Creep in model pillars of saskatchewan potash

Int. J. Rock Afech. Min. S c L & Geomech Abstr. Vol. I0. PP. 363--371. Peribamon Pres= 1973. Printed in Great Britain

CREEP IN MODEL PILLARS OF SASKATCHEWAN POTASH M. S. KiNG University of Saskatchewan. Saskatoon, Canada ( Receiced 30 September 1972) Abstract--Results are reported of creep tests on model pillars of Saskatchewan potash ore. The first series of tests, each having a duration of 1000 hr. shows the effect of changes in temperature and vertical stress on the creep behaviour of pillars in a homogeneous material. In the second series, each having a duration of 1500 hr, are incorporated the effects of the presence of clay seams in the roof and floor. The test conditions in both series of tests represent those existing at subsurface depths of between 3400 and 4500 ft in Saskatchewan, for extraction ratios of 0.32-0.51 at 3400 ft and • 10-0.36 at 4500 ft. For the first series of tests, with a pillar diameter-to-height ratio of 4, the vertical natural strain i on the pillars could be related to the time T by a simple power law of the form, tr - aT ~. for T greater than 200 hr. Thus the rate of vertical creep of the model pillars was found to decrease with an increase of time. For the second series of t~.~ts it was found that a pillar dian~eter-to-height ratio of at least 8 was required to prevent brittle failure at vertical strexses equivalent to depths of 3400 ft. With this diameter-to-height ratio of 8 the creep bchaviour for tests equivalent to this depth was very similar to that of pillars in a homogeneous material at the same depth, but having a diameter-to-height ratio of 4. However, the ell'cotof the increase in temperature associated with an increase in depth to 4501) ft was very much more pronounced when di~ontinuities were pre~ent. INTRODUCTION IN TlW. absence of knowledge of the creep properties of evaporites, potash producers in Saskatchewan, C a n a d a , have been reluctant to increase the extraction ratio in r o o m - a n d pillar mining much above 30 per cent. They have been deterred for the same reason from c o n v e n t i o n a l m i n i n g at subsurface depths greater t h a n 3400 ft. In Saskatchewan, the problem is aggravated by two further factors: the presence o f water-bearing strata above the evaporites a n d the occurrence in several mines of clay seams adjacent to the ore. Mine pillars must be designed therefore to preclude the possibility of fracture of overlying strata, taking into a c c o u n t the adverse effect of clay seams where pre.~nt. The results of a research p r o g r a m m e intended to provide creep data for design purposes in potash mines are reported in this paper. Because of difficulties in d e t e r m i n i n g the mechanical properties of materials behaving in as complex a m a n n e r as evaporites by c o n v e n t i o n a l means, it was decided to study the deft)= m a t i o n o f model potash pillars as a function of changes in stress and temperature. In this way, empirical laws governing creep in potash have been obtained. The temperatures and stresses at which the tests have been conducted were chosen to be representative of those existing in Saskatchewan at subsurface depths of between 3400 a n d 4500 ft, for extraction ratios up to 0.5. In Fig. I, extraction ratio is plotted in the range 5000-7000 psi. The temperatures of 80 ° and 110°F c o r r e s p o n d i n g to subsurface depths of 3400 a n d 4500 ft respectively, are typical of those occurring towards the top of the Prairie Evaporite in Saskatchewan. A n o v e r b u r d e n stress gradient of I psi/ft depth of burial is a realistic a p p r o x i m a t i o n for subsurface depths between 34(X)--4500 ft in Saskatchewan.

363

364

M.S. KING llh PILLAIq V|IITIT,J~L. r r l l l f L ~ l • 1"-4 ~ll~lrll~ I ' • I PSI I~11 fOOT O f O I I ~ H PK.LLLR vIr wrlcAL. o.s

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Fuc. I. Extraction Talm vs depth for dilfcTcm v c r t ~ l stresses.

