10) developed in the above section is for determining the size of a square pillar. However,

297 3

4

PILLAR WIDTH, lOft 8 5 6 7

9=10

11 12

0.5 1 2 34 67 UNIAXIAL COMPRESSIVE STRENGTH, lO~psi

Fig. 20. Nomograph for the determination of chain pillar size.

in practice both square and rectangular pillars are c o m m o n l y used. Before the formula can be validated by the field data available (for which rectangular pillars are mostly used), a relation which can transform results for a rectangular pillar into results for a suqare pillar having the same strength has to be established first. To solve this problem, nine

finite-element models were established. The chain pillars for five of them were square with 80.68 ft. (24.7 m), 75 ft. (22.9 m), 65 ft. (19.8 m), 50 ft. (15.2 m), and 40 ft. (12.2 m) width and for the other four models rectangular pillars with the sizes of 75 ft. x 86.67 ft. (22.9 m × 2 6 . 4 m), 65 ft. x 1 0 0 ft. (19.8 m X 3 0 . 5 m), 50 ft. x 130 ft. (15.2 m x 39.6 m), and 40

298 or

f t . × 162.5 ft. (12.2 m × 49.5 m) were used. The smaller dimensions of the pillar are measured perpendicular to, and the larger dimensions parallel to the direction of mining. The element size for the pillars was 5 ft. × 5 ft. (1.52 m × 1.52 m). Figure 21 shows that if pillars have the same cross-sectional area, the rectangular pillars are less stable than the square pillar and the rectangular pillar with smaller pillar width will be less stable than that with larger pillar width. The notation Sfr , Sfs , Wpr, and Wps for b o t h vertical and horizontal axes represent stability factors for a rectangular pillar, and a square pillar, rectangular pillar width, and square pillar width, respectively. A log-linear relationship between the ratio of Sfr/Sfs and Wp~/Wpscan be expressed as

log(SeJSes)=0.6 log( Wpr/Wps)

0.9

S, s

(12)

Equations 11 and 12 are only valid for the pillars of different shape having the same cross-sectional area, that is, W2 = Wpr x PL,, where PL, is pillar length for rectangular pillar. A simplified relationship for the square pillar and its stability factor can be found by regression analysis to be ~-pp-

~

(13)

Substituting eqn. (12) into eqn. (13), we obtain

l/l/;s- (S;s)1165 (Wpr) 0"7

(14)

Wps

(11)

°

0.8 o

° 0.7

\

0.6

0.5

0.9

018

O)

016

O'.S

0:4

Wpr/Wps

Fig. 21. Relationship between ratios of stability factor and Wpr/Wpsfor the pillars having the same cross-sectional area.

299

ever, very small. When the pillar length, Pcr, increases to four times the pillar width, Pwr, that is, the cross-sectional area of the pillar increasing four times, the pillar strength increases by only 11.55%. It is therefore apparent that pillar width is the major factor for the supporting ability of a pillar. In other words, pillar dimension parallel to the direction of mining may not be as important as the dimension perpendicular to the direction of mining when it comes to chain pillar design.

Let Sis = S f r , that is, the square pillar and the rectangular pillar have the same uniaxial compressive strength. Then

W;s= Wp°s3W0"7 Since Wps =

(15)

(WprPe~) 1/2, we obtain

W;s= l/[z°85p°' pr --Lr 15,,

(16)

Equation (16) is the conversion equation which can be used to obtain the size of a square pillar of equivalent strength to a rectangular pillar. The equation clearly indicates that the pillar length has much less influence than the pillar width during the conversion process. Figure 22 shows the pillar strength variation of a rectangular pillar with respect to pillar length. It indicates an increase of pillar strength with increasing pillar length if the pillar width, Pwr, is fixed. The increasing rate, r, which is defined as the ratio of the additional strength obtained by increasing the pillar length of the rectangular pillar to the pillar strength of a square pillar which has the same width as the rectangular one, is, how-

VALIDATION OF CHAIN PILLAR DESIGN FORMULA

Ten longwall panels in five different coal seams are employed to verify the chain pillar design formula developed here. Mines A, B, D, E, and F were in the Pittsburgh seam; Panels 4 and 6 of Mine H were in the York Canyon seam; Mine C was in the Herrin No. 6 seam; Mine G was in the Pocahontas No. 4 seam; and Mine I was in the Harlan seam. Table 3 lists the basic information which is

1.2,

f

J

_6

J

,~ 1.1" ec

/

-i-

i,i Ioo

Y

J

J PLr/Wpr

Fig. 22. Variation of strength with respect to PLR/mpr when comparing PLa/Wpr = 1.

