v097n03p135

Introduction

Knowledge of rock deformation and yieldsurrounding deep level openings in hard rockis of significant interest to engineers in theSouth African mining industry. Althoughimportant progress was made in research ofthis topic over past decades, a completeunderstanding of the fracture zonedevelopment surrounding these excavationshas not yet been achieved. Commonly, elasticand elastoplastic constitutive models are usedto determine stresses and strains aroundopenings. A disadvantage of these models isthat the time factor is ignored.

As the term creep is commonly used todescribe different types of time-dependentrock behaviour, the following definitions areintroduced to avoid confusion. Creep iscontinued deformation due to a constantapplied stress and will be used exclusively inrelation to laboratory-sized specimenscontaining no large- scale discontinuities.Time-dependency is a more general term

encompassing concept like creep, rate-dependent behaviour, delayed fracturing andlong-term strength. As the rheologicalbehaviour of the rockmass underground is acomplex interrelation of these factors, it willtherefore be referred to as time-dependency.When used in relation to undergroundmeasurements, time dependency is alsounderstood to refer to deformations notrelated to geometric changes in thedimensions of an excavation. It occurs on atime scale of days to years and is thereforenot related to elastodynamic behaviour.

Creep of rocks has been studied since theearly part of this century (Griggs1) resultingin the availability of a vast amount of data.Most of the studies however focused on thesofter saltrocks because they show significantcreep under stress and temperatureconditions easily applied in the laboratory.(See Lama and Vutukuri2 and Dusseault andFordham3 for a detailed summary of creepstudies.) This paper will focus on the time-dependent behaviour of hard rocks found inSouth African gold mines. Results of thelaboratory creep of quartzite and lavaspecimens will be presented. This will becontrasted with time-dependent behaviourmeasured underground.

The need for research into time-dependent rock behaviour

Researchers (Roux and Denkhaus4;Denkhaus et al.5) recognised as early as thefifties that the time-dependent behaviour ofrock is important as it may cast light on whyrockbursts do not always occur at blastingtime but also when there is no externalinfluence which could account for changes instress distribution. Significant time-dependent deformation may also cause agradual non-violent release of abutment

135The Journal of The South African Institute of Mining and Metallurgy MAY/JUNE 1997

Time-dependent behaviour of hard rockin deep level gold minesby D.F. Malan*, U.W. Vogler*, and K. Drescher*

Synopsis

In deep level hard rock mining the rheological behaviour ofthe rock is important as time-dependent aseismic processescan lead to a stable dissipation of energy thus reducingviolent outbursts. Underground closure measurements,observations of time-dependent fracture formation andsiesmic data indicate that the rock in deep South Africangold mines shows significant time-dependent behaviour.The objective of this work is to quantify the time-dependentrock behaviour for laboratory specimens and undergroundconditions. Laboratory experiments indicated that lava andquartzite specimens undergo measurable creep strain atstress magnitudes below the failure stress. Quartzite ishowever prone to more significant creep at lower stresslevels. A viscoelastic analysis showed that laboratory creepresults can not fully explain the behaviour observedunderground. The in situ behaviour is governed mainly bythe rheological behaviour of the fracture zone and theresulting time-dependent formation of new fractures. Aviscoplastic discontinuity model implemented in a boundaryelement program is used to simulate this behaviour.

* CSIR Division of Mining Technology, P.O. Box91230, Auckland Park, 2006.

The South African Institute of Mining and Metallurgy,1996. SA ISSN 0038223X/3.00 + 0.00. Paperreceived Dec. 1996; revised paper received Apr.1997.

Time-dependent behaviour of hard rock in deep level gold mines

stress and hence diminish the danger of rockbursts.Although not directly related to hard rock, Pomeroy6carried out creep experiments on a number of coalspecimens. Anthracite samples did not creep (within thelimits of sensitivity of the equipment used) and alwaysfailed explosively. He related this to the frequentoccurrence of violent outbursts in anthracite mines.These outbursts are much less common in mines wheresignificant creep is observed in the coal. Similarly,Denkhaus et al.5 noted that the susceptibility to burstswas much more prevalent in stopes in the Central Rand,where the reef lies between hard brittle quartzite bands,than on the Far East Rand where the reef lies on ductileshale.

