Strength of rectangular pillars in partial extraction

Int..1. Rock Mech. Mi~l. Sci. & Geomech. Ahstr. Vol. 11, pp. 41 44. Pergamon Press 1974. Printed in Great Britain.

Strength of Rectangular Pillars in Partial Extraction P. R. SHEOREY and B. SINGH*

Sandstone specimens of rectangular cross-section were tested to obtain a relationship between the effbctive width o] these specimens, average of the m'o widths w~ and w2, aml their compressive strength. The resuhing straight line regression is shown to be similar to the variation in strength of simple ,square prisms with width height ratio. The strength increase in rectangular specimens is shown to he a combination g[ the ir~fluences of width height ratio and size. The q([bet of size on strength was reduced by preparing the rectangular specimens in ,such a way that the), were greater than the k'ritieal size', this being the size beyond which a fall in strength is slow. It is ultimately shown that the strength gf a rectangular specimen w~ x w2 x h is the same as that of a square specimen (w 1 + w2)/2 x (w 1 + w2)/2 x h. This equivalence is further proved by in situ strength trials on rectangular and cubic specinwns of coal. A strength fi)rmulajbr rectangular pillars is proposed at the end, based on these labora tory and in situ finding.s. The forntula shows that higher extractions can he achieved by Jbrming rectangular stooks or adopting some wide stall method wherever partial extraction is contemplated.

1. I N T R O D U C T I O N In pillar mining, partial extraction or stooking is commonly adopted in India as second workings, while extracting coal below rivers, important surface features or waterlogged old workings. This method consists of splitting original pillars into several stooks, square or rectangular in cross-section, and leaving them as such. It would be of considerable importance to estimate the strength of these stooks correctly in order to obtain the best percentage of extraction as well as safeguard the workings. Several formulae are available for estimating the strength of square stooks [1-5], but references to rectangular stooks are scanty in the literature. Bieniawski has mentioned that no scientific evidence was available with reference to pillars of rectangular section [5]. His compression tests on a single set of rectangular coal specimens, 3.5 x 2 in. in cross-section and 2 in. in height, however, do indicate that they are likely to be significantly stronger than cubes. It was decided to carry out experiments in the laboratory and corroborate laboratory results by underground strength trials on coal. 2. A H Y P O T H E S I S FOR S T R E N G T H EQUIVALENCE

The well-known fact that a cube of rock is slightly stronger than a cylinder of the same width height ratio can be explained if it is considered that the effective * Central Mining Research Station. Dhanbad. Bihar. India.

41

width of the cube is the average of its diagonal and side. This makes it wider in reality and hence stronger than the cylinder whose diameter is equal to the cube side. Arguing along the same lines, a rectangular specimen under compression carl be treated as having an average width height ratio (w 1 + w2)/2h where w~ and w2 are its two sides and h its height. In other words, a rectangular specimen of dimensions w 1 x w2 x h should have the same strength as a square specimen of dimensions (wl + w2)/2 x (wl + w2) 2 x h. An increase in the longer dimension w2 should give progressively greater values of the effective width-height ratio (w~ + w2)/2h. Thus it was anticipated that a plot between compressive strength and the effective width-height ratio {w~ + w2)/2h should give a regression similar to the wellknown one between strength and width height ratio w/h for simple square prismatic specimens, if the above hypothesis was valid. It will also be noticed that an increase in the longer dimension w 2 produces increasingly larger cross-sections, i.e. greater sizes. Hence the influence of size must also be present in the regression. However, in order to reduce this effect in the regression for simplification, the rectangular specimens could be so prepared that the equivalent sizes (w 1 + w2)/2h were all greater than the 'critical size' for the rock under test, the "critical size' being the one beyond which a further increase in size produces only small, but not insignificant, changes in strength. It depends upon the macroscopic flaw size in the rock and, as can be shown from the weakest-link theory equation of Epstein [6], it is the size of a cube containing about 4000 flaws.

42

P.R. Sheorey and B. Singh TABLE

l.