OmZRT [! ] developed a technique for testing model evaporite pillars malisticalty related to the mine prototype. His data has used by BRADSHAWel al. [2] successfully to predict the creep of pillars in Kansas Salt mines up to 70 years old. Lou~:NICI¢and BIumstlxw [3] extended Obert's technique to testing model salt pillars at elevated ~ and ruing the results to predict the deformation of openings in salt for the disposal of ~ e wastes. The only published quantitative information on the /n situ creep properties of Saskatchewan potash have been presented by BAItION and Toews [4], Z*tlAItY [5] and by COOt~AUGH [6]. However, the data presented in these three studies were of i ~ n t duration to draw finn conclusions on the creep hehaviour of potash. Obert's testing technique has been developed for use in the research reported here. Dimensional analysis of a material possessing a characteristic viscosity shows that, for a model pillar of the same material as its prototype and sul~ected to the same state of stress, the creep rates for model and prototype will be the same, provided the dimemions of the model are scaled directly from the prototype.

TEST PROCEDUR E In choosing the size, shape and loading of the model pillars, the following simplifying assumptions have been made. I. The behaviour of mine pillars of rectangular cross-section can be represented by that of model pillars of circular cross-s~tion. Obert indicated that this is a valid assumption, provided the diameter-to-heiBht ratio of the model pillar is eqmd to the width-to-height ratio of the mine pillar.

CREEP IN MODEL PILLARS OF SASKATCHEWAN POTASH

365

2. The behaviour of mine pillars of large volume in a crystalline material can be represented by that of very much smaller model pillars. Provided the model pillar contains at least 500 crystals, this assumption is considered justified. 3. The deadweight of the overlying strata is applied to the pillar immediately the surrounding openings are made. Because of elasticity of the overlying strata, the deadweight is in fact transferred to the pillar over a period of time. This assumption is therefore on the conservative side. Two series of tests have been performed. Results of the first series apply to the case where the evaporite formation being modelled is homogeneous. It is assumed that no discontinuities such as clay seams are present in the roof and floor. In Saskatchewan this condition applies only to certain areas. Results of the second series of tests apply to the case where clay seams are present in the t o o l and floor of the mine openings. The model pillar dimensions chosen for the two series of tests are shown in Fig. 2. The diameter-to-height ratio of 4 used in test series I and lla is the minimum suggested by Obert

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for model evaporite pillars. Since the mean crystal size of the potash used in these tests is approximately 0.3 in. there were at least 2000 crystals in each model pillar. For reasons discussed later in the paper, a diameter-to-height ratio of 8 was used in test series lib. For this series, therefore, there were at least 1000 crystals in each model pillar. The model pillars were all machined from a single block of ore, as described by KiNG and ACAR [7], with their axis of loading perpendicular to the bedding place. The cylindrical and plane surfaces of the model pillars were finished to a tolerance of +0-001 in. In the first series of tests, steel rings provided lateral constraint on the upper and lower projections adjacent to the central ground-out section which represented the rooms. This constraint

366

M.S. KING

was intended to represent the lateral stress provided by the roof and floor in the mine. The steel rings, having an internal diameter slightly larger than the specimen diameter, were epoxy-cemented in the positions illustrated in Fig. 2. The hoop strain in the steel rings was sensed by two strain gauges attached to the centreline of each ring. The lateral stress in the roof and floor was then calculated from the hoop strain. The vertical deformation of the model pillar was sensed by a pair of linear potentiometers mounted between the upper and lower steel rings. The loading system, shown diagrammatically in Fig. 3, has been described by King and Acar. This system permitted control of the axial load on the model pillars to within ~0-5 per cent over a complete test. The temperature-controlled chamber maintained a constant PRESSURE GAUGE