300

~q

C~ o

)<

I

~

)<

0 • 0~

v

0 o~

0~

C~

oo

00

o~ ~q v

v

v

0

©

~

0

o'~ ~~"

~

~

~-

o0

C~

CD

C~ o

0 o

~q

0)

~q

0

301 necessary for the verification of eqn. (10). It also lists the pillar sizes predicted by eqn. (10). The numbers in parentheses below the actual pillar sizes are the equivalent square pillar sizes under which the square pillar has the same strength as the actual reactangular pillar. The conversion was made by using eqn. (16). According to Table 3, chain pillars are properly sized as predicted in only three cases. These are for Mines A, B, and C. Their stability factors, that is, the ratio of actual pillar size to the predicted size, are 1.3, 1.5, and 1.08. There were no adverse roof conditions in the entries and no crushed pillars reported for the three cases, which leads to the conclusion that the actual pillar sizes have provided sufficient protections to the entry roofs and, therefore, are adequate. This verifies the applicability of the design formula developed in this study. Among the cases which are predicted to have inadequate pillar size are Mines D, E, F, G, Panels 4 and 6 of Mine H, and Mine I. Their stability factors are 0.76-0.79, 0.48 0.53, 0.42, 0.65, 0.99, 0.53, and 0.82, respectively. The predictions correlate well with the adverse roof conditions reported in the literature except for the case of Panel 4 of Mine H. The stability factor predicted for Panel 4 is 0.99 which is only marginally below the stable condition and it suggests that bad entry conditions might be encountered. However, no such condition has ever been reported in the literature [23]. The adverse roof conditions for the cases with prediction of inadequate pillar sizes are illustrated and discussed briefly in the following sections: Mine D. Five rows of chain pillars of 40 f t . × 7 0 ft. (12.2 m × 2 1 . 3 m) were in the headentry side and the entry width was 17 ft. (5.2 m). Bad roof conditions and roof falls occurred at the T-junction areas of the entries and crosscuts due to either a weak roof (clay vein intrusions) or mining activities [19]. The

formula predicts occurring problems corrctly. Mine E. The tailentry of the first panel was four entries on 50 ft. (15.2 m) centers with the pillar 37.5 ft. (11.4 m) wide. The crosscuts were on 100 ft. (30.5 m) center. Once the longwall had retreated 1000 ft. (305 m) from the set-up entry, roof falls in the tailentry occurred and spread completely across it. The ventilation of the section was affected. Three rows of chain pillars were in the headentry side; the first row of chain pillars was 37.5 ft. × 87.5 ft. (11.4 m × 26.7 m) and the others were 87.5 ft. × 87.5 ft. No headentry problem was reported during the first panel mining. However, bad roof conditions and roof fall problems began to occur when the second panel had retreated 800 ft. (243.8 m). The next two panels experienced the same problems [20]. Compared with the predicted sizes, the chain pillar in the tailentry side and the first row chain pillars in the headentry side were far too small. They were only 48-53% of the predicted size. Consequently, bad roof conditions were certain, which was confirmed by the field observations. Furthermore, the tailentry pillar for the second panel was 87.5 ft. wide which was barely equal to the predicted size (89.5 ft. or 27.3 m) under 1000 ft. (305 m) depth. Therefore, the tailentry problems were expected to occur from time to time. Mine F. The panel was developed by three entries with two rows of chain pillars on 50 ft. (15.2 m) and 90 ft. (27.4 m) centers, respectively; the corresponding pillar sizes were 34 ft.× 74 ft. (10.4 m × 22.6 m) and 74 ft.× 74 ft. (22.6 m × 22.6 m) with the smaller size pillar near the active panel. Choi et al. [21] reported that the tailentry was very stable as long as the face was 200 ft. (61 m) or more away; but, as the face approached, the roof conditions became worse. They described the b'ad roof condition as an unsatisfactory experience. Compared with the predicted size, the

