Design of Coal Pillar Arrays and Chain Pillars

24 Design of Coal Pillar Arrays and Chain Pillars PRAKASH R. SHEOREY Central Mining Research Station, Dhanbad, India

24.1 24.2

INTRODUCTION PILLAR STRENGTH 24.2.1 24.2.2 24.2.3

24.3

631 632 632 634 636

Factors Affecting Pillar Strength Pillar Failure Behavior Strength Equations

PILLAR L O A D

642 642 643 645 645 648

24.3.1 Arrays in Level Seams 24.3.2 Arrays'in Inclined Seams 24.3.3 Chain Pillars 24.3.3.1 Wilson's method 24.3.3.2 Alternative method for one-sided goaf 24.4 24.5

PERFORMANCE OF STRENGTH EQUATIONS SAFETY FACTORS A N D PILLAR SIZING

654 654 655 655 656 659

24.5.1 Unstowed and Stowed Arrays 24.5.2 Chain Pillars 24.5.2.1 Size based on strength 24.5.2.2 Size from safety of gate road 24.5.2.3 Numerical method 24.6

24.7 24.8

24.9

650

PILLAR DESIGN FOR SUBSIDENCE C O N T R O L

659 659

24.6.1

Pillar Arrays

24.6.2

Chain Pillars for Noneffective

660

Extraction

B O L T E D PILLARS

661

Y I E L D PILLAR T E C H N I Q U E 24.8.1

Theory of the Method

24.8.2

Applicability

664 664 666

of Yield Pillars

SUMMARY AND CONCLUSIONS 24.9.1 Pillar Strength 24.9.2 Pillar Load 24.9.3 Special Extraction Methods 24.9.4 Safety Factors

24.10

ADDENDUM

24.11

REFERENCES

24.1

INTRODUCTION

666 666 667 667 668 668

Pillar formation in underground coal mining is either done as a requirement of the method of extraction itself i.e. in bord and pillar (or room and pillar) mining or for fulfilling various functions, viz. panel isolation, protection of roadways, shafts or surface features, protection of current mine 631

632

Applications

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workings from dangers of water inundation and as a guard against roof collapses in the face area while depillaring. Pillars for panel isolation, commonly termed as chain pillars, and those for protection against the goaf in depillaring, called ribs, are generally required for temporary stability and can have lower safety factors than the remaining pillar types, which must be permanent in nature. Of the various types, this chapter considers the design of pillar arrays in bord and pillar mining and of chain pillars, which may be required in both bord and pillar and longwall mining. The former method of coal extraction is extensively used in the United States, South Africa and India. Therefore, the problem of designing pillar arrays is of special importance in these countries. Pillars in the development stage or 'first workings' are formed as arrays, their size being chosen based on the Coal Mines Regulations prevalent in the country. These pillars are considerably oversized if we consider the first workings only, but this initial overdesign is essential as the pillars are required to carry additional rock pressures as chain pillars during depillaring or 'second workings'. Pillar mining may alternatively be done by forming small pillars or narrow ribs in the first workings, as in the American room and pillar system. Chain pillars are also formed in rows by driving multiple entries in the case of longwall mining. In both methods these pillars serve to protect gate roads as well as to isolate the extraction panel upon completion. Design of pillar arrays is commonly required under shallow covers when subsidence at the surface, or at an upper coal seam, cannot be induced within the permissible limits specified. In such cases, the oversize pillars of first workings are either thinned down, heightened (seam thickness permitting) or split into smaller pillars. This second working operation, termed pillar reduction, may be done with or without sand stowing or filling. As in any design of structures, the pillar design procedure essentially consists of estimating the pillar strength and the load on pillars and linking the two through a proper safety factor. 24.2 24.2.1

PILLAR STRENGTH Factors Affecting Pillar Strength

Before coming to the pillar strength equations proper, it will be in order to define and discuss briefly the factors influencing pillar strength as given below: (i) uniaxial and triaxial coal strength; (ii) width to height (w/h) ratio of pillar; (iii) pillar size or volume; (iv) shape in plan; (v) preexcavation horizontal stresses; (vi) end conditions or conditions at the roof-pillar and/or floor-pillar contact and also presence of bands in the seam; (vii) water and weathering underground; and (viii) method of road drivage, viz. with road headers or with blasting. Factor (vii) is usually accounted for in the safety factor. Regarding factor (viii), Wagner and Maden [1] have found that blasting cracks can occur up to 0.3 m inside the pillar, so the effective dimension of a machine-formed pillar is 0.6 m greater than a drill-blasted pillar. Preexcavation stresses can be accounted for in pillar design in 'normal' coal measure strata but if the horizontal stress is abnormally high, it is best to resort to numerical stress analysis of the pillar. Similarly, the presence of unusual end conditions, e.g. soft wet fireclay, or an unusual geological condition calls for a special treatment of the problem and cannot be covered under the usual design procedure. As seen later, some authors of pillar strength equations have included the laboratory small specimen compressive strength of coal, some others the in situ large-scale strength, while some a constant strength or no strength. Since the stresses at pillar corners are uniaxial, at the sides biaxial and deeper inside triaxial,. it is reasonable to assume that both uniaxial and triaxial coal strengths will influence pillar strength. In many of the formulae, triaxial effects are included in the w/h effect. Strength increase with w/h (Figure 1) may be assumed to be linear up to w/h = 4 to 6, whereafter it may rise rapidly as indicated by Bieniawski's tests on sandstone [ 2 ] . A similar rise may not necessarily be obtained on coal, as shown in the same figure for tests on coal conducted at the Central Mining Research Station (CMRS). The third factor, pillar size, incorporates a strength decrease due to volume effect (see Volume 3, Chapter 2) including the effect of geological discontinuities. According to Bieniawski this effect may be negligible if a sufficiently large coal cube is tested, the recommended size being 1.5 m! Size effect is generally described by S = kw~ (1) where k is the unit cube strength and a varies between 0.2 and 0.5, as will be seen from various pillar strength equations later. This logically brings us to a discussion of in situ large-scale testing and laboratory small-specimen tests. The former tests are of two kinds: the first consists of conventional a

633

Figure 1

— _

Uniaxial compressive strength (MPa)

r

Design of Coal Pillar Arrays and Chain Pillars

Influence of width to height ratio of specimens on compressive strength

uniaxial compression by hydraulic jacks placed over the specimen top and applying a uniform loading rate [ 3 ] , while the second is done by placing the jacks in a slot at mid-height of the specimen and applying a uniform strain rate for all the jacks [4] (Figure 2). The second test was suggested to simulate real pillars in which the middle horizontal plane remains plane because of symmetry. This test also gives the postfailure characteristic of large specimens in situ. It is worthy of note that a simple laboratory specimen tested between steel platens in a compression machine also satisfies the requirement of loading symmetrically with respect to the middle horizontal plane. The CMRS have conducted extensive tests on 30 cm coal cubes using jacks or employing an easier alternative procedure of Schmidt hammers [5] as a part of their earlier pillar design procedure. They have also obtained the corresponding lab strength of 2.5 cm cubes. A plot of these strengths [6] against the depth of cover in Figures 3(a) and (b) shows that the in situ strength decreases with depth, while the lab strength is less affected by depth. Similar tests on a single seam at the same mine [7] also confirm these results as seen from Figures 4(a) and (b). The reason for such a behavior is that the zone of failed coal in a pillar increases with depth, while the testing recess cut in the pillar is of roughly the same depth. The reason why the lab strength shows less bias is probably that the intact coal material does not participate in the failure process as much as the discontinuities. Therefore, the lab strength is less affected by the depth of cover. The laboratory strength test has the added advantages of simplicity, ease and less expense, with another, though smaller, advantage that it satisfies the requirement of symmetrical loading with respect to the horizontal mid-plane (though not the end conditions). (a)

Figure 2

(b)

Schematic set-ups for in situ large-scale tests on coal: (a) uniform load test (after Bieniawski [3]); (b) uniform displacement test (after Wagner [4])

634

Applications is

r

to Rock Engineering-Mining

Engineering

(a) \

200

O

O

X o

So

o °

X o

o

X

o

o

>o So cpoo °

Lab strength (MPa)

PdW) Mi&uajjs mis ui

o° °

(b)

O

60

o o
Depth (m)

(a)

50

•(b)

-0. ° CL 1

\ o °

x: 30

1

9)

1

5 20

1-

Xi

1

o

100

-

_L

! I

In situ strength (MPa)

o

Influence of depth of cover on: (a) in situ strength of 0.3 m cubes of coal; and (b) lab strength of 2.5 cm cubes, representing different Indian coals [6]

15

Figure 4

8

200

400 Depth (m)

Figure 3

o o

200 300 Depth of cover (m)

380

1

10 100 0 —

_L

_L

200 300 Depth of cover (m)

400

Effect of overburden on: (a) in situ; and (b) lab strength in Dishergarh seam, Barmondia colliery (after Das et al. [7])

The shape of a pillar in plan is usually considered by substituting an equivalent pillar width w for the square pillar width w in any strength equation, the exception being Wilson [ 8 , 9 ] who has given separate equations for square, rectangular and long pillars. The relation proposed by Wagner [4] based on servo-controlled in situ tests c

w

e

=

4^1/C

P

(2)

(A is plan area and C is perimeter of the pillar) is considered widely acceptable. This equation can be applied to irregular pillars unless they are highly irregular. p

24.2.2 Pillar Failure Behavior Since the horizontal confining stress increases towards the pillar center, pillar failure always progresses from the sides to the center. Unless the pillar is exceptionally narrow the'failure process is always progressive and proceeds from the pillar edge to its center. The author of this chapter had a unique, and hair-raising, experience in 1978 of watching actual pillar failure and being present only a couple of hours before complete collapse of several panels together. This was a case of robbed pillars and therefore he could observe pillars of different w/h ratios in the process of failure. The mode of failure of a real pillar is much the same as a rock specimen under compression. The author has observed both shear and tensile failures in mines, the latter occurring in the presence of a soft, watery shale roof. Section 24.8 will discuss pillar failure based on load-deformation characteristics. Also of interest is the postfailure behavior of coal [10] for a complete range of w/h ratios as in Figure 5(a), which shows that the postfailure characteristic rises again after an initial fall, if the test is

Design of Coal Pillar Arrays and Chain Pillars - (a)

635

/

(DdlAI) ssajis

(b)

•

Figure 5

l

l

2

l

3

l

4

l

5

l

6

l

(a) Postfailure behavior of 70 mm diameter coal specimens at different w/h ratios (after Das [10]); and (b) the corresponding behavior of different sections of a mine pillar [13]

continued long enough. This reconsolidation increases with w/h and at very high w/h ratios it is probable that the postfailure modulus will be very nearly the same as the prefailure value. This probably proves the oft-quoted concept that pillars with w/h ratios 15-20 are virtually indestruct­ ible. Actually, the pillars at these w/h ratios do fail but still retain about the same resistance after failure. One thing that should be remembered about such 'indestructible' pillars is that although they are by themselves stable, their failure will give rise to considerable roadway closure, which has to be controlled by supports at the roof as well as at the sides. The depths at which such wide pillars are required will be considerable (greater than 400 m) and in all probability squeezing ground condi­ tions will prevail, at least at the roadway walls, and supports will be required anyway. The process of reconsolidation starts at w/h = 4 to 6 in the postfailure stage, so a mean value of w/h = 5 may be approximately taken to divide pillars into two categories viz. slender and flat or squat. This value was proposed by Salamon and Munro [ 1 1 ] as the upper limit for using their pillar strength equation and was later adopted by Bieniawski [ 1 2 ] for distinguishing between the above two categories. It is also the value beyond which pillar strength may increase at accelerated rates, according to Bieniawski (Figure 1). The postfailure behavior of Figure 5(a) may be directly applied to represent the behavior of different segments of a pillar (Figure 5b) [ 1 3 ] .