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FiG. 3. Hydraulicpressure system. temperature in the range 80°-i40~F within ~ 0-2°F of the set value throughout the t ~ t runs. The relative humidity within the chamber did not rise above 20 per cent during any of the tests reported here. in the second series of tests, the model pillars were loaded directly between parallel steel platens, with pairs of polythenc sheets greased in between providing friction reducers to simulate clay seams in the roof and floor. The vertical deformation was sensed by a pair of linear potcntiomctcrs mounted between the loading platens. in all the tests reported, the model pillars were first preloadcd to a vertical stress of 1000 psi for 16 hr, in order to bed down the plateHpecimen contact surfaces. DISCUSSION OF RESULTS The results ofthe first series of tests are indicated in Figs 4 and 5, which show creep curves for three axial stresses at temperatures of 80° and I IOOF.The lateral stress on the steel rings, calculated from the hoop strains measured on the rings, was in each case constant at approximately 60 per cent of the vertical stress after some 30 hr of testing. Since the vextic~ dd'ormation of the pillars was a large fraction of their initial height, natural strains were calculated for the results reported here. On logarithmic co-ordinates the natural sU*ain in the vm~Jcal direction calculated for all three stress levels is linear with time after approximate~ 200 hr testing. The creep rate therefore decreases continually with time during the test period to

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1000 hr. The slope b of the resulting relationship ~ = a T ~, in which g is the natural strain in the vertical direction, T is the time in hours and a,b are constants, is shown in Table I. The elTcct of an increase in temperature for a test at a given vertical stress is to increase the strain at a particular time. However, the value of the exponent b is seen to decrease as the natural strain at a given time increases. This tends to strengthen the conclusion that, for the range of temperatures and stresses employed for this series of tests, failure by tertiary creep is unlikely to occur on pillars of these dimensions.

M. S. KING

368

TAm.E 1 Test series

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Fro. 6. Natural grain vs time, Series ila tests: simulated clay ~ams. 5000 psi. Obviously the pillar diameter-to-height ratio of 4 was insufficient for the pillar loaded at 5000 psi, since it failed by tertiary ~ p between 4 and 6 hr after testing commenced. The creep behaviour o f the pillar loaded at 3000 psi was similar to that found for model pillars in the first series o f tests. A third model pillar o f t h e same dintensiens, subjected to a vertical stress o f 6000 psi, failed immediately it was loaded. The results o f test series lla led to increasinll the model pillar diameter-to-height ratio to 8 for the remainder o f the tests on pillars with simulated clay ==an= in the r o o f and Ik)or. The results of test series lib are shown in Fig. 7 for test temperatures o f 80° and ! rOOF. The pillar with a vertical stress o f 7000 psi at ! I0°F failed by tertiary creep within several

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minutes of loading. When considered in terms of vertical strain, the remainder o f the curves show similar creep behaviour to that shown in Figs 4 and 5 for pillars in a homogeneous material. On logarithmic co-ordinates the data again shows a continual decrease in creep rate with time during the test period to 1500 hr. The exponent b o f the resulting relationship i = a T b is shown in Table I. The results of the first series of tests can be compared with data given recently by BAAR [8] in a Saskatchewan R e . a r c h Council report for convergences in mined-out panels in a Saskatchewan potash mine. In this particular mine there are no clay seams present in the roof and floor. The results from a measuring station situation near the centre of a minedout panel arc show,1 in Fig. 8. together with those from the corresponding model pillar. It

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will be seen that the model pillar initially exhibited considerably greater vertical strain than did the mined-out panel. There are probably two reasons for this: first, whereas the full overburden deadweight was applied directly to the model pillar, it took a considerable time to be transferred entirely to the mine pillars; second, the width-to-height ratio of the mine pillars (approximately 7) was appreciably higher than that of the model pillars. Baar reported that after several years the vertical creep rates in the mined-out panels became constant at approximately 10 -+ in./day. The creep rate for the mined-out panels is shown in Fig. 9, together with those extrapolated from the corresponding model pillar tests for the two series. The creep rates predicted from these model pillar tests are very. close to the measured in situ creep rates. +"F iI

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CONCLUSIONS For pillars designed to bear the full overburden deadweight the following conclusions can be drawn: I. In the absence of clay seams in the roof and floor, a pillar width-to-height ratio of 4 or more is sufficient to preclude tertiary creep failure. 2. If clay seams occur in the roof and floor, a pillar width-to-height ratio of 8 appears to provide a similar assurance for subsurface depths presendy mined. 3. At subsurface depths presently mined, the creep behaviour of pillars in mines with clay seams present in the roofand floor will be similar to that of mines without clay seams, when the pillar width-to-height ratio is 8 in the former and 4 in the latter. Where clay seams occur in the roof and floor, a pillar width-to-height ratio of 8 provides a guide to the design of buttress pillars for multiple entry mining systems. 4. in the absence of d a y seams in the roof and floor, the increase in temperature assoc~ted with an increase in depth of mining from 341)0 to 4500 ft is expected to have approximately the same effect on creep hehaviour as an additional !000 psi vertical stress on the pillar.