302 smaller and larger pillars were only 42 and 81% of the predicted sizes, respectively. Bad roof for the tailentry was, therefore, as expected. Mine G. The first two rows of chain pillars for the longwall panel in the headentry were 40 ft. × 75 ft. (12.2 m × 22.9 m) and the third row was 125 ft. × 75 ft. (38.1 m × 22.9 m). In the headentry, vertical shear failure along the intersection of chain pillar rib line and the roof occurred at irregular intervals and kept approximately 25-30 ft. (7.6-9.1 m) ahead outby the face after the panel was advanced beyond the first 3 crosscuts [22]. The headentry roof problem could be attributed to the undersized chain pillars (Table 3). Mine H, Panel 6. Two rows of chain pillars of 32 ft. x 100 ft. (9.7 m × 30.5 m) were in the headentry and one row of chain pillars of 52 f t . × 100 ft. (15.9 m × 30.5 m) was in the tailentry side. The tailentry problem began when the silstone roof sheared off and fell along the faceline and the condition continued to deteriorate [23]. The conditions confirm the prediction that the chain pillars in both headentry side and tailentry side are of inadequate size. The combination of inadequate pillar size and of extremely weak immediate roof made the conditions of entry roofs even worse. The mining of Panel 6 was finally stopped. Mine I. Two rows of equal-sized chain pillars (70 ft. x 102 ft. or 21.3 m x 31.1 m) were in the tailentry side of the panel. In the headentry side, the larger pillar (90 ft. x 102 ft. or 27.4 m X 31.1 m) was close to the current panel while the smaller one (50 ft. x 102 ft. or 15.2 m X 31.3 m) was next to the panel to be mined. The overburden depth varied from 1560 ft. (475.5 m) above the tailentry side to 1410 ft. (429.8 m) above the headentry side. Due to the difference in overburden depth, the safe pillar size required would be different. Unfortunately, the design parameters E i / E c, E m / E c, and E f / E c were not available. Those parameters were obtained

from an adjacent mine [15]. Comparing those parameters with other cases, it was found that they were relatively higher. It was hoped that the larger numbers chosen would give a conservative prediction. According to the calculation, the pillar size in the tailentry side was 82% of the predicted one and it was 107% for the headentry side. The tailentry pillar of inadequate size was reaffirmed b y the bad roof conditions in the tailentry. In conclusion, the design formula developed in this study makes a fairly reasonable prediction for the cases studied. The applicability and effectiveness of the formula are therefore justified.

EFFECTS OF HIGH IN-SlTU HORIZONTAL STRESSES ON CHAIN PILLAR STABILITY The existence of high in-situ horizontal stresses other than those induced by Poisson's effect was widely reported in the past [25,26]. For instance, k >/2, where k = oi~/o v and o H and o v are horizontal and vertical stresses, respectively, is c o m m o n l y encountered in the U. S. Eastern Coalfields where tectonic forces are still active. It has been well k n o w n that the presence of high horizontal stresses will alter the coal mine entry stability. The effect of high horizontal stresses on the chain pillar stability is, however, unknown. In order to assess the role of high horizontal stresses on pillar stability, six cases were adopted in the analysis, with k equal to 0.67, 0.72, 0.99, 1.57, 2.04, and 3.2, respectively. Throughout the analysis, the size of square pillars, entry width, panel width, and overburden depth were fixed at 100 ft. (30.5 m), 20 ft. (6.1 m), 700 ft. (213.4 m), and 1787 ft. (544.7 m), respectively. The material properties used in the model are listed in Tables 1 and 2. Figure 23 shows the variations of the stability factor of a chain pillar as a function of k. Curves a, b, and c represent the stability

303 4-

f-'~\ J

i

t

\ \

\ ..