636

Applications

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24.2.3 Strength Equations Pillar strength equations, which are being used the world over, have been derived using one of five methods, viz. laboratory compression tests, large-scale in situ tests, closed-form methods, case studies of collapsed and stable pillars and mixed methods. Before giving the various formulae and discussing them it may be pointed out that some very old rules of thumb or formulae and Mines Inspectorate's or any other statutory directives, which we sometimes come across in the literature, are eliminated from this review. Also not given are those pillar strength approaches which have been developed as location-specific and may not be generalized or have been developed for noncoal mines or are found to be clearly impracticable for application. Table 1 gives the various formulae, their methods of derivation, applicability to slender or squat pillars and type of strength parameter employed. Several good reviews of some of these equations are available [2, 12, 14] and the reader may refer to them for further details. A strength equation should be examined in the light of the following requirements or desirable features. (i) It should fit as many cases of collapsed and stable pillars as possible, especially the former ones. (ii) It should preferably be applicable to both slender and squat pillars. (iii) It should incorporate as many of the factors (defined in Section 24.2.1), which influence strength, as possible. Equations which are derived from lab tests on specimens of various w/h ratios and sizes require excessive extrapolation to real pillar sizes, e.g. equations (3) and (4). This drawback may, however, be overlooked provided these equations fit the case studies. Equation (5) was derived from rather scanty in situ large-scale tests, while equation (6) was derived from a large number of in situ tests. In the latter equation, as well as in equation (4), the strength of a 'critical' coal cube is required, the effect of size on strength being negligible beyond the critical size as per Bieniawski. It has been suggested later [14] that the critical size may be taken as 0.9 m instead of 1.5 m and instead of actually testing this size the 0.9 m cube strength may be estimated as h =

0.16cr 0.9-° c

5

* 0.16cr

c

MPa

(16)

where o is the strength of 2.5 cm (1 in) cubes. Equation (7), which is proposed as a modification of equation (6) for squat pillars (w/h > 5), produces a break at w/h = 5 i.e. we get two pillar strength values. One of these two equations, preferably equation (7), may be uniformly used for all w/h ratios. Probably because of the problems of extrapolation, Salamon and Munro developed their equation (8) from actual cases of collapsed and stable pillars, using the statistical method of maximum likelihood estimation. This original approach yields two important conditions for c

Table 1 Coal Pillar Strength Equations How derived

Equation*

Author(s)

w: — h 0

For slender or squat pillars

Kind of strength employed (k)

5

(3)

Lab tests

Slender

Lab, size = 25 mm (1 in)

2. Obert and Duval S = /c^0.78 + 0 . 2 2 ^ [18]

(4)

Lab tests

Slender

In situ, size 'critical'

3. Greenwald et al. s [19]

(5)

In situ tests

Slender

In situ, size = 30 cm (1ft)

(6)

In situ

Slender

In situ, size 'critical'

(7)

—

Squat

In situ, size 'critical'

(8)

Pillar case studies

Slender

Constant strength

1. Holland and Gaddy, Steart [15-17]

4. Bieniawski [3]

5. Bieniawski (modified [12]) 6. Salamon and Munro [11]

S = 0.16 k

s = k (oM

+ 0-36^

/ wVs = kl 0.64 + 0.36-1 w

s = 72

0.46

4

637

Design of Coal Pillar Arrays and Chain Pillars Table 1 (continued) Author{s)

Equation'

w

7. Salamon and Munro (generalized)

How derived

1

Kind of strength employed (k)

0.46

S = 0.79/c^

—

(9)

Slender

Squat Case studies and theoretical analysis

8. Salamon [20] where R = critical w/h = 5, R = w/h of pillar, V = pillar volume, s = a constant = 2.5 (proposed). 0

9. Wilson [8]

For slender or squat pillars

Case I. w > 2x (Figure 7a)

In situ, size = 30 cm

In situ, size = 30 cm

Theoretical analysis

Both

No strength

Theoretical analysis

Both

In situ strength

(All equations (11) are in ton, ft units) Rectangular pillars 5=

' ww x

[ww!

1.5(w + w )hH

xlO'

3

r

2

+ 3/i /Y xlO- ] 2

2

(Ha)

6

Long pillars 4y H S — ——(w — 1.5 hH x 1 0 ) w

(lib)

-3

Case I I . w ^ 2x (Figure 7b) Rectangular pillars w

5 = 667,

( —

w\ (

H

e

)

Long pillars S = 661 y^H x = 0.0015 hH is the failed coal zone y = 0.0707 t f t " is the rock density.

(lid) (lie)

3

10. Wilson [9]

Case I. Roadways stable (Figure 7c)

lab strength 5 = WW!

5

(w - 2x)(wj - 2x)d<7

J

qp

+ qp + —

(w - 2x)(w! - 2x)

(12a)

WW!

Case I I . Roadways unstable (Figure 7d) 1 5 = WWj

f ( w - 2 x ) ( w j -2x)d
J

(12b)

qp

(w where a' = qp\—+

V " \ \

1

or qp exp(wF/2fc)

G = in situ strength p = a constant for broken coal = 0.1 MPa (suggested) q = triaxial constant = 3.5 (average suggested) These equations are subject to the following two ground conditions. Q

638

Applications

to Rock Engineering-Mining Table 1

Author(s)

Engineering

(continued)

Equation*

How derived

For slender or squat pillars

Kind of strength employed (k)

(i) Yield in roof, seam and floor

(12c)

(12d) (ii) Yield in seam, rigid roof and floor h a x = — In — F qp

(12e)

. h yH x = - In — F p

(12f)

where F = (tan 11. Sheorey et al [21]

-1

* + — — — t a n " J~q 1

q

in radians)

5 = 0.66

fc/T

035

+ 6.3 { m y H [ l - exp(-1.5 w / D ) ] }

(13)

Theoretical method and case studies

Both

In situ, size = 30 cm

(14)

Theoretical empirical method and case studies

Both

Lab, size = 25 mm

(15)

Case studies

Slender

Lab, size = 25 mm

0 8

where Z) = 25 + 0.1 H m - virgin horizontal-vertical stress ratio. 12. Sheorey et al. [6] S = 0.27fe/i-°- + ^ - ^ - l 160\Ai 36

>

) /

13. Sheorey et al. [6]

5 = pillar strength (MPa) (except in equation 10), w = width of square pillars or long pillars or smaller width of rectangular pillars (m), w = longer width of rectangular pillars (m), h = extraction height (m), and H = depth of cover (m).

8

l

assessing the performance of any pillar strength equation: (i) the line of safety factor = 1 . 0 must be the best regression fit to all collapsed cases; and (ii) all stable cases must have safety factors greater than 1.0. We consider the general form of equation (8) for pillar strength S = kh*w

fi

(17)

and the tributary area load P over uniform pillar arrays (see Section 24.3.1) P

=

yH

(18)

where y is the unit rock pressure, B is the roadway width and H is the depth of cover. The safety factor F is defined as s

(19)

The constants fc, a, fS have to be determined using the maximum likelihood method which satisfies the above two conditions.

Design of Coal Pillar Arrays and Chain Pillars

639

The frequency distribution of F for failed cases is taken to be log-normal s

(20)

ZiOogF.) = (2«<5)-°- exp 5

and the cumulative density function of F for stable cases is s

MF.)

(2D

= O l ' ^ l

where d is the deviation or measure of scatter. Then the two conditions (i) and (ii) are satisfied by maximizing the product of the maximum likelihood functions L and L given below x

2

Lt

= /i(logF )-/i(logF ). . . ./!(lo F )

(22a)

L

= MF. yf (F, )....f (F )

(22b)

2

i l

l

2

i 2

2

2

g

s m

M

where m and n are the numbers of failed and stable cases. The product L

=

L

X

L

(23)

2

can be conveniently maximized if we take l n L i 4- l n L

= InL

2

(24)

differentiate with respect to the unknowns a, /?, fc, S and equate to zero (25) These four nonlinear algebraic equations have to be solved iteratively to obtain the four unknowns. If the first function L only (involving unstable cases) is maximized, the estimates of the unknowns are only slightly different from those obtained by maximizing the product L [11]. Maximization of Lx is identical with performing a regression analysis, which is much simpler computationally than maximizing L and the results are reasonably accurate. The whole procedure of maximum likelihood estimation thus basically boils down, for practical purposes, to performing a simple regression analysis of the safety factor equation for unstable cases. Sheorey et al. [ 6 ] have shown that a slight error in the pillar width (0.3 m say) can cause ^n appreciable change in the value of /?, the exponent of w, and the strength k but very little change occurs in a and 5. They consequently propose that a pillar strength equation should be developed first from known scientific premises and then applied to case studies, adjusting the constants involved so as to satisfy Salamon and Munro's conditions (i) and (ii) at least approximately. The generalized Salamon and Munro formula (equation 9) uses the in situ strength of 30 cm coal cubes. This formula was in use for over 15 years in Indian coal mines and was found to be reasonable for slender pillars under shallow covers. The rather complicated squat pillar formula (10) gives a smooth transition in strength across the critical w/h of 5, unlike equations (6) and (7). Since the equation is sensitive to the value of the constant e, its value needs to be known reliably from case studies. Both the old and new approaches of Wilson are basically derived from elasto-plastic theory for stresses around a circular opening in failed rock, which behaves as a Coulomb material [22]. The equation to the vertical stress a is derived by considering the equilibrium of a seam element in the crushed coal zone of an infinitely wide pillar (Figure 6a). Wilson's earlier approach [ 8 ] gives x

(26)

which relates the vertical stress a with distance x. The extent of the broken zone x is obtained from the condition at x = x,

x

=

yH

G

=


G

Q

+ qa

x

=

(T

0

+ qyH

(27)

640

Applications

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Engineering

in keeping with Coulomb's linear relation between the horizontal and vertical stresses o and cr. In the broken coal zone Wilson takes a = 1 p.s.i. in equation (26) and o = 0 in equation (27) and so proposes x

Q

0

\r\4yH

x

(28)

in which q = 4 on an average for coals (Figure 6 b). This is then linearized to x -

0.0015 hH

(29)

in which h, H are in ft. If a rectangular pillar is surrounded by infinite excavations on all sides, the ultimate load over the pillar (which is also its strength) is obtained as a pyramidal frustum (Figure 7a), whose volume divided by the base area gives equation (11a). The peak pressure is 4yH and is assumed to be uniform over the unbroken pillar core. When w = W j , equation (1 la) gives the strength of square pillars. A similar equation can be derived for long pillars (equation lib). When w < 2x we get regular pyramids (Figure 7b) whose height is less than 4yH and equations (11c) and ( l i d ) are obtained. Wilson's new approach [ 9 ] is considerably more complicated. Vertical stresses in the failed zone are now given for two conditions: (i) yield in roof, seam and floor q-l