One strategy which may be useful in controlling thestability of the fracture zone is the rate of stope faceadvance. An appropriate time-dependent constitutivelaw could lead to some generalisations regarding safevalues of extraction rate and better control of thefracture zone. Research is being directed towardsfinding this appropriate constitutive description of hardrock in the South African mining industry.

Time-dependent rock behaviour plays a furtherimportant role in determining the long-term stability ofservice excavations and the behaviour of pillars wheredelayed fracture may lead to eventual failure. Potts andHedly7 pointed out that:

One of the most important features of a materialwhich exhibits creep characteristics is the incidence ofdelayed fracture. In mining this would imply that aroom-and-pillar area, which is stable immediately afterextraction deteriorates in time and ultimately goes tofailure.

Laboratory testing of creep in South African hardrocks

In an attempt to quantify these effects in the SouthAfrican industry, some initial studies on the time-dependent behaviour of hard rock were conducted in thesixties by the Rock Mechanics Division of the CSIRsNational Mechanical Engineering Research Institute(Wiid8; Kovcs9). These studies concentrated on thecreep of intact specimens and on long-term strengthmeasurements. Unfortunately a systematic study of thecreep of hard rock throughout the industry was neverconducted, probably due to the long duration of

individual tests and the lack of funding. The situationwas further aggravated by a school of thought whichassociated creep phenomena exclusively with soft rockslike halite and potash. The need for the time-dependenttesting of hard rock, whether for intact samples, discon-tinuities or in situ, has not always been recognised.

The following laboratory work on the time-dependent behaviour of South African hard rocks wasnevertheless conducted. Roux and Denkhaus4 publishedresults for the creep of quartzite at room temperature asshown in Figure 1. Unfortunately no information on thetype of quartzite or test methodology is available.However, what is significant is that measurable creepwas observed for the quartzite specimen. Typicalprimary and secondary creep phases can be distin-guished from Figure 1 with the primary phase lastingapproximately 2 days (See Lama and Vutukuri2 for adefinition of primary, secondary and tertiary creep). Thecreep strain rate in the secondary phase for the appliedstress of 32.9 MPa was calculated as 2.610-11 s-1.

The CSIR10 conducted further experiments onquartzites from the Hartebeestfontein mine. Thequartzite specimens were medium-grained argillaceoussamples obtained from a single borehole. The rockproperties, however, varied considerably along thelength of the borehole due to alternating argillaceousand siliceous bands in some sections. The uniaxialcompressive strength for different samples variedbetween 117 MPa and 248 MPa with an average 192MPa. Specimens were subjected to a constant uniaxialcompressive stress of 138 MPa in a deadweight testingmachine. Examples of the strain-time curves obtainedare displayed in Figure 2. It is immediately evident thatthe creep behaviour also showed appreciable differencesbetween different samples. Unfortunately no attemptwas made to analyse this behaviour quantitatively or tolink it to the geology of individual specimens. The creeprate in the secondary phase (calculated from Figure 2)varied between 1.610-8 s-1 and 110-9 s-1. Thesevalues should however be considered as approximateonly as it is difficult to determine the onset of thesecondary creep phase.

Further studies concentrated mainly on the long-term strength of rock. Bieniawski11 showed that thelong-term strength of rock under uniaxial loading canbe determined from the plot of axial stress versus

136 MAY/JUNE 1997 The Journal of The South African Institute of Mining and Metallurgy

Figure 1Creep curve for quartzite at room temperature (After Roux andDenkhaus4). The applied stress is 32.9 MPa in metric units