CREEP IN MODEL PILLARS OF SASK-~TCHEWAN POTASH

3"~1

5. ~k'here clay seams occur in the roof and floor, the increase in temperature associated with an increase in depth of mining from 3400 to 4500 f't has a considerably greater effect than that expected in the case where no clay seams are present. Ve~" large deformations would be expected to occur under these conditions when mining by conventional means at a subsurface depth of 4500 ft. Comparison of the laboratory results with the ,,ery limited creep data available from potash mines in Saskatchewan leads to the conclusion that creep tests on model pillars can yield information of practical application to the design of pillars underground. In particular. the influence on creep behaviour of the increase in temperature associated with mining at greater depths can be studied by this means with some contidence. .4c/,m~,h'dL.,emcm's-Th,.: major support for this rcg:arch c a m e from the Sa,~katchcwan Research (_'oum:d and the Department of Energy. Mines and Resources. Ottawa. Funds from the International Minerals and Chemical Corporation (Canadal Limited and the Saskatchewan Mining Association permitted purchase and con'~truction of the equipment

REFERENCES I. ( ) a ~

r L. ('r('cp 01 Ahnl,'l Pillars. Bureau o f Mines. Report o f Invc,,ltgations 6,703 (1~)65l.

2. Iea u ) s l , ^ w R. L.. i}orta v W. J. and EM,'s,)~ F. M. Correlalion o f Convergence Mea,qtrements lit Salt Mines with Laboratory ('recp-tcst Data. Proccedines o f the Sixth Svmposhon ,m R, wk McchanicL LInivcrsity o f Missouri ~,t Rolla. pp. 501 -5 I$ (1964). 3. L,)',u xl('g T. F. and Bx,u)sH,~,w R. L. Deform:ttion o f r¢~k ,~alt in oix:nings mined for the d,',po~d of radioactive wastes. Rock Ah.ch. t, 5 3 0 (1')60). 4. ll.XRR~,~ K. and Tol.WS N. A. [)¢l'ormation ;.trotlnd a Mnt¢. Shaft in Sail. l'rocccdi.¢s o~ the Scroml ("amldi~m ,~vmposhou on R,,c£ ~h'clumics, ()ucen's tJnivcrsity, pp. I 15. 136. ( ) n a w a : Information ("anad.t 5. Z~llxav (;. R~dk M~.~halli~. ;.it International Mincr;.ll~ arid (.'heroical ('orl'~or;|tion (('~lrlad;.l) |.td, I'rocccding's" o]" the 77rffd Canadian Nrmpo.~ium on Roc£ .~h.chanh's. University of t o r o n t o , pp. I 17. ( )ttaw;t : Information Canadlt ( I ~,I(~5L 6. ('(NH IIAtl(;ll ~t. J. Special problems of mining in dccp potash. TrLIIIS. ,'lilt. [n,~'l. AIBI. l~ll(,l'~"238, 323 32') (1967). 7. KIN(; M. S. and A('.~,R K. ~. (.'rccp Prt)l~rlies of Saskatcht:wan Potash .;is a Function t)f (hallgc>, HI r,.:mr, cratur¢ and Strc,,s, Proc('cdin¢~ o f flu' Third Syml~sium on Salt, Cleveland. pp. 226 -235 (1970). 8 B,x,~x ('. A. ,.Ipplicd Rock .%h.clu#m.s in Deep Potash Mines, Saskall2h(2wan Research Council Intcrn,d Report NL). E71.'2 (1'971).