(30)

a = qp (ii) yield in seam, rigid roof and floor a =

(31)

qpexp

where p and F are defined in Table 1. Equation (27) is again applied, this time
(a)

Figure 6

' I

(b)

(a) Forces acting on a seam element in the broken coal zone of a pillar; and (b) its corresponding triaxial behavior (after Wilson [8])

641

Design of Coal Pillar Arrays and Chain Pillars

(a)

(b)

(c)

(d)

(e)

Figure 7

Ultimate loading pillars can accept as per Wilson [8, 9] when: (a) w > 2x; (b) w < 2x; (c) roadways stable; (d) roadways unstable; and (e) shows the overestimation due to the shaded area

Wilson's derivations give rise to a few problems. (i) Both the old and new approaches specify the vertical stress in the failed coal zone in an infinite pillar with a single excavation on one side, which is assumed to be the same when a pillar is finite and bounded by roadways. It is difficult to conceive that the roadways will not interact and change the expressions for vertical stress. (ii) The old method and the condition of stable roadways in the new method assume the stress to be uniform over the intact pillar core, while in reality it is nonlinear. This assumption causes an overestimation of pillar strength which increases with w/h, as shown in Figure 7(e). (iii) In the closed-form solution for stresses in the failed zone around openings, a discontinuity in the vertical stress occurs at the limit of the failed zone x = x, if the properties change suddenly from the failed to the intact zone [23]. This is reflected in Wilson's new method (Figure 7c, roadways stable). It is assumed in equation (27) that at x = x,
<7j

=


C

+

aa\

x

(32)

where o and o are the major and minor principal stresses and a, b are constants, which are assigned the average values 6.3 and 0.8 based on a new failure criterion for jointed coal seams. Of importance x

3

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Applications

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in equation (13) is the virgin stress r&tio m which makes the equation flexible enough for use in high horizontal stresses. However, further work needs to be done in such situations, because mere inclusion of a higher value of m for high horizontal stresses may not be appropriate. High horizontal stresses may cause tensile stresses at the pillar sides although they induce a higher confinement at the pillar center. Besides, the two horizontal virgin stresses may be, more often than not, different, causing m to acquire two different values in two directions. The form of equation (13) recommended for normal coal measures (y = 0.025 M P a m " and m — 0.75) is 1

S = 0.66/c/T

0

3 5

+ 0.26{//[l - e x p ( - 1 . 5 w / D ) ] } 0

8

(33)

The drawback of this equation is that when w/h ^ 1, the second term always remains positive giving pillar strengths greater than that of a cube of side h. Also D = 25 + 0.1H is the width of the abutment pressure zone, which does not agree with field observations (see Section 24.3.3.1). Equation (14) also consists of two terms, the first defining the strength of a cube of side h and the second the increase due to triaxial and w/h effects and the virgin stress ratio. The constants involved were determined by adjustment of the equation against 23 unstable and 20 stable cases of pillars. When w/h < 1, the pillar strength is less than that of a cube of side h. It is often opined that the uniaxial strength becomes less important at higher w/h ratios. Since equation (14) consists of two additive terms, this concept is well accounted for. Equation (15) was proposed from 14 cases of failed slender pillars as a simpler alternative to equation (14) for quick hand calculations. Surprisingly, the exponents are close to those in equa­ tion (5) proposed by Greenwald et al. The performance of some of these equations will be studied against pillar cases in Section 24.4.

24.3 PILLAR LOAD The load or rock pressure on pillars comprises the vertical virgin stress (in level or near-level coal seams) and the stress induced by the excavations around pillars. In inclined seams, the virgin horizontal stress must also be considered.

24.3.1

Arrays in Level Seams

On a regular array, consisting of pillars of a more or less uniform shape and size, the vertical virgin stress is taken equal to the cover weight of the strata in normal coal measures. In geologically disturbed areas, in situ stress measurement results should be used. Figure 8 shows the block of rock each pillar has to support. The average rock pressure P over the pillar is simply the weight of this block divided by the pillar area (34)

for square pillars and for rectangular pillars (35)

using the nomenclature of Table 1. This method is termed the tributary area theory. These equations work very well in practice for regular arrays, provided the extent of the array, e.g. width of a panel of pillars, is at least equal to the depth of cover. If it is less, the pillar load may be less. The most commonly accepted pressure distribution over a pillar in an infinitely wide uniform pillar array is as in Figure 8, the average being given by equation (34) or (35). The value of the unit rock pressure is generally taken as 0.025 M P a m . For irregular pillar arrays or for pillar panels whose width is less than the depth of cover H, it is best to adopt a numerical method, the displacement discontinuity method [24] being probably the most convenient. Figures 9 and 10 give sample plots of rock pressure for these two situations as obtained using the displacement discontinuity program developed by Crouch Research Inc. of the USA. The corresponding tributary area loads are also shown in the figures. In an irregular pillar array we see that the load is overestimated for small pillars by the tributary area theory and underestimated for large pillars. - 1

Design of Coal Pillar Arrays and Chain Pillars

643

S u r foce Overburden supported by each pillar

_l

r-

i

Theoretical elastic

Actual

r

fl

Pressure at AA Figure 8

Pillar load according to the tributary area theory in a wide array

-Tributary area pressure

i

o

ro

i

a> a>

Pillar load (MPa)

i

300 m 156 m W= 12 m B- 12 m

HL -

Y//////////////A

-L/2 • Figure 9

Pillar loads in a narrow panel as compared with the tributary area loads

These example plots will be subject to change depending on strata stiffness. For example, under hard uncavable sandstones, the over- and under-estimation in irregular arrays will be further magnified and over a narrow pillar panel the pillar load will be further reduced. Therefore, the roof-seam modulus ratio should be chosen with care.

24.3.2 Arrays in Inclined Seams The rock pressure normal to inclined seam pillar arrays according to one approach [25] is given by 2

(cos a + m s i n a) 2

2

(36)

Applications is

to Rock Engineering-Mining

Engineering

r

Pillar load (MPa)

644

Loads over an irregular pillar array

Figure 10

Figure 11

Stresses over an inclined seam pillar

S u r f a c e

w = 15m B — 5m E m

r00

Figure 12

Pillar loads in a dipping seam

Design of Coal Pillar Arrays and Chain Pillars

645

which is obtained by simple resolution of forces (Figure 11), a being the angle of inclination of the seam with the horizontal. The sample plot of Figure 12 for the central pillar in a wide panel of uniform pillars was again obtained using the displacement discontinuity method for the following in situ stress field: (i) vertical stress = 0.025// MPa; and (ii) horizontal stress = 2.0 + 0.003// MPa, and the other data shown in the figure. The value of m at H = 198.75 m works out to be 0.5225. Equation (36) agrees exactly with the average normal stress over the pillar obtained by the computer method.

24.3.3 Chain Pillars 24.3.3.1

Wilson's

method

For these pillars the load accepted by the goaf has also to be known because whatever load the goaf does not accept is transferred on to the chain pillars, which is in addition to the dead weight of the strata. Wilson has found from underground measurements that the goaf pressure stabilizes to the cover pressure at a distance of about 0 . 3 / / from ribsides [8, 9 ] . Wilson assumed the distribution to be linear, so if we have goaves on both sides of the pillar chain, the average pillar load is obtained from Figure 13 as (37) This equation is valid when the extraction width is greater than 0.6 H. When it is less, the average pillar load is

(wi + B)

(38)

where L is the extraction width. (<3)

j l

(b) r

Figure 13

Scheme for estimating load on chain pillars with extractions on both sides (after Wilson [8]): (a) L ^ 0.6 H ; (b)L<0.6tf

646

Applications to Rock Engineering - Mining

Engineering

Sand stowing or filling in depillaring or longwalling is getting increasingly scarcer, but it is worthwhile finding chain pillar load with stowed goaves, which stabilize earlier than caved ones. Though only a few observations are available at the CMRS, the distance at which goaf stabilization takes place can be approximately taken as 0.2 H. The pillar load formulae can then be written for both caved and stowed goaves. L^lfH [w + fH)(w

x

+ B)

(39)

L<2fH (Wi

+

B)

(40)

f — 0.3 for caving and / = 0.2 for stowing. This method of Wilson, though simple, is found to be practically sound in the author's experience, when goaves exist on both sides. When an extraction panel exists only on one side of the chain pillars, the vertical stress distribution is as shown in Figure 14. In fact, the chain pillars are either a part of an array adjoining the panel or have a virgin portion of the seam adjacent to them. The average pillar load in this case will be the integral of the abutment pressure curve across the pillar width. Numerical methods may again be thought of for this case but these present some difficulties. Since pillar load depends on load acceptance by the goaf, realistic goaf behavior must be simulated in the numerical model. Constitut­ ive relations for goaves, especially caved ones, are very difficult to specify so as to simulate goaf stabilization at a distance fH. Alternative closed-form or logical methods, though not mathemat­ ically or structurally exact, are better suited, provided they simulate goaf as well as pillar loading in agreement with field experience. Figure 14 shows two abutment pressure curves, one the elastic distribution and the other the final distribution after development of the failed coal zone. If the goaf loading remains the same, the average pillar loadings as obtained from these two curves are identical. Wilson [9] has proposed the peak abutment stress to be F eak P

Figure 14

=

o-o +

qyH

Wilson's scheme for estimating load on chain pillars with goaf on one side of an array [9]

(41)

Design of Coal Pillar Arrays and Chain Pillars

647

using the notation of Table 1. He then assumed an exponential decay in stress over the pillars given by (42)

a = yH + M e x p

where M = a

+ (q -

0

C =

A

A /M w

f = -yH J

w

l)yH

for

2

L^lfH

The constant A defines the total load not taken by the goaf. The average load over the chain pillars is obtained by integrating equation (42). Thus w

(43)

According to equation (42) the cover pressure yH is reached at x = oo . For practical purposes we can find the distance at which the stress drops to within, say + 5 % of the cover pressure. This distance, which is the zone of abutment pressure D, can be found out using equation (42) as M e x p ( - D / C ) = 0.05 yH

or

D =

-

Cln

(44)

Figure 15 gives the variation of D against depth for q = 3.5, o = 5 MPa and L ^ 0.6H (caving) and also the mean variation as observed in longwall faces [26]. The plot in this figure excludes some obviously extreme or absurd values from the data. In general, Wilson's method gives greater abutment zones. The simple relation from these data is 0

D = 0.12H

(m)

(45)

Peng and Chiang [27] have proposed the relation D =

5.1//°

5

(m)

(46)

Abutment zone, D (m)

from stress measurements in ribsides. This relation, shown in Figure 15, is much on the higher side, probably because of the influence of adjoining longwall panels.

0

200

400

600

800

Depth of cover, H (m) Figure 15

Observed and estimated widths of abutment pressure zones.