\ "\\\ 3'

a. f a c e is 7Oft away b. f a c e is 19Oft away c. face is 3lOft away

d, roof stability above pillar

if°

¢v-

22

£

\

\ \\

\ \ \ ~ \ \ \\ \ \ \ ~o \\

"

\\ \, \ \,

>.A

¢/)

0 K Fig. 23. The chain pillar stability as a function of K.

factors of the chain pillars which are 70 ft. (21.3 m), 190 ft. (57.9 m), and 310 ft. (94.5 m), behind the face, respectively. Except for the case when k = 3.2, chain pillars become more stable as k increases. However, the influence of k will gradually diminish when the face moves away from the pillar, and finally becomes insignificant. Curve d represents the safety factor for the immediate roof above the chain pillar. The roof reaches maximum stability as k increases to 0.99, then it starts to deteriorate rapidly as k increases further. For the models simulated in this study, the roof becomes unstable when k > 2.7. It is interest-

ing to note that the shap drop in stability factor for the case with k = 3.2 coincides well with the yielding of the roof above the pillar, that is, the high in-situ horizontal stresses affect pillar stability indirectly. If the roof is sufficiently strong and capable of sustaining high horizontal stresses without yielding, the horizontal stresses will not affect pillar stability. It is therefore obvious that the effect of high horizontal stresses on pillar stability is greatly dependent on the strength characteristics of the roof. Even the roof is weak (i.e., yielding due to high horizontal stresses), the chain pillar design formula (eqn. 10) devel-

304

oped in this paper may still be used for high horizontal stress fields.

CONCLUSIONS (1) The development of the yield zone in the chain pillar is highly controlled by the Young's moduli of the roof and floor. When the ratio of Young's moduli of the immediate roof, main roof, and floor to that of coal becomes smaller the yield zone increases. (2) A chain pillar design formula which was based on the three-dimensional finite-element analyses was developed. It includes several important parameters such as the ratios of Young's modulus of the immediate roof, main roof, and floor to that of coal, overburden depth, uniaxial compressive strength of coal, and panel dimension. The formula can be expressed as follows: log Wp = - 4 . 6 8 6 × lO-3Ei/Ec - 4.04

× l O - 3 E m / E c - 3.33 × 10 .2 log(Ef/Ec) - 0.0789 log Occ + 0.5144 log h +0.0494 l o g ( L p / 2 ) + 0.1941 10g Pw (3) The advantages of the formula are that: (1) it is presented in a simple form although theoretically complicated, (2) the mechanical properties of the roof and floor have been taken into consideration, (3) the yield zone in the pillar has been taken into account implicitly and there is no need to determine the width of the yield zone separately, and (4) it is easy to use. The applicability and effectiveness of the formula have been substantiated by the cases studied. (4) The conversion formula which can be used to obtain an equivalent square pillar from a rectangular pillar depends very much more on the rectangular pillar width than on its length. Therefore, the strength increment will be small if one is to elongate a square

pillar along the side parallel to the mining direction. (5) The effect of high horizontal stresses on pillar stabifity depends greatly on roof strength. If the roof is strong, high horizontal stresses will have no effect on pillar stability. For chain pillar design under high horizontal stress fields the formula that was developed under weak roof conditions (eqn. 10) may be used.

REFERENCES 1 N.P. Kripakov , Analysis of pillar stability on steeply pitching seam using the finite element method, USBM RI 8579, 1981, 33 pp. 2 W.J. Euler, Improving longwall entry development and operation, Min. Congr. J., 65 (5) (1979) 21-27. 3 C.O. Babcock, Effect of end constraint on the compressive strength of model rock pillar, Trans. AIME, 244 (1969) 357-364. 4 C.O. Babcock, T. Morgan and K. Haramy, Review of pillar design equations including the effects of constraint, Proc. 1st Conf. on Ground Control in Mining, West Virginia University, Morgantown, WV, 1981, pp. 23-34. 5 S.S. Peng and A.M. Johnson, Crackgrowth and faulting in cylindrical specimens of Chelmsford granite, Int. J. Rock Mech. Min. Sci., 9 (1972) 37-86. 6 S.S. Peng and S.M. Hsiung, Development of roof control criteria for longwall mining--parametric modeling I, Proc. Symp. on Strata Mechanics, University of Newcastle Upon Tyne, U.K., April 1982, pp. 51-58. 7 S.S. Peng, K. Matsuki and W.H. Su, 3-D structural analysis of longwall panels, Proc. 21st U. S. Symp. on Rock Mechanics, University of Missouri, Rolla, MO, 1980, pp. 44-56. 8 C.W. McCormick (Ed.), The NASTRAN User's Manual (Level April 1984), National Aeronautics and Space Administration, Washington, DC, 1984, pp. 1.1-1-7.1-1. 9 G.S. Rice, Tests of strength of roof supports used in Anthractie mines of Pennsylvania, USBM Bul. 303 (1929) 44 pp. 10 S.S. Peng and W.H. Su, 3-D structural analysis of retreating longwall panel, Proc. 4th Joint Meeting of MMIJ/AIME, Tokyo, Japan, 1980, Vol. B4, pp. 1-16. 11 S.M. Hsiung, Structural design guidelines for longwall panel layout, Ph.D. Thesis, West Virginia University, Morgantown, WV, February 1984, 217 pp.