Figure 2Creep curves obtained for quartzite from HartebeestfonteinGoldmine (after CSIR10). The applied stress was 138 MPa

volumetric strain. The onset of unstable fracturepropagation (the point on the plot where the slopechanges from negative to positive) indicates the long-term strength. Tests on norite samples showed that thelong-term strength can be as low as 73% of the uniaxialcompressive strength. Bieniawskis hypothesis wasconfirmed by experiments conducted by Wiid8 ondolerite and sandstone. Again, the long-term strengthcould be as low as 70% of the uniaxial compressivestrength. Kovcs9 investigated the relationship betweentime to failure (tF) and applied load (t) for samples ofquartzite with L


where B, C and D are positive constants, n and m are integersrepresenting number of days and H is the Heaviside unitfunction (H(t) =1 for t 0 and 0 for t



Laboratory testing methodology

Load application principlesLaboratory creep tests on the quartzite and the lavaspecimens were performed as part of other investigationsusing different testing equipment. Full details of the testshave been reported by Vogler26 and Vogler and Drescher27.The data has however never been analysed. Thesimilarities and the differences in the testing methodologyare summarised in Table I.

Two methods of conducting laboratory creepexperiments are available namely:

Specimens are loaded to a pre-determined, constantstress level. This stress level may, for instance, bethe stress level expected around a miningexcavation. The creep strain and the time to failuremay be monitored. If, however, the aim of the testingprogramme is to fully characterise the creepbehaviour of the material or its time-dependentstrength characteristics, many tests have to beperformed at different stress levels. If the materialproperties vary considerably it may be difficult todetermine the time-dependent strength (the time tofailure for the material when loaded to a particularstress) or the long-term strength (the stress belowwhich failure will not occur). It may happen that aspecimen loaded to a certain stress level fails after afew days while another loaded to the same stresslevel does not fail after a period of months. Thiscould be the result of a stress level chosen which isjust above or below the specimens long-termstrength.

The same specimen is loaded to different stresslevels by starting at a low value and increasing thestress in steps after allowing a certain time intervalfor creep. The obvious advantage of this approach isthat the creep strain may be monitored for anidentical material at different stress levels and thateach specimen will be tested to failure within areasonable time. The total test duration isdetermined by the choice of the stress level of thefirst creep stage, the duration of each creep stageand the magnitude of subsequent stress levelincreases. A similar methodology was used byTan28.

This second approach was used for the tests describedin this paper. When performing long duration testsrequiring attention at regular intervals, it is advisable touse 24-hour creep cycles or multiples thereof. For the teston the quartzite, the duration of the creep stages was 24hours and for the lava, 72 hours.

Testing equipmentFor the tests on the quartzite, a servo-controlled Amslercompression testing machine was used. Minor fluctuationsin load (below 0.1 MPa) took place as the machine contin-uously made the necessary adjustments. Loading to eachsuccessive stress level was achieved by adjusting thesettings of the load control.

For the tests on the lava the CSIR creep testingmachine, described by Bieniawski11, was used. Thismachine makes use of deadweights and cantilevers to

maintain the desired load. Loading to the next stress levelwas done by adding further weights. For this test, eachloading step was preceded by a partial unloading step tomonitor any change in deformation modulus duringloading and unloading.

Strain measurements

Strain measurements were obtained by using straingauges and inductive transducers. The inductivetransducer measurements were used to monitor anypossible creep in the strain gauges. No noticeable creepwas observed and the strain gauge measurements, givinghigher resolution, were used for subsequent evaluations.

Due to the minor fluctuations in the load applied to thequartzites by the compression testing machine, the strainvalues measured for the creep period were corrected to aconstant stress level by using the elastic modulus for thespecimen as determined from the initial loading cycle.

Temperature

The laboratory experiments were performed at roomtemperature. The Amsler machine is housed in an openlaboratory, subject to ambient temperature variations. Thiswas in turn influenced by the heat generated by themachine. Therefore the temperature of the test specimenwas monitored throughout the experiment. For thequartzite, the experiment lasted 24 days and the minimumand maximum temperatures recorded were 20.6C and28.0C respectively.

The CSIR creep testing apparatus is installed in atemperature controlled laboratory with the temperaturemaintained at 22C.

Control specimens

Before performing the creep tests, uniaxial compressiontests were conducted to determine strength as well asdeformability characteristics for the material. This datawas necessary in order to plan the stress levels for thecreep cycles.