648

Applications

to Rock Engineering - Mining 8

—

7

- 1

6

-

Engineering

Sheorey (caving)

\

5

4

-

3

Sheorey (stowing)

2

1 1 0

1

200

1

400

600

Depth of cover (m)

Figure 16 Peak abutment stress as a multiple of cover pressure as per Wilson [9] and author

To examine the method further, equation (41) may be used to obtain the ratio P e a k / y i f , as in Figure 16. This ratio falls with cover. There is no structural reason why this fall can be taken as valid. Also, equation (41) is given for caving, hence this method for a one-sided goaf cannot be used for stowing. P

24.3.3.2

Alternative

method for one-sided

goaf

Because of the problems with the Wilson method, an alternative method was devised so as to account for field observations of goaf and abutment pressure. The theory of beams on elastic foundations [28] was adopted for defining the exponential decay of stress over the abutment as well as goaf pressure stabilization at a distance fH. This theory employs the thin beam concept, so it is by no means structurally exact for simulating strata behavior. The success of the method, however, depends on fitting this theory to observed facts. From Figure 17(a) for L^fH, the equations for vertical displacements over the goaf and abutment can be written down straightaway. (i) Over the goaf f exp(a'x)(y4i cosa'x + / 4 s i n a ' x )

(47)

- exp( — a x ) 0 4 c o s a x + / t s i n a x )

(48)

2

(ii) Over the seam 3

4

in which c, c' = foundation moduli of seam and goaf, A -A = integration constants, a = (c/4£> ) , a' = ( c ' / 4 D ) , and D — flexural rigidity of strata. To these equations are applied the following four continuity conditions 1/4

x

4

r

1/4

r

dl

A

-

T

U,

v — v',

(49)

to yield the four unknown constants A -A . are x

4

Of interest are A and A for pillar loading and these 3

4

(50)

(51)

649

Design of Coal Pillar Arrays and Chain Pillars (a)

\ _

\

rH_

v

w/a

X

(b) Area A

Figure 17

Scheme for load on chain pillars with one-sided extraction based on the theory of beams on elastic foundations, when: (a) L ^fH; and (b) L < fH

and the loading over the pillars becomes a = cv = yH + cexp( — ax)(A

3

According to this theory, cover pressure is attained at a distance the goaf. Hence [29] 0.12H

and

so that

(52)

cos ax + A s i n a x ) 4

tl/OL

over the seam and at n/a' over

(Figure 15)

(53a)

fH

(53b)

(53c)

a=

and

(53d)

a =

Also

or

(53e)

c' =

(53f)

If the seam foundation modulus c is conveniently chosen as 1000 M P a m (elastic modulus/seam height) we get c'. These values of material constants will ensure agreement with field observations. 1

650

Applications to Rock Engineering - Mining Engineering

The average chain pillar load is then calculated by integration of equation (52) as before (i) L > 2fH B

Caving

Stowing

w + — + 0.147H(0.4 + exp( —z)sinz — 0.4exp( —z)cosz)

P

=

B

w + -

where

+ 0.042H(0.6 + e x p ( - z ) s i n z z =

(TI/0.12H)(W

+

0.6exp(-z)cosz)

(54a)

(54b)

B/2).

The abutment peak pressure in the two cases is obtained as Caving

P

= yH + c A = 6.38 yH

p e a k

(55a)

3

Stowing

P

p e a k

= 2.777 H

(55b)

These values are shown in Figure 16 to compare with Wilson's. It should be remembered that these are the elastic prefailure values and will therefore be different from the actual postfailure values. For the case when L < 2/H, the goaf displacements are + Ai cosh a'x cos a'x 4- A s i n h a ' x s i n a ' x 2

(56)

due to symmetry, the origin of the (x, v) coordinates being shifted to the goaf center (Figure 17 b). The seam displacement equation remains the same as for L ^ 2fH. The continuity conditions are again to be applied at the goaf-pillar boundary, i.e. at x — L/2. The resulting simultaneous equations are cumbersome to solve for the integration constants. An alternative simpler procedure may therefore be followed. The goaf load when L < 2fH is less than when L ^ 2fH by the area A as shown in Figure 17(b) where A

(57)

=

If an equal area is subtracted from the abutment pressure it gets distributed over a distance n/
P

=

0.147H(0.4 + e x p ( - z ) s i n z -

[1 -

Stowing

P

=

24.4

exp(-z)]

f 0.047H(0.6 + e x p ( - z ) s i n z -

[1 -

0.4exp(-z)cosz)

exp(-z)]

(58)

0.6exp(-z)cosz)

(59)

P E R F O R M A N C E O F STRENGTH E Q U A T I O N S

Any pillar strength formula may be accepted for practical use if it fits actual cases of pillars, whatever its method of derivation. Comparisons of different equations have often been made in the past based on their behavior with w/h ratio or extraction percentages, but seldom based on case studies. The best basis for comparison of performance is failed and stable cases, keeping in mind the two conditions of the maximum likelihood estimation method given in Section 24.2.3. Unfortu­ nately, most of the failed cases are for arrays, so for estimating the performance for chain pillars the

651

Design of Coal Pillar Arrays and Chain Pillars

best way is to study an equation for arrays and then see what sort of chain pillar sizes are obtained at different depths. Tables 2 and 3 give the failed and stable cases from Indian coalfields [ 6 ] . Unfortunately, details of the valuable South African cases are not available for study because only a summarized table has been published [11]. While selecting the cases the following criteria were applied: (i) pillars in arrays were more or less regular in formation; in failed cases the average pillar size and roadway width were taken over the collapsed area; (ii) the width of the pillar array was at least equal to the depth of cover; and (iii) the collapse was not affected by neighboring workings or faults. The first 14 cases in Table 2 and the first 15 in Table 3 are from arrays in bord and pillar mining while the rest are from the shaft pillar area at Jitpur colliery which was surrounded by three longwall panels. Pillar failure was slow and squeezing conditions existed around roadways. The tributary area method (equation 34) was used for the cases of bord and pillar arrays, while a finite difference computer program was used for pillar load in the Jitpur cases because of varying pillar sizes and the presence of longwall panels [30]. In the cases of rectangular pillars, the equivalent pillar width was calculated using equation (2) except when applying Wilson's formulae. The Jitpur cases are for failed and stable squat pillars and as such were included despite the conditions (i)-(iii) above. Figures 18(a)-(g) show plots between w/h ratio and safety factor for the various strength equations of Table 1. Equations (4), (5), (6), (8), (12a) and (33) are not being considered for case study application for the various reasons already discussed in Section 24.2.3. From these plots the following observations may be made regarding the performance of the different equations. (i) The Holland-Gaddy-Steart equation (equation 3) gives all failed cases and many stable cases below the line of unit safety factor, thus underestimating pillar strength for all w/h ratios (Figure 18a). (ii) Bieniawski's equation (equation 7) works well at w/h ratios less than about 4, whereafter it underestimates strength slightly. (iii) Equations (9) and (10) have been shown jointly in Figure 18(c), the latter being used for w/h > 5. Although Salamon's modification of the Salamon and Munro formula gives some improve­ ment in the strength of squat pillars, underestimation is still apparent because of, for one reason, the Table 2 Mine (seam) 1. Amritnagar (Nega Jamehari) 2. Amritnagar (Nega Jamehari) 3. Begonia (Begonia) 4. Amlai (Burhar) 5. Sendra Bansjora (X) 6. W. Chirimiri (Main) 7. Birsinghpur (Johilla top) 8. Pure Kajora (Lower Kajora) 9. Pure Kajora (Lower Kajora) 10. Shankarpur (Jambad bottom) 11. Ramnagar (Begonia) 12. Ramnagar (Begonia) 13. Kankanee (XIII) 14. Kankanee (XIV) 15. Jitpur (XIV) 16. Jitpur (XIV) 17. Jitpur (XIV) 18. Jitpur (XIV) 19. Jitpur (XIV) 20. Jitpur (XIV) 21. Jitpur (XIV) 22. Jitpur (XIV) 23. Jitpur (XIV)

Data for Failed Pillar Cases

h(m)

w(m)

B(m)

w/h

30

4.5

3.6

5.7

0.8

16.5

45

5.06

30

6.0

3.6

5.4

0.6

16.5

45

4.79

36 30 23 90 129

3.0 5.4 8.1 3.75 3.6

3.9 4.5 4.65 5.4 7.5

6.0 4.5 5.55 6.0 6.0

1.3 0.83 0.57 1.44 2.08

7.6 5.9 6.7 11.2 8.8

26 25 24 45 38

5.87 3.03 2.74 10.14 10.45

54

3.6

5.4

6.0

1.5

7.2

33

6.08

56

3.6

4.95

6.45

1.38

7.2

33

7.45

42

4.8

4.5

4.5

0.94

10.6

47

4.25

70

1.8

2.85

3.15

1.58

7.6

26

8.65

51

1.8

3.0

3.6

1.67

7.6

26

6.25

160 140 450

6.6 8.4 3.6

4.2 5.4 6.0

3.0 2.2 6.5 3.08 4.13 5.33 5.83 6.67 6.25 6.25 5.67

4.4 5.7 3.0

27 25 19

5.88 5.83 17.75 16.23 17.82 16.16 17.13 20.51 18.23 17.13 15.81

H(m)

19.8 18.6 18x34.5 10.5x12 12x21 18x21 18x25.5 15x63 18x30 18x30 15x33

Cube strength (MPa) Pillar load 30 cm 2.5 cm (MPa)

652

Applications

to Rock Engineering-Mining Table 3

Engineering

Data for Stable Pillar Cases

Mine (seam)

H(m)

/i(m)

w(m)

B(m)

w/h

1. Belampalli (Ross) 2. Nimcha (Nega) 3. Morganpit (Salarjung) 4. Ramnagar (Ramnagar) 5. Lacchipur (Lower Kajora) 6. N. Salanpur (X) 7. Bankola (Jambad top) 8. Bankola (Jambad top) 9. Surakachhar ( G - I ) 10. Lacchipur (Lower Kajora) 11. Sripur (Koithee) 12. E. Angarpathra (XII) 13. Kargali Incline (Kathara) 14. Jamadoba 6 & 7 Pits (XVI) 15. Topsi (Singharan) 16. Jitpur (XIV) 17. Jitpur (XIV) 18. Jitpur (XIV) 19. Jitpur (XIV) 20. Jitpur (XIV)