] ' A B I I ~, "~ ~ ! R I : N G I ' t t I)A'IA I)] M O D J i

S T R E N G T H VARIA I'ION W I T H SIZE O f ( ' [ :J'~l-s

SIDI [, 0 = 2 0 m m :

Cube size (mm)

Strength (kg/cm 2)

10 20

15(X) 1267

4(t 60

1279 1243 1238

70

Standard deviation (kg/cm 2)

Mean width heighl (w~ 4 w:)"2h

Length lmm)

45

%1 ! ~2 ~i~

2{) ~i ~7 S~

i!,

109 i 5h

Considering limitations of cutting very long rectangular specimens and in order to obtain a sufficiently large number of values of w2/% above the critical size, a finegrained sandstone with indistinct bedding planes was chosen. Tests were conducted for (a) the effect of size on strength to determine the critical size for this sandstone, (b) obtaining the regression between the compressive strength of rectangular specimens and the effective width-height ratio (w, + w2)/2h, (c) obtaining the regression between the compressive strength of simple square prisms and width--height ratio w/h. Specimens were prepared with the usual accuracy of +_0-03 mm and loaded to failure at the same loading rate of 25 kg/cmZ/sec between the rigid platens of a universal testing machine. In order to ensure uniform loading, especially on longer rectangles, thin paper caps were used for all the tests (a), (b) and (c). The test results are given in Tables 1, 2 and 3 respectively. The critical size can be seen to be nearly 20 mm for this sandstone. The rectangular specimens were accordingly prepared, keeping w, = h = 20 ram, we being increased. The number of replications in each case was three except for 10 mm cubes, for which it was five. Figure 1 shows the finished rectangular specimens and the longest rectangular specimen after failure. The strength regression for rectangular specimens is shown plotted in Fig. 2 along with that for simple square prisms. The regression equations for the strength of rectangular specimens and simple square prismatic specimens were obtained respectively as (correlation coeffÉcient 0.996 in both cases)

,~1 -:: 2 0 nln-I

,.."16 276 : O~ "~2S q03 so4

t~i ~1 iTi I xs 27 94 !t

Rg()

']'ABLE 3. STREN(}TH VARIATJ()N SVt vH \ v i i ) I l l

Width/height

Strength. ,'%

w ih

fk g/cm 2~

0"50

i ] ;> 122::; 1279 i 397 t 542 20(X}

0,67 1.00 I 33

2 (Xt 4(X)

5,umda~ d deviation (kg, cm21

Strcngth, at, (kg/cm 2)

1.000 1275 [925 2.57<, ' "~'~ ~ sso 4.45q

134

3. LABORATORY EXPERIMENTS AND RESULTS

i ~ . l / [ A N O k L A R P l [ I AP, S. ~tt(~R IFR

tllI(HVL

H E I ( ; H I RA |1',~

Standard dewation (kg/cm ~ ~9 i~)

~ 23

,~4 i30

because of the slight influence of size as said to bc present in "super-critical" rectangles of increasing length. This is in support of the proposed hypothesis of equivalence for the strength of rectangular specimens. As a further check, rectangular specimens with the smaller side less than the critical size of 20 mm were tested, together with their equivalent square specimens of the same height. The sizes chosen for these two were: wj , tSmm, w2 - 4 5 m m , h ~ 15ram(rectangular)and w= 2

: = 30 mm square, h = 15mm (equivalent square).

The strength values were obtained as 1812 ~: 158 kg/'cm 2 and 1785 +- 64 kg/cm 2 respectively. These values are not significantly different.