Number of creep stages

For the quartzite the total number of creep stages was 24.The reason for this was that the compressive strength hadbeen underestimated due to the low strength of the control

Figure 4Stress-strain curves for quartzite and lava during the creeptests



specimen. It was subsequently established that thestrength of the control specimen had been influenced by apre-existing plane of weakness. This impacted on thestress level chosen for the first creep stage as well as onthe magnitude of the subsequent load increments. Only thelast four creep stages showed significant creep. Thereforethe detailed evaluations described in the following sectionswere only done on these four creep stages.

For the lava the number of creep stages was 4.

Results for laboratory specimens: Quartzite and Lava

The complete stress-strain curves are illustrated in Figure4. Figure 5 shows the complete strain-time records whileFigures 6a and 6b show the incremental creep strain as afunction of time for the individual creep stages for thequartzite and the lava specimens respectively.

Effect of stress level on the secondary creep phase

It is well known for soft rocks that the creep rate of thesecondary phase (steady-state creep rate) depends on thestress level2. From Figures 6a and 6b, this also appears tobe true for the creep of lava and quartzite specimens. Themost widely used steady-state creep law for salt is3

[7]

where is the steady-state creep rate, A is a constant, isa principal stress, Q is the activation energy for the creepmechanism, R is the universal gas constant and T is thetemperature in degrees Kelvin. For both rock types, thetests were conducted at a constant temperature underuniaxial conditions. Equation 7 can therefore be reduced to

= A'n [8]

where

with units Pa-ns-1 and = 1 is the applied axial stress.The coefficient n can be determined from the slope of thecurve of a log() vs log()plot. Figure 7 show these graphsfor typical lava and quartzite specimens. The linear natureof the curves illustrate the applicability of equation 8 as amodel. The values of n are given in Table II.

=A AeQRT

= ( )A enQRT

1 3

Figure 5Complete strain vs time record for the quartzite and lavaspecimen during the creep tests

Figure 6aIncremental creep curves at the different stages for quartzite

Figure 6bIncremental creep curves at the different stages for lavaFigure 7Log (strain rate) versus Log (stress) for lava and quartzite.The straight lines were fitted using linear regression

Table II

Rock Maximum strain Maximum Stress Exponent nx 10-3 MPa

Lava 4.1 329 3.5Quartzite 1.9 107 9.1*Granite 1.0 344.8 3.3

(Lama and Vutukuri2)Shale 3.0 9.7 2.7

(Lama and Vutukuri2)

.

.

.

.

* See comment in text

The value of n=3.5 for the lava specimen is of thesame order as that obtained for the granite and shale. Thevalue of n=9.1 for the quartzite is however much largerand needs to be confirmed by further experiments. It ispossible that this value is too high as the time duration ofindividual loading steps for the quartzite was only 24hours. Dusseault and Fordham3 suggested that the steady-state creep rate can only be calculated after 4 to 5 days ofmeasurements at a particular stress level. For the quartzitethe strain-rate for the assumed secondary phase could stillbe artificially high due to the influence of primary creep.

Figure 8 illustrates a comparison between the strainrate of quartzite and that of lava in the secondary creepphase for different stress levels. The single datum pointfrom Roux and Denkhaus4 is also included. It is of signif-icance that the quartzite samples experience strain rateswhich are comparable to lava at less than a third of thestress levels. Mining in quartzite host rock as opposed tolava at a particular depth will lead to a more stable fracturezone extending further away from the stope. At theboundary between fractured and unfractured rock, theintact rock will undergo secondary creep leading to thetime-dependent formation of new fractures. This time-dependent process zone will extend further into the rockfor quartzite. As stable fracturing dissipates energy, thisbehaviour may be advantageous in reducing violentoutbursts. Mining of the Ventersdorp Contact Reef (lavahangingwall, quartzite footwall) in areas where the lava isparticularly hard can be problematical due to the rollingnature of the reef. In areas where the reef rolls into thefootwall, the mining is sometimes slow to follow, resultingin mining taking place entirely in the lava. The stableformation of the fracture zone could then be disruptedleading to face bursting. This phenomenon has beenobserved at mines in the Carletonville area (Handley29).