36 48 270

3.0 6.0 3.0

5.4 9.9 8.1

6.0 6.0 3.6

1.8 1.7 2.7

12.4 11.8 11.4

48 50 46

3.93 3.03 13.80

75

2.7

9.9

6.6

3.7

6.2

28

5.10

38

5.1

7.2

3.9

1.4

7.2

33

2.18

30 102

5.1 4.8

9.0 10.1

6.0 2.4

1.8 2.1

5.8 11.9

21 35

2.04 4.54

75

3.0

6.3

4.2

2.1

11.4

35

5.10

106 38

3.5 5.1

16.0 18.3

4.0 4.2

4.6 3.6

13.2 7.2

29 33

4.04 2.18

266 30

4.8 2.1

40.0 6.0

5.0 6.0

8.3 2.9

6.1 7.0

43 19

8.25 2.94

36

3.6

9.3

5.7

2.6

8.1

40

2.29

80

2.0

5.8

5.5

2.9

6.8

29

7.44

85 450

1.8 3.6

7.0 21x39 18x48 19.5 x 30 18x31.5 18x42

3.9 6.0

3.9 7.6 7.3 6.5 6.4 7.0

11.0 3.0

41 19

5.05 15.33 15.81 16.64 14.92 15.68

Cube strength (MPa) Pillar load 30 cm 2.5 cm (MPa)

inclusion of in situ strength. Since this strength shows a greater bias at depth, safety factors of all Jitpur cases are very low. (iv) Wilson's earlier approach (equations 11) gives a rising trend in the failed cases (Figure 18d) underestimating the strength at lower w/h ratios. Several stable cases give safety factors less than 1.0. This rising trend takes place for two reasons: (a) roadway interaction is not considered for defining failed zones; and (b) stress over the intact pillar core is uniform. Wilson's later equation (equa­ tion 12 b) for the unstable roadways condition leads to the following two equations, (i) Yield in roof, seam and floor (60) (ii) Yield in seam, rigid roof and floor (61) These equations were applied to the cases with the recommended values of p = 0.1 MPa and q = 3.5. Figure 18(e) shows that equation (60) gives unrealistically low safety factors for almost all (stable and failed) cases. The performance of equation (61) is not shown plotted because while it behaves in much the same way as equation (60) for low w/h ratios, for squat pillars it gives extremely high safety factors due to the exponential nature of the equation. Equation (60) may perhaps behave reasonably if the values of the material constants p, q are suitably changed (see Section 24.7). (v) Since the constants in equation (14) were derived from the case studies themselves, its performance (Figure 18f) is obviously reasonable for all w/h ratios. Equation (15) which was proposed for slender pillars indeed shows an underestimation of strength for squat pillars (Figure 18g). Having studied the safety factor behavior of various equations against w/h ratio, we may now see the bias introduced due to the in situ coal strength. Figure 19 shows the safety factor variation

653

Design of Coal Pillar Arrays and Chain Pillars

ro —

Safety factor

3 r (a)

O

4

w/h (C)

6

8

• I

I

4

6

2

—

ftw ° 00

L

8

W/h

(e) —

d)

. !

o

4

° _ J

r

2

Safety factor

w

Safety factor

(b)

o

o

i

1

4

oj

4 —

w/h

1

^ **a o 0<

ro

i

Safety factor

i

•• *

i

Safety factor

1

o oo°

(g)

w

Safety factor

o

ro

oo

—r~—i

—

. . t V

4

w/h

O

Safety factor

1

1

O

(f)

• A*.

L_ 4

w/h

Figure 18 Performance of various pillar strength equations against stable and failed cases: (a) Holland and Gaddy, Steart (equation 3); (b) Bieniawski (equation 4); (c) Salamon and Munro, Salamon (equations 9 and 10); (d) Wilson (1972) (equations 11a and 1 lc); (e) Wilson (1982) (equation 12b); ( f ) Sheorey et al. (equation 14); and (g) Sheorey et al. (equation 15) (failed cases shown by solid circles; stable cases having safety factors greater than 4.0 not shown in b and g)

654

Applications

to Rock Engineering - Mining

Engineering

2

o

Safety factor

o

0

100

o

Equations (9) and (10)

•

Equation (3)

200

300

400

500

Depth (m) Figure 19

Safety factor variation against depth of overburden according to equations (3) and (9) and (10)

against depth, using equations (3) and (9)/(10). These equations were chosen because one incorpor­ ates the laboratory small-scale strength, while the other in situ large-scale strength. This figure supports the earlier argument that the in situ strength is more affected by depth than the laboratory strength.

24.5

SAFETY FACTORS A N D PILLAR SIZING

Various safety factors have been recommended for pillar design by different authors, the range being 1.5-2 for unstowed arrays, 0.6-1 for stowed arrays and 1.0-2.0 for chain pillars. The proper safety factor will depend on the nature of the pillar strength equation. For example, an equation which underestimates pillar strength of squat pillars (either due to the in situ strength or due to the fact that it does not account for the w/h ratio effectively in squat pillars), will require lower safety factors as the w/h ratio increases. Such equations will therefore considerably complicate pillar design procedure, unless they are suitably adjusted to fit the available case studies. Such adjustments will obviously consist of changing the empirical constants and/or the material constants. Safety factor specification is made here considering equation (14) only, because it fits the pillar cases for all w/h ratios.

24.5.1

Unstowed and Stowed arrays

The author's experience has shown that the design safety factor of 2.0 for long-term stability of unstowed pillar arrays is sufficient. It may be noticed that this safety factor also envelops all the failed cases in Figure 18(f). Stowed pillar arrays are a much more complicated proposition for safety factor specification because it has not been possible, so far, to estimate the real triaxial confinement offered by the fill. The overall increase in pillar strength is the sum total of: (i) initial instantaneous strength gain due to triaxial confinement after fill placement; (ii) subsequent strengthening with time due to lateral pillar creep expansion and the corresponding reaction offered by the stowed pack due to its compression; and (iii) reduction in strength, simultaneous with the increase in (ii), because of creep. Figure 20 shows schematically the gain in strength in the 03-01 plot, 03 being the confining stress and (7i the augmented (triaxial) strength for single lift pillar reduction and multilift working. The initial gain in pillar strength can be reasonably estimated from soil mechanics principles, e.g. using deep and shallow soil bunker formulae for wall pressure. A few calculations will show that these pressures are quite small (less than 0.1 MPa) and consequently give a strength gain generally less than 10-15% only. The other two factors (ii) and (iii) are much more difficult to determine realistically. Because of this, it is difficult to arrive at a suitable safety factor for stowed pillars based on any kind of mathematical treatment. A South African experiment [31] for pillar heightening in a 12 m thick seam has indicated that the safety factor (calculated according to equation 9) of the pillars could be as low as 0.6, without

655

Design of Coal Pillar Arrays and Chain Pillars (b)

(a)

cr

<^3

3

Figure 20 Gain in pillar strength due to filling: (a) single lift pillar reduction; and (b) multilift reduction

causing any collapse. The pillar width was 16 m and bord width 6 m. It is not known whether the pillars subsequently collapsed or not, but in one similar instance in India they did, causing subsidence in an upper seam. In this Indian example of Kargali colliery (Kargali seam), the method of pillar reduction consisted of splitting the existing pillars into 7.8 m square pillars with 5.4 m wide roadways at a depth of 100 m and heightening them to 21 m, which was the full seam thickness, with hydraulic sand stowing. From equation (14) (k = 27 MPa) we get the safety factor of these very tall pillars as 0.3! Another Indian example is of Chalkari colliery where the same seam was worked by 9 m wide pillars with 6 m wide roadways, the total height extracted being 9 m. The safety factor according to equation (14) was 0.5 and the pillars were stable. These examples point out that the probable design safety factor for stowed pillars may be 0.6 or less. A tentative value proposed is 0.6.

24.5.2

Chain Pillars

Because of the paucity of failed chain pillar cases, a safety factor is somewhat difficult to specify. It is possible though to fix a reasonable range based on mining experience. The width of chain pillars can be fixed in one of three ways, (i) Choose a pillar strength formula, determine the average load (depending on one- or both-sided goaf, caving or stowing) and find the width with a suitable safety factor, (ii) Choose the pillar width such that the gate road beyond is not much affected by the longwall or depillaring face movement, (iii) Perform numerical stress analysis of various chain pillar sizes also varying other geomining parameters and define pillar size applying a suitable failure criterion to the seam. There can be several pitfalls in such a method, e.g. realistic simulation of the constitutive behavior of the caved goaf and choice of the failure criterion for in situ seam conditions. According to the first approach, it is assumed that the gate road beyond remains unaffected so long as the pillar is stable. The second approach does not make this assumption and specifies the pillar width based on abutment stress decay over the pillar [ 9 ] or on roof to floor closure (convergence) [32]. Pillar strength thus becomes immaterial in the second method. In the third method neither pillar load nor strength is required to be estimated.

24.5.2 .1

Size based on strength

Figures 21(a) and (b) have been constructed using equations (9), (10) and (14) for pillar strength and equations (39) and (54) for pillar load (wide extraction panel, caving) with the following data: pillar height, h = 3 m; roadway width, B = 4.8 m; safety factor, F = 1.0; lab coal strength (2.5 cm cubes) = 30 MPa; and in situ coal strength (30 cm cubes) = 9 MPa. The Indian Coal Mines Regulations specify various initial square pillar sizes depending on roadway width and depth when the working height is less than 3 m. These sizes have generally worked reasonably well in depillaring and longwalling. They are therefore also shown in the figures for comparison. Figure 21(a) was constructed for both-side goaf loading only, using equation (9) for shallow covers up to 150 m, whereafter equation (10) for squat pillars was used. s

656

Applications

to Rock Engineering - Mining

(a)

Engineering

(b)

r ;

Depth (m)

°r :

0

20

40

60

80

0

20

40

60

80

Pillar width (m) Figure 21

Width of square chain pillars as per: (a) Salamon (equations 9 and 10) for both-sided goaf; and (b) Sheorey (equation 14) for both-sided and one-sided goaf

The safety factor for chain pillars recommended by Wilson in his earlier approach [8] is 1.0. A low safety factor is sufficient for chain pillars because they are meant for panel isolation (unless they are designed for subsidence control) and have a short life in second workings. A safety factor of 1.0-1.5 thus appears to be prudent while using equation (14). Since 30 MPa is a fair average of coal strength and since equation (14) is not sensitive to coal strength at higher w/h ratios, it may be simplified for chain pillar design to S =

8/T 0

(62)

3 6

obviating the need for strength tests. An important point in chain pillar design is the concept of 'indestructible' pillars (as discussed in Section 24.2.2) based on which an upper limit on pillar width of 20h may be fixed. It may be noticed that the Indian Coal Mines Regulations suggest 15h as the maximum size for the values of B — 4.8 and h = 3.0 m used in constructing Figure 21. Equations (9) and (10) are sensitive to coal strength and an error in its determination is likely to cause not insignificant errors in pillar width, especially at depth. Figure 21(a) is therefore slightly misleading as it is based on the constant in situ strength of 9 MPa.

24.5.2.2

Size from safety of gate

road

In the second approach for pillar sizing, Wilson [ 9 ] recommends that the gate road in the adjoining panel should be at a 'safe' distance given by w =

2(C + x)

(63)

where C is a constant and x is the yield zone given by equations (12d) or (12f) (Table 1). The exoonential stress decav over the pillar is represented bv a - yH = [ > o + (q ~ l ) V # ] e x p

(64)

instead of equation (42) to include the yield zone. A triangle of an area equal to the exponential loading will give A

s

=

| " (a -

yH)dx

=

C[(J

0

+ (q -

l)yH]

(65)

Design of Coal Pillar Arrays and Chain Pillars

657

Considering l o a d balance', the various areas in Figure 22 are related by A

w

A

w

A

or

w

+ Ai

=

+ Ai

+ A

+

A$

+

=

s

=

2

yHx

A

X

A

+

s

A

+

b

+ A

3

=

s

A

A

2

+

b

C[<7

0

+

(g

-

l)y#]

or

(66)

(67)

where A is defined in equation (42) and the loading A equation (30) or (31), over the failed coal zone, (i) Yield in roof seam and floor w

h

is obtained by integrating the stress,

(68)

(ii) Yield in seam, rigid roof and floor [yH

-

pi

(69)

The chain pillar width w is so chosen that the gate road is at a safe distance of w = x + b + x

where b is the base of the area A , obtained from s

[<7

or

0

+ (q -

l)ytf]

=

C O o + (q~

l)yH]

b = 2C

(70)

This leads to the safe pillar width (equation 63). As per Wilson, this pillar width will allow the second failed zone due to the adjoining panel to develop without endangering the pillar, as well as keep the gate roads stable. This width of pillar is thus recommended for one-sided as well as both-sided extraction. Figure 23 shows that this pillar width varies almost linearly with depth, which is difficult to accept. Chain pillar sizing based on gate road closure cannot be done precisely and only approximate recommendations for pillar width are possible. Only one such study, by Whittaker and Singh [32], is considered here. An interesting approximate relationship is shown to exist between the average

Figure 22

Scheme of load balance for obtaining the safe chain pillar width (after Wilson [9])

Applications to Rock Engineering-Mining

Engineering

Depth (m)

658

0

20

40

60

80

100

120

Pillar width (m)

Figure 23 Safe chain pillar width according to Wilson [9]

pillar load and gate road closure (Figures 24a and b). For the average pillar stress they have used the equation yH P = — (w + Htan<£),

(71)

L ^ 2Htan<£

Average stress (MPa)

for long pillars without intervening roadways. They term as the angle of shear. This equation is the same as Wilson's equation (39) if tan 4> = / a n d if intervening roadways are introduced.