1

c% = G 0"836 + 0'164

O'p = O'e ( 0 ' 8 1 8

+ ()'182 h )

2h

J

(1)

(2)

where crh = compressive strength of a rectangular specimen of size wt x w2 x h c& = compressive strength of a cube equal to or greater than the critical size ao = compressive strength era square prism with

w/h # 1. Equations (1)and (2) are seen to be very similar. Also, the slope of the former equation is seen to be a little less

J'ig. I(A). Rectangular specimens ready t<)r testing (above) and I(BL failure of the longest rectangt, lar specimen 20 x 158 x 20 mm high (belo~ )

43

Strength of Rectangular Pillars in Partial Extraction it

2000

o

1800

0

1600

£ o L

140C

,.//

120C

~ooc --

I

1

I

I

I-0 2.0 3.0 4.0 50 w/h , ~,+ w2/2h Fig. 2. Variation of strength of rectangular and square prismatic specimens with mean width and width height ratio respectively.

4. I~NDERGROIIND STRENGTH TRIAI.S In order to ensure prevention ola collapse of the parting bclwccn IWO conligut)tis SCaI/lS by crushing or file rib pillars left iri the wide stall workings of the lowcr seam, underground strength trials werc conducted on cubic and rectangular specimens in a colliery. Three pairs of a 1 ft cube and an equivalent rcctangular specimen 18 x 6 in. in cross-section and 1 ft in height were isolated at the floor level of a manhole side by side. The specimens were initially rough-hewn by picks and later tinished to size by hand saws. The top surface of the specimens was given a thin layer of a sand~cement mixture, adding a rapid hardening compound. This layer ensured uniform loading of the specimens. Figure 3 shows such.a pair before testing. The specimens were loaded to failure by a 100-ton hand-operated hydraulic jack. A spherical seating with steel rails packed to the roof of the manhole were placed on the jack. The assembly was tightened at the roof level by means of wooden wedges. Figure 3 shows the loading assembly mounted. Table 4 gives the test results. It will be noticed that there is no significant difference between the strength values of the two sets of specimens. This is again in support of the hypothesis of equivalence. 5. S T R E N G T H F O R M U L A P R O P O S E D FOR R E C T A N G U L A R STOOKS A N D C O N C L U S I O N At present it is customary in India to assess the stabi-

Fig. 3(A). I ft cubical and cqnivalcnt rectangular specimens of coal 6 × IS × 12 in. high rcad~ for ill .',ilu ICSl (ahovc~ alld 3lI}). the lest assembly for the rectangular specimen (below).

lity of stooks in partial extraction by using the Salamon strength formula for square pillars [4]: ~,,~10• 4(1

S = 1320 ,@:g~ lb/in 2 where the first empirical constant, 1320 lb/in 2 is the strength ofa 1 ft cube of coal. An application of this formula in its present form to all coals in India sometimes

TABLE 4

Cubes Rcctangularspccimcns

No. of specimens tested 3 3

Dimensions

Compressive strength 1b/in 2

Standard deviation [b/in 2

I x I x 1 ft 6 x 18 x 12 in.

1151 Ills

81 79

44

P . R . Sheorev and B. Smgh

introduces a significant error in estimating the pillar size. Hence it was decided to test 1 ft cubes in situ and substitute its strength value in the above formula for the figure 1320, modifying it to the following form: ,W 0 - a t 6

S = K. hO~,~,-

(3)

where K = 1 ft cube strength of the seam under consideration. T h e a u t h o r s ' experience in a few seams shows that K differs significantly from 1320 Ib/in 2 in several cases. In the light of the present investigation, it can be seen that the above formula needs further modification in order to estimate the strength of rectangular pillars. The equivalence established between rectangular (w~ × w2 × h) and square specimens ( w 1 + w z)~2 x (w~ 4 w:i/2 x h indicates that the S a l a m o n formula should be modified for rectangular pillars to the following form:

S=K.