305 12 P.H. Lu, Stability evaluation of chain pillars in retreating longwall, workings with regressive integrity factors, Proc. 5th Congr. Int. Soc. Rock Mech., Melbourne, Australia, April 1983. 13 Z.T. Bieniawski, In situ large scale testing of coal, Proc. Conf. on In Situ Investigation in Soils and Rocks, Br. Geotech. Soc., London, 1969, pp. 67-74. 14 B.L. Acharya, In-mine assessment of pillar stress and entry load in main and tail entries in retreating longwall mining at Quarto No. 4 mine, M. S. Thesis, West Virginia University, Morgantown, WV, 1982, 101 pp. 15 R.E. Thill and J.A. Jessop, Engineering properties of Coal Measure rocks, Paper presented at the AIME Annual Meeting, Dallas, TX, February 1982, pp. 1-26. 16 S.S. Peng, Rock quality and property determination for federal No. 2 Mine, TBM Project, Final Report submitted to USBM, January 1976, 64 pp. 17 P.J. Conroy, Rock mechanics studies, United States Bureau of Mines, Longwall Demonstration, Old Ben No. 24, Benton, IL, Phase III, Preliminary Report Panel 1, Job No. 7734-002-07, August 1977, 110 pp. 18 N.N. Moebs and R.E. Curth, Geologic and ground control aspects of an experimental shortwall operation in the Upper Ohio Valley, USBM, RI 8112, 1976, 29 pp. 19 S.S. Peng and D.W. Park, Rock mechanics study for the shortwall mining at the Valley Camp No. 3 Mine, Triadelphia, WV, Final Report submitted to

20

21

22

23

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USBM, Contract No. J0155125, December 1977, 30 PP. B. Dangerfield, Longwall experience in the Pittsburgh seam, Proc. 1st Conf. on Ground Control in Mining, West Virginia University, Morgantown, WV, 1981, Supplement, 6 pp. D.S. Choi, H.D. Dahl and H. yon Schonfeldt, Design of longwall development headings, Trans. AIME, 258 (1975) 358-363. S.S. Peng, Roof control studies at Olga No. 1 Mine, Coalwood, WV, Final Report submitted to USBM, Contract No. J0155125, July 1976, 22 pp. C i . Stewart, Rock mechanics instrumentation program for Kaiser Steel Corporation's demonstration of shield-type longwall supports at York Canyon Mine, Raton, NM, Final Technical Report submitted to U.S. DOE, May 1979, 318 pp. M.G. Schuerger, personal communication, 1983. J.R. Aggson, Coal mine floor heave in the Beckley coalbed, an analysis, USBM RI 8274, 1978, 32 pp. J.F.T. Agapito, S.J. Mitchell, M.P. Hardy and W.N. Hoskins, Determination of in situ horizontal rock stress on both a mine-wide and district-wide basis, Final Report to USBM, Contract No. J0285020, March 1980, 173 pp. P.J. Conroy and J.H. Gyarmaty, Characterization of subsidence over longwall mining panels--eastern Coal Province, Final Technical Report submitted to DOE, Contract No. DE-AC22-80PC30335, May 1983, 87 pp.