Gate vertical closure per m of height (%)

50

100 150 Chain pillar width (m)

Depth range ° 0 to 300m • 300 to 900m

300 to 900 m

0 to 300 m 100

150

200

250

300

Chain pillar width (m)

Figure 24

Dependence of: (a) average chain pillar load; and (b) vertical gate road closure on width of chain pillars (after Whittaker and Singh [32])

659

Design of Coal Pillar Arrays and Chain Pillars

Whittaker and Singh recommend that leaving no pillar is better for gate road performance than leaving a pillar 10-30 m wide, because this range gives the highest gate road closure. Although the scatter in Figure 24(a) is high, their conclusions are perhaps general enough when we consider the similarity between Figures 24(a) and (b). Such an approach is far too approximate for chain pillar design.

24.5.2.3

Numerical

method

Hsiung and Peng [33] have developed an equation to estimate the width of chain pillars from detailed finite element analysis of longwall chain pillars. Their equation is given for strong and weak strata separately and expresses the pillar width directly in terms of several other parameters. (i) Strong roof logw = 1 0 "

172 log (j + 751 log H + 39 log

3

c

(72)

(ii) Weak roof logw =

10"

- 1021og
3

:

c

(73)

where w, h and H have the same meanings as in Table 1, E , E , E are elastic moduli of the immediate roof, main roof and seam, H is the main roof thickness and L is the panel length. All dimensions are in ft and the strength cr in p.s.i. Since these equations are independent of panel width, pillar sizes may be in error. {

m

c

m

c

24.6 PILLAR DESIGN FOR SUBSIDENCE CONTROL 24.6.1 Pillar Arrays In this section it is not intended to give the procedure for pillar design from draw angle considerations for subsidence control. In subsidence engineering some situations arise when stability of pillar arrays existing below surface features becomes unimportant. In such instances arrays are to be designed for keeping the surface strains and slopes due to subsidence within permissible limits [34]. This design consists of forming small pillars whose safety factor is less than the prescribed values. Thus if we adopt a safety factor of 1.2-1.3 for unstowed pillars or 0.3-0.6 for stowed ones, they will ultimately lead to collapse (see also Section 24.8 for such problems). The design must ensure that the resulting subsidence strains and slopes are within permissible limits. This method is more beneficial for stowed thick seam extractions. If subsidence slope and strain are denoted by the symbol s and the subsidence at the trough center (maximum subsidence) by S, we have the following well known general relation [35] £ =

(74)

where the factor /? depends on the excavation width to depth (L/H) ratio. Also we have S = a-h-e

(75)

where a is the subsidence factor, h is the extraction thickness and e is the extraction ratio. If we replace s by £ m > the maximum permissible slope or strain for a given surface feature, equation (74) becomes p e r

(76)

Thus the extraction increases linearly with depth, whereas with normal design having stable pillars the extraction falls. To illustrate the method, let us take an example of working below a river with three different extraction thicknesses for the following data: extraction thickness, h = 6, 12, 18 m; roadway width,

660

Applications

to Rock Engineering - Mining

Engineering

Extraction (%) 0

40

60

80

1

1

1

1

100

1 —

Depth (m)

I

20

Figure 25

Example plot for extraction below a river in multilift pillar reduction with stowing in thick seams

B = 4.8 m; subsidence factor (for complete extraction with stowing), a = 0.1; maximum permissible strain at river bed, e = 3 m m m " ; and multiplier (supercritical extraction), f} = 0.5. It can be shown that this method will give poor extractions under very shallow covers when filling is adopted. Therefore pillars have to be designed for stability down to a certain depth, whereafter this design can be undertaken. Figure 25, in which pillars with the safety factor of 1.0 (stowing) are designed using equation (14) down to a certain depth, illustrates that this method is more beneficial for thicker seams. Similar graphs may be constructed for different values of slope/strain depending on the surface feature to be protected. 1

p e r m

24.6.2 Chain Pillars for Noneffective Extraction The term noneffective extraction is of relatively recent origin in subsidence engineering and defines the maximum excavation width up to which no surface subsidence takes place. The L/H ratio of such extractions is observed to be 0.3-1.17 in Indian coal mines [ 3 6 ] , the latter figure corresponding to workings below hard massive strata. These ratios may be somewhat less for long-term stability. Such extractions have been practised with success in a number of cases in India and Australia [37]. Such limited span extractions are generally useful beyond those depths after which pillar reduction starts giving poor extraction percentages. The method requires that extraction panels are flanked by permanently stable chain pillars. Equation (14) in its modified form (equation 62) is recommended with the safety factor of 2.0, the pillar load being calculated using equation (39) or (40), with the factor / = 0.3 since no stowing is required in this method. Considering long-term stability the minimum width of such pillars is recommended to be w = 5h and an upper limit of 20 h is given for the concept of indestructibility [34]. Figure 26 compares the size of such pillars for the sample data shown with the corresponding Australian norms which prescribe the pillar width to be either w = 12h or 0.16H, whichever is greater [37]. Figure 27 indicates how extraction is better by this method than by pillar reduction, when pillars are designed for stability. Figures 26 and 27 thus show that normal pillar reduction can be economical under very shallow covers only. At depths beyond 60 m or so the possibility of adopting either the limited span method or the method of 'unstable' pillars must be investigated.

Design of Coal Pillar Arrays and Chain Pillars

661

Pillar width (m) 40

60

80

Depth (m)

o

100

o

200

300

Figure 26

L

Pillar widths between noneffective extractions using equation (14) and the Australian norm [37]

Extraction (%) 20

40

60

80

100

ro

Depth (m)

—

0

Figure 27

24.7

Example plot illustrating extractions in pillar reduction and noneffective extraction

BOLTED PILLARS

When filling is not available at a mine, poor extraction percentages result. Unfilled pillar workings can also invite pillar robbing and undergo slow slabbing after a long time. Lateral bolting of pillars can offer an attractive alternative to filling. Admittedly, there is no real substitute for filling and if sand is not available, alternatives like fly ash should be considered. Design of bolted pillars is somewhat tricky since rock bolts, like filling, offer a passive resistance, i.e. most of the constraint given by them to the pillar can develop only upon lateral pillar deformation. Unlike filling, however, it is possible to estimate the maximum ultimate constraint a bolt can give in terms of its anchorage strength. Past research in this topic has been mostly concerned with failed model or in situ pillars [ 3 8 - 4 0 ] . Agapito et al. [ 3 8 ] have reported failed but standing pillars subsequently supported in an oil shale mine. They obtained the oil shale triaxial Mohr envelope by in situ stress measurement in failed and intact pillars and used it for predicting the gain in pillar strength due to bolting. Stress values were found to be less in failed pillars and the envelope was obtained as curvilinear. According to them the strength increase may be up to 90%, depending on the extent of failure in the pillar existing before

662

Applications

to Rock Engineering - Mining

Engineering

bolting. The gain in pillar strength Ao was simply calculated from 1

(77)

in terms of the angle of internal friction cj> and the horizontal confinement Arj . The latter was assumed to correspond to the ultimate bolt support pressure. Failed but standing coal pillars are comparatively rare except when they have high w/h ratios, e.g. the failed cases at Jitpur colliery in Table 1. As far as pillar reduction for surface protection is concerned, the small pillars formed will mostly be slender. As such, this section deals with slender (bolted) pillars only. The relatively large deformations required for bolts to be effective are often coupled with the development of a failed zone around pillars. The stresses within this zone can be calculated using elastoplastic theory [22], assuming some simple failure criterion. With the implicit assumption that bolts or supports have been placed before formation of the broken zone, this theory shows that the size of the broken zone varies inversely as the support pressure. It also shows that the failed zone accepts higher stresses when laterally supported. Wilson's equations (30) and (31) for vertical stress in the broken or yield zone are basically of this theory. His pillar strength equations (60) and (61) therefore offer the means for estimating the strength of bolted pillars which are intact before bolting [41]. The original form of equation (30) (equation 31 and the corresponding equation 61 are not being considered) is given by Wilson as [ 9 ] 3

(78)

a = 4 ( P s + P,

where p is the lateral support pressure. The material constant p, whose value Wilson recommends as 0.1 MPa, is defined as [ 4 2 ] s

where a' is the in situ strength in the broken coal zone. If o' is expressed as o /C where c is the lab compressive strength and C is a reduction factor, this will account for a realistic in situ broken coal strength. The triaxial factor q is given by 0

0

q = [(1 +p ) '

2 1 2

c

c

(80)

+ pY

where p is the coefficient of internal friction. This is the slope of the linear Coulomb-Navier failure criterion in principal stress coordinates. Since the triaxial strength behavior of coal is nonlinear [41], q has to be estimated by drawing a chord to the triaxial curve at some point (Figure 28).

Triaxial strength, a,

120 r-

20

O

20

40

60

Confining pressure, 0-3

Figure 28 Suggested method for estimating triaxial factor q

663

Design of Coal Pillar Arrays and Chain Pillars Equation (60) now becomes

(81)

including support pressure p and the factor C . A realistic estimation of the constants q and C can be made by applying this equation to the first 14 case studies of slender failed pillars in Table 2. Since these are square pillars the strength equation is written as follows, (i) Bolted pillars s

(82)

(ii) Unbolted pillars (83)

The result of applying equation (83) to the cases is shown in Figure 29, which gives us the values q = 3.4 and C = 20. The value of q thus comes close to q = 3.5 recommended by Wilson. It may be noted that this figure does not show case 13, Table 2, which had the highest w/h ratio of 3.0. While applying these cases, it was noticed that equation (83) was sensitive to q and the strength rose rapidly and unrealistically with w/h. Elimination of case 13 gave a much better plot (Figure 29) and more reasonable estimates of q and C . For the average strength
or

(84)

where A is the anchorage strength of each bolt and a is the bolt spacing. While the value of C is substituted above, q is retained as a variable. It has been shown [41] from triaxial data on 17 coals that q = 3.4 on average, if it is determined for each coal as the slope of the chord joining the points (0, o- ) and (30, a ) MPa in the (0-3,0-!) plot (Figure 28). This can thus become the standard procedure for estimating q. For the two extreme values of q = 2.5 to 4.5, o = 1000 to 6000 t m " , A = 101, a = 1 m, equation (84) gives the gain in pillar strength as 5-70%. s

c

x

2

s

Pillar strength (MPa)

c

Pillar load (MPa) Figure 29

Fitting Wilson's modified equation (83) to the first 13 unstable cases of Table 2 for estimating C and q

664

Applications to Rock Engineering-Mining

Engineering

The strength of bolted pillars is thus (85)

where the unbolted pillar strength S is defined by any acceptable pillar strength formula. This method has n o t undergone any systematic field trial so far, at least not by design. Since n o filling is involved, a safety factor of 2.0 is suggested while using equation (85). The length of bolts obviously cannot cover the entire estimated failure zone, which will be u p to the pillar center in most cases. The best policy is t o install bolts such that the t o p and bottom ones in a vertical row enter the roof and floor at a n angle. T o prevent both spalling a n d robbing it will be necessary t o place the bolts over a wire mesh. Grouted or resin-anchor pretensioned bolts should be preferred to other types. If the pillars are very narrow, bolts may be installed right across the width a n d tightened at both ends. Winding of such pillars by wire ropes has also been suggested [40].