!4)

which gives a better percentage of extraction. The formula can also be used for designing barrier pillars of rectangular section.

l ' o summarize, rectangtflar pdlars arc stronger d3a~~ square pillars of the same area and a rectangular pilku w~ < ~, :< h and a square one { ~ ~212 : {~, w : / 2 × h in size are equivalent in strength. l'his shows thal strength formula lot square pillars of the torm (~) needs modification to the fornt (4t for rectangular pillars. Formula (4)indicates that ~ higher extraction can be achieved by splitting original square pillars into rectangular slooks. Rcceiccd 21 .Ima i97~

REFERENCES

I. Greenwald H. P., Howarth H. C and Hartman t. Experiments on strength of small pillars of coal in ~he Pittsburgh Bed. U,S, Bureau Mines, Report Inv. 3575 {1941). 2. Steart F. A. Strength and stability of pillars in coat mines, d. (hem. Metall. Min. Soc. S. Aft. 54, 30%325 (19541. ?. Holland C. T. and Gaddy F. L. Some aspects of permanent support of overburden on coal beds. Proc. West Virginia Coal Min. Inst. 54 55 (1956). 4. Salamon M. D. G. A method of designing bord and pillar workings. J, South AJk. Inst. Min, Metall. 68, 68 78 {1967). 5, BieniawskiZ. T. The effect of specimen size on compressive strength of coal. Int. d. Rock Mech. Min'. Sei, 5, 325-335 {1968). 6. Epstein B. Statistical aspects of fracture problems. J, appL Phys. 19, 140-147 (1948).

Geomechanics Abstracts CONTENTS

General Education Companies, institutes and laboratories Books Bibliographies Conferences Nomenclature

1A 1A 1A 1A 2A 2A 3A

Properties of Rocks and Soils Texture, structure, composition and density Fracture processes in rocks Strength characteristics Shear deformation characteristics Granular materials and influence of interlocking Time dependent behaviour Physico-chemical properties Permeability and capillarity Compressibility, swelling and consolidation Vibration

3A 4A 5A 5A 7A 7A 7A 7A 8A 8A 9A

Geology Mechanism of faulting and folding Tectonic processes Environmental effects, weathering and soil formation Earthquake mechanisms and effects

9A 10A

Hydrogeology Groundwater Measurement of water pressure and its effects

I1A I1A IIA

Underground Excavations Mines Tunnels Power plants In situ stresses in ground and stress around underground openings Surface subsidence and caving Temporary and permanent supports

I1A IlA 12A 12A

9A 9A 9A

12A 12A 12A

Geological factors of importance in underground excavations Construction methods Groundwater problems Experimental and numerical techniques

13A 13A 13A 13A 14A 14A 15A 16A 17A

Surface Structures Embankments and embankment dams Foundations Slopes Harbours, canals and coast protection works Deep water marine structures other than above Base courses and pavements of roads, railways and airfields Geological factors of importance in surface structures Construction methods Groundwater problems Experimental and numerical techniques

17A 18A I8A 18A

Comminntion of Rocks Drilling Blasting Crushing and grinding

21A 21A 22A 23A

Rock and Soil Improvement Techniques Bolts and anchors Grouting and freezing

23A 23A 23A

Site Investigation and Field Observation Planning, geotechnical and structural mapping Core recovery, logging, probing, boring and sampling Photographic techniques Geophysical techniques Presentation and interpretation of data

23A

24A 24A 25A 25A

Subjects Peripheral to Rock Mechanics General geology

25A 25A

17A 17A

24A

Explanation of Abstract Format The in]urination contained in tile ab.stract entries themst, h,es is described in the h~lltm in$¢ e.vamplc Abstract number

-427

Author

~ H U D S O N , JA C R O U C H , SL FAIRHURST, C

Title

,Soft, stiff s e r v o - c o n t r o l l e d testing machine. A review with reference to r o c k failure. 23F, IT, 5 4 R

" I R A N S P . R O A D RES. LAB. C R O W T H O R N E , B E R K S , G B D E P T . ('IV. M I N E R . E N G . U N I V . M I N N E S O T A , U.S.A D E P T CIV. M I N E R . E N G . U N I V M I N N E S O T A , 1J.SA

T ..............................................

l

Number of reJerences Number of tables

......................................................................

Number o]~figures

................................................................

Source

,ENGNG.

GEOLOGY.

V6, N3, 1972. P155 t 8 9

] .......................

2/51,i//"2',i

................................................................. ................................................................................................ Abstract

Affiliation

Volume Tide qf iournal

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