24.8 YIELD PILLAR TECHNIQUE 24.8.1 Theory of the Method The concept of using the postfailure pillar strength in bord and pillar design was p u t forward by Starfield a n d Fairhurst [ 1 3 ] a n d Salamon [ 4 3 ] . Pillar failure in a panel can be catastrophic (unstable) or progressive (stable) depending on strata stiffness and proximity of wider (stiffer) pillars. The behavior will thus be akin t o the laboratory behavior of a rock specimen being loaded in a stiff machine (see Volume 3, Chapter 4). T h e explanation provided in the former reference is worth considering in this context. If a pillar in a panel is replaced by a hydraulic jack (Figure 30a), which is slowly retracted, the initial force o n it due t o rock pressure will d r o p linearly with roof lowering (convergence) (Figure 30b). T h e slope of this characteristic, which is termed local stiffness of the roof, will be different for different pillar locations, depending on proximity of wider pillars or barriers. W e now replace the jack by a real pillar and superpose the local stiffness on the complete load-convergence characteristic of the pillar (Figures 30c and d). The failure of this pillar (if its safety factor is less than unity) will be either stable o r unstable depending o n whether the local stiffness is steeper or gentler than the steepest postfailure stiffness of the pillar. In an array of uniform pillars surrounded by wide

(a)

i ! Barrier

>/

/

(0

'///A

Barrier

(d) Load on pillar

Load on pillar

Force on jack Convergence

> /

Jack

(b)

Figure 30

1

Displacement

Displacement

(a)-(d) Scheme of Starfield and Fairhurst [13] for stable and unstable pillar failure in terms of the local stiffness of the roof

Design of Coal Pillar Arrays and Chain Pillars

665

b a r r i e r s , t h e l o c a l stiffness will h a v e t h e g r e a t e s t n e g a t i v e v a l u e n e x t t o t h e b a r r i e r a n d t h e l e a s t a t t h e p a n e l c e n t e r . T h e r e f o r e , t h e d e s i g n o f s u c h a p a n e l w i l l b e e n t i r e l y g o v e r n e d b y t h e c e n t r a l p i l l a r (s). T h e c o n d i t i o n s i n F i g u r e s 3 0 ( c ) a n d ( d ) c a n b e w r i t t e n f o r s t a b i l i t y a n d i n s t a b i l i t y a s (/c, A a r e n e g a t i v e ) : K < A for s t a b i l i t y , a n d K ^ A for i n s t a b i l i t y , w h e r e K is t h e l o c a l stiffness a n d A is t h e postfailure pillar

stiffness.

F o r a p a n e l of n pillars S a l a m o n h a s g i v e n a c o m p l e t e m a t h e m a t i c a l t r e a t m e n t . T h e c o n v e r g e n c e a t p i l l a r i(i=

1 t o n) i s d e f i n e d

as Si

where s

=

Sei

+

(86)

7i

is t h e c o n v e r g e n c e p r o d u c e d b y a p p l y i n g a f o r c e P

ei

t

t o a weightless rock m a s s at the pillar

l o c a t i o n a n d y is t h e c o n v e r g e n c e d u e t o t h e r o c k w h e n t h e r e a r e n o p i l l a r s . C o n v e r g e n c e s t

i t h p i l l a r is r e l a t e d t o a l l t h e p i l l a r f o r c e s

at the

e i

by CijPj

where c

i j

(87)

a r e t h e influence coefficients. T h u s in g e n e r a l in m a t r i x

[S ] =

-[C][P]

e

Salamon has also shown

notation

(88)

that

{in

[ P ] = icy

1

- LSI} = [ K ] { [ r ] - [S]}

(89)

w h e r e t h e m a t r i x [ X ] , w h i c h is t h e i n v e r s e of t h e i n f l u e n c e coefficient m a t r i x [ C ] , is t e r m e d h

t

T h e c o n d i t i o n for stability for all t h e pillars t h e n specifies t h a t t h e m a t r i x [ X ]

+

[ A ] must

p o s i t i v e d e f i n i t e , w h e r e [ A ] is a n n x n d i a g o n a l m a t r i x c o n t a i n i n g t h e p o s t f a i l u r e p i l l a r

X {i t

=

the

y

stiffness m a t r i x a n d [ 5 ] a n d [ T ] a r e t h e m a t r i c e s c o n t a i n i n g c o n v e r g e n c e s s a n d

be

stiffnesses

n).

1 to

U n s t a b l e f a i l u r e c a n n o t o c c u r t h r o u g h o u t t h e l o a d - c o n v e r g e n c e c h a r a c t e r i s t i c if t h e l o c a l s t i f f n e s s is s t e e p e r a t e v e r y p o i n t of t h i s c h a r a c t e r i s t i c . T h i s c o n d i t i o n , w h i c h S a l a m o n t e r m s p e r f e c t s t a b i l i t y , i s s a t i s f i e d if

A where

> A < 0

m

(90)

c

— A is t h e s m a l l e s t e i g e n v a l u e of t h e stiffness m a t r i x [ X ] a n d A c

m

is t h e m i n i m u m

(steepest)

s l o p e of t h e p o s t f a i l u r e c u r v e . B y this c o n d i t i o n t h e e l e m e n t s A of t h e m a t r i x [ A ] will satisfy X ^ f

A .

{

m

It c a n t h u s b e realized t h a t a p r a c t i c a l d e s i g n u s i n g this refined t e c h n i q u e will d e p e n d o n o b t a i n i n g realistic l o a d c o n v e r g e n c e c u r v e s of a c t u a l pillars. A large-scale e x p e r i m e n t for this p u r p o s e conducted by Wagner

[4]

using the servo-controlled

in situ

was

t e s t ( F i g u r e 2).

I n o r d e r t o p u t t h i s d e s i g n m e t h o d i n p r a c t i c e , t h e stiffness m a t r i x [ X ] h a s t o b e d e t e r m i n e d

by

c o m p u t a t i o n a n d u s e d for c h e c k i n g t h e c o n d i t i o n ( e q u a t i o n 90). T h e p r o c e d u r e c o n s i s t s of a p p l y i n g a uniform stress c

z

a t t h e l o c a t i o n o f a p i l l a r j o v e r i t s a r e a Bj

PJ

giving

o dA

=

(91)

2

w h e r e A is t h e t o t a l p a n e l a r e a . T h e c o n v e r g e n c e v a l u e s s

a r e d e t e r m i n e d for all pillar l o c a t i o n s . T h e

ei

b e s t w a y t o d o this will b e t o e m p l o y a n u m e r i c a l t e c h n i q u e like t h e d i s p l a c e m e n t method.

Such

load

application

is r e p e a t e d

for all pillar l o c a t i o n s

to ultimately

discontinuity determine

the

influence coefficient m a t r i x [ C ] . A n i n v e r s e of this m a t r i x will give [ X ] . T w o p o i n t s a b o u t t h i s 'critical stiffness' A m u s t b e m e n t i o n e d h e r e : c

firstly,

A -> 0 w h e n t h e p i l l a r c

p a n e l is w i d e a s c o m p a r e d w i t h t h e c o v e r ; a n d s e c o n d l y , A r e d u c e s a s t h e n u m b e r o f p i l l a r s i n c r e a s e s c

for t h e s a m e p a n e l , k e e p i n g t h e e x t r a c t i o n t h e s a m e . T h e

first

point thus s h o w s that this

design

m e t h o d d o e s n o t w o r k w h e n t h e pillars u n d e r g o t h e t r i b u t a r y a r e a l o a d , s o t h a t pillars will h a v e t o b e d e s i g n e d for safety factors g r e a t e r t h a n u n i t y in w i d e p a n e l s . A r e c e n t t h e o r e t i c a l s t u d y [44]

shows that A

0 a t p a n e l w i d t h - d e p t h r a t i o s (L/H)

c

in excess of

a b o u t 5. T h i s a p p e a r s t o b e c o n s i d e r a b l y o n t h e h i g h e r s i d e a s p r a c t i c a l e x p e r i e n c e s h o w s t h a t L/H

=

1-2, t h e t r i b u t a r y a r e a l o a d m a y a c t o n p i l l a r s , u n l e s s t h e s t r a t a a r e h a r d a n d

The

limit

o f L/H

= 5 was

arrived

at

load-convergence

behavior

of

pillars,

m o d u l u s ratio.

real

using

numerical we

must

methods.

also

This

estimate

shows

realistically

that the

at

uncavable. besides

the

roof-seam

666 24.8.2

Applications to Rock Engineering-Mining

Engineering

Applicability of Yield Pillars

The method is thus more applicable for the following geomining conditions. (i) It is ideally suited for extraction under hard uncavable strata (particularly at some depth) which would otherwise cause problems of airblasts in caving. (ii) It is more applicable to those countries where partial extraction is adopted as a matter of practice rather than only for surface protection. The American room and pillar system, which consists of wide rooms separated by narrow rib pillars, is more suitable for this design method. In India, after the initial development, depillaring operations achieve 8 0 - 9 0 % recovery under normal conditions, causing roof caving as in longwall mining. This yield pillar design therefore may not normally be required in India, except under hard strata. (iii) In a burst-prone seam this technique has considerable potential for application to depillaring or formation by small pillars. (iv) Another area of application for this technique is for the design of arrays at depth for subsidence control (Section 24.6.1). Pillars will have to be designed for a safety factor of 2.0 to a certain depth, whereafter they may be designed using this technique. For practical design Salamon suggests a safety factor of 1.0 for the pillars, so that in reality some of them will have safety factors less than 1.0 and some more than 1.0. It is then a matter of working out the critical stiffness A for different variations of panel width, extraction percentage and number of pillars within the panel until condition (90) is satisfied, while at the same time obtaining an acceptable extraction percentage. Obviously, numerical or analog methods [13] will have to be employed. Several papers in recent literature assume that yield pillars are those in which the yield zone reaches the pillar center, i.e. no solid core is left, as per Wilson's equations. Such pillars may function as yield pillars, e.g. because they are adjacent to larger pillars in a multientry longwall panel and because they satisfy condition (90), but it is incorrect to call them yield pillars on the basis of Wilson's equations. c

24.9 24.9.1

SUMMARY AND CONCLUSIONS Pillar Strength

A pillar strength formula should satisfy the following requirements. (i) It should fit failed and stable cases of pillars, satisfying the two conditions of maximum likelihood. (ii) It should preferably be applicable to both slender and squat pillars. (iii) Most of the factors which influence pillar strength should be incorporated in it. One more requirement, which has not been explicitly mentioned earlier, is that the pillar size must increase with overburden depth at a reduced rate (see, for example, Figure 21). A linear increase (as in Figure 23) is not acceptable. Pillar strength should generally be defined in terms of two components: (i) strength component; and (ii) component of shape, end condition and horizontal stress. The first should define the uniaxial strength of the seam including the effect of size and the second component the strength change due to w/h shape in plan, horizontal stresses and unusual end conditions, if any. The strength component should preferably include the small-specimen laboratory strength, since the in situ large-scale strength gets biased with cover depth (not to mention that lab tests are much easier and cheaper to perform than in situ tests). The two components should be additive rather than multiplicative, so that even if the in situ strength is included, the second component will be dominant at depth and pillar strength will remain largely unaffected. The effects of high lateral in situ stresses and unusual end conditions due to the presence of soft bands are not explicitly included in any of the formulae and further research is required. The forms most suitable for including these effects are those of equations (13) and (14). Of all the failed cases of Table 2 only one probably had a high horizontal stress condition and that is case 10. There was a thick dyke adjoining the pillar collapse area in this case. It may also be pointed out that this case gave the highest safety factor among the failed cases while using equations (14), (15) and, incidentally, equation (7). Considering the performance against case studies and the above discussion, some possible modifications in the different pillar strength formulae might be suggested as in Table 4, while keeping their general forms intact. 9

Design of Coal Pillar Arrays and Chain Pillars Table 4

Suggested Modifications in Different Pillar Strength Formulae

Author (s)

Equation

667

(3)

Holland and Gaddy, Steart

(6) and (7)

Bieniawski

(9) and (10)

Salamon and Munro

(12b)

Wilson

(14)

Sheorey et al.

Possible modifications with remarks Change of exponents of w and h to those in equation (5), (9) or (15), in which case equation (3) will become identical with one of them. General form of this equation unsuitable for squat pillars. Equation (7) is more suitable, but it should be applied to all w/h ratios. Suggested value of exponent is 1.5 instead of 1.4. 'Critical' cube strength k = 0.16 x (2.5 cm cube strength) acceptable. Incorporation of lab strength instead of in situ strength, values for constants in equation (10) suggested as e — 3.5 and R = 3.0. Change constant p to the form o /C/{q — 1), (where o is lab coal strength, C = 20) instead of p — 0.1 MPa. Value of q = 3.5 suggested by Wilson acceptable. Equation should not be used for w/h > 3. No changes at present suggested. The constant in the second term will have to be changed for unusual horizontal stresses and end condi­ tions. Other equations above not very suitable for this change. 0

c

c

24.9.2 Pillar Load For wide uniform pillar arrays the tributary area method is completely satisfactory in both level and inclined seams and therefore equations (34)-(36) are recommended for such arrays. For irregular arrays and narrow panels, whose width is less than the cover under soft to average strata or less than about twice the cover under hard massive strata, numerical methods should be resorted to for pillar load estimation. A proper simulation of the roof-seam modulus ratio is necessary for this. A simple procedure to achieve a proper modulus ratio can consist of a few trial runs for an arbitrary array of pillars with large (infinite) barriers. When the zone of abutment agrees with field observations we get the correct modulus ratio. In the absence of field data, this zone may be estimated as 0.12H, unless the strata are hard. Numerical methods are found to be very cumbersome for obtaining chain pillar load. Equations (39) and (40) for both-sided extractions and (54), (58) and (59) for one-sided goaf are recommended. Some recent work [45] points out the possibility of an increase in the pillar stress level beyond the tributary area pressure in a seam due to pillar development in another seam above. Such increases were observed (by stress meters) to be greater at greater depths. Numerical modeling of one such case (cover of upper seam 105 m, innerburden or parting rock between the seams 19.5 m) gave the pillar load increase of only 3%! More research is required to establish this finding. Another seam interaction problem can be the existence of remnant pillars or chain pillars adjoining goaves in an upper seam. Numerical modeling is again the obvious answer. While we are on interaction, a problem, which has not been satisfactorily dealt with in the past, can arise regarding the stability of contiguous pillars separated by thin innerburdens of rock or coal. Such thin partings may collapse on some or all sides creating 'sandwich' pillars. Further research is required for defining the stability of such pillars.

24.9.3 Special Extraction Methods As was shown, conventional design of pillar arrays for surface protection gives acceptable extraction percentages only under shallow covers. Under moderate covers noneffective span extrac­ tion, with intervening stable chain pillars, should be used. Another attractive proposition is the design of unstable pillars, which will subsequently fail and induce subsidence within permissible limits. The yield pillar technique will also give good extraction percentage at depth. This technique consists of designing pillars with a safety factor of 1.0, ensuring progressive or stable pillar failure. This method will require a realistic estimation of the postfailure characteristic of pillars as well as the roof-seam modulus ratio. For the purpose, in situ large-scale testing with servo-controlled hydraulic jacks may be performed. Tests on laboratory small specimens may not be relied upon. The yield pillar technique will be particularly useful where partial extraction is adopted as a matter of practice and also for depillaring under hard strata. Unfortunately, to the author's best knowledge, systematic field trials of this method have not been reported, although the method was thought of over two decades ago.

668

Applications

to Rock Engineering - Mining

Engineering

24.9.4 Safety Factors The following safety factors are recommended for forming stable pillars: (i) unstowed arrays, 2.0; (ii) stowed arrays, 0 . 6 - 1 . 0 ; (iii) laterally bolted arrays, 2.0; (iv) chain pillars for gate road protection or panel isolation, 1 . 0 - 1 . 5 ; and (v) chain pillars for noneffective extraction method, 2.0. For the last type the minimum and maximum sizes of 5h and 2 0 h (h is extraction thickness) should also be remembered. The mechanism of stabilization with filling needs to be understood better and quantified for a more exact specification of the safety factor of stowed arrays. Similarly, further research is required for fixing a proper safety factor of chain pillars used for panel isolation. The upper bound width of 20 h should again be remembered for such chain pillars. For bolted pillar arrays it should be remembered that the safety factor of 2 . 0 is to be used after the gain in strength is accounted for i.e. using equation (85). A systematic field trial of bolted pillars is necessary for checking the validity of equation (85).

24.10

ADDENDUM

Some recent publications, which could not be referred to in the chapter, have made important contributions to pillar design. Of these, numerical or site specific approaches are omitted here for brevity. (i)

Pillar strength considering stress

gradient

Mark and Iannacchione [ 4 6 ] propose an analytical method for estimating the vertical stress gradient in the outer yield zone of pillars corresponding to any pillar strength formula. The gradient is shown to have the same general form as the original strength equation. Thus if stress gradient measurements are taken in a mine, the pillar strength equation can be back estimated. Using Bieniawski's strength formula (equation (7), Table 1) and Figure 3 1 , pillar resistance jR is R = k

The increase in pillar resistance dR due to an increase in pillar width dw is then dK =

fc^l.28w+

(44)

1.08

If the vertical stress cr increases continuously with distance x from the pillar edge we have v

w/2 dK = 4 |
(45)

Equating (44) and ( 4 5 ) and solving we get k

0.64 + 2 . 1 6

:

Then if the stress gradient measured underground is of this linear form, the pillar strength formula back estimated will be of the general form of Bieniawski's equation. This method, though site specific, can lead to a general pillar strength formula if sufficient stress gradient measurements are available.

J 6A=2w Aw

X L 6w Figure 31

Design of Coal Pillar Arrays and Chain Pillars (ii)

Pillar strength considering in situ

669

stresses

An important modification of equation (13), Table 1 has been suggested by the author [47] because this equation assumes that the horizontal to vertical in situ stress ratio m remains constant with depth. From world stress measurements it has been shown that m = p + q/H

(46)

the empirical constants p and q varying greatly with local conditions. Due to paucity of in-seam in situ stress data these constants have been estimated using a theory developed by Sheorey [48]. According to this theory the average horizontal stress is given by (47) where E is the elastic modulus (MPa), v is Poisson's ratio, T is the thermal gradient in the earth ( ° C m ) and ft is the coefficient of linear expansion. Equation (47) is shown to fit stress measure­ ment data reasonably in different rocks. Dividing (47) by the average vertical stress yH and using the following values for coal [49] y = 0.025 M P a m " , v = 0.3, E = 3000 MPa, x = 0.03 ° C m " \ and j? = 3 x 1 0 " ° C " we get equa­ tion (46) as _ 1

1

5

1

on an average lor coal seams. Equation (13) can then be modified to the form S = 0.27<7 /T

0 3 6

C

+

CH[

Constant C is determined using the failed and stable cases of pillars in Tables 2 and 3 so that finally S = 0.27(7 /r°c

36

+

This is the only equation that considers in situ preexcavation stresses and is recommended instead of equation (13).

ACKNOWLEDGEMENTS

The author remembers with gratitude the free and untiring help given by Mr D. Barat and Mr C. Mukherjee as well as other colleagues in his research group for preparing this chapter. Permission given by the Director, CMRS to publish this work is also acknowledged.

24.11 1.

2. 3. 4. 5. 6. 7. 8.

REFERENCES Wagner H. and Maden B. J. Fifteen years of experience with the design of coal pillars in shallow South African collieries. In Proc. ISRM Symp. Design and Performance of Underground Excavations, Cambridge (Edited by E. T . Brown and J. A. Hudson), pp. 391-399. British Geotechnical Society, London (1984). Bieniawski Z. T . Rock Mechanics Design in Mining and Tunneling. Balkema, Rotterdam (1984). Bieniawski Z. T . The effect of specimen size on compressive strength of coal. Int. J. Rock Mech. Min. Sci. 5, 325-335 (1968). Wagner H. Determination of the complete load-deformation characteristics of coal pillars. In Proc. 3rd ISRM Congr. Advances in Rock Mechanics, Denver, pp. 1076-1081. NAS, Washington, D.C. (1974). Sheorey P. R., Barat D., Das M. N., Mukherjee K. P. and Singh B. Schmidt hammer rebound data for estimation of large scale in situ coal strength (Technical Note). Int. J. Rock Mech. Min. Sci. & Geomech. Ahstr. 21, 39-42 (1984). Sheorey P. R., Das M. N., Barat D., Prasad R. K. and Singh B. Coal pillar strength estimation from failed and stable cases. Int. J. Rock Mech. Min. Sci. & Geomech. Ahstr. 24, 347-355 (1987). Das M. N., Barat D., Prasad R. K. and Sheorey P. R. Considerations for influence of overburden depth on coal strength. In Proc. Int. Symp. Underground Engineering, New Delhi (Edited by B. Singh), pp. 55-60. Oxford & India Book House, New Delhi (1988). Wilson A. H. Research into the determination of pillar size. Min. Eng. (London) 131, 409-416 (1972).

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