Rheological parameters for the laboratory creep oflava and quartzite

The viscoelastic rheological parameters for the laboratoryspecimens were calculated to facilitate comparison withunderground measurements. The Burgers viscoelasticmodel (Figure 9) has been used frequently to modellaboratory creep results as both the primary and secondaryphase can be simulated. Lama and Vutukuri2 derived thetime-dependent strain for the Burgers model as

[9]

tM M K

E t

Et

Ee

K

K= + +

31 3



Figure 8Strain rate of the secondary creep phase as a function ofstress for lava and quartzite

Figure 9Burgers viscoelastic model

Table III

Source EM (GPa) EK (GPa) M (GPa.h) K (GPa.h)

Quartzite 60 1400 4.5x104 900laboratory creep

Lava 88 2100 1.8x105 3800laboratory creep

Deelkraal Goldmine 147 5000 2.3x103 250in situ measurements

Figure 10bBurgers viscoelastic model fitted to the creep of lava at aconstant stress of 367 MPa

Figure 10aBurgers viscoelastic model fitted to the creep of quartziteat a constant stress of 107 MPa


where EM and EK are the Youngs moduli for the Maxwelland Kelvin units, K and M are the viscosity coefficients forthe Kelvin and Maxwell units and t is time. This model wasfitted to the data of the last creep stage for the quartzite andlava specimens. The results are illustrated in Figures 10aand 10b. The calibrated parameters are included in Table IIIfor comparison with underground data. The strain rate of thesecondary phase is determined by the viscosity coefficientM. The quartzite has a lower value of M at a much lowerstress and will therefore be prone to higher creep rates in thesecondary phase than the lava.

From the discussion in the previous section it followsthat M is not a fundamental material constant but afunction of stress and temperature, M=f(,T). To describethis dependence, the following derived model utilises theempirical creep law just described. For the Maxwell model,the steady-state strain is given as2

[10]

Inserting equation 7 and rearranging gives

[11]

As the tests were conducted at a constant temperature underuniaxial conditions, equation 11 becomes

[12]

with = 1 the applied axial stress. This equation is plottedin Figure 11 using calibrated values of n and A togetherwith the values of M obtained directly for the creep of thelava specimen at the different stress levels. The experimentalresults illustrate the clear stress dependence of the viscositycoefficient. Equation 12 gives a similar trend and appears tobe successful in describing this stress dependancy.

Time-dependent behaviour of hard rock on a miningscale

To analyse continuous closure data, Malan30 derived aBurgers viscoelastic convergence solution for a parallel-sided

panel (Appendix A1). Care should, however, be exercised inthe application of this model as it is not valid for stopeswhere total closure has taken place in the back area andwhere the geometry is such that the assumption of plainstrain is impossible.

Closure data collected from a stope with 200 m span inDeelkraal Gold Mine suited these requirements. TheVentersdorp contact reef is mined with the hangingwallconsisting of lava and the footwall of quartzite. The depth ofthe excavation was 2700m, the dip 25 degrees and theclosure instrument was installed 16,6 m from the face. Afterthe blast (one side only), the increase in span was 1,4 m.The Burgers convergence model was fitted to the data asillustrated in Figure 12. The calibrated values for the modelare given in Table III and compared with values obtained forthe laboratory creep of quartzite and lava specimens.

For the Burgers model, the instantaneous response afterload application or change is determined by the Maxwellmodulus EM. From Table III this value, calibrated for theunderground measurements, is relatively large at 147 MPaindicating that the instantaneous closure at the time of faceadvance is quite small. This is in agreement with McGarr18who provided data and an analysis illustrating that theinstantaneous closure at blasting time is small. This effect iscaused by the fractured nature of the face ahead of thestope. The stress carried by this fractured rock ahead of theface is less than would be expected for a stope where nofracturing took place. Blasting in this fracture zone results ininstantaneous redistribution of stress. This stress distri-bution is, however, smaller than expected for a completelyelastic material. When simulating this process withviscoelastic theory (which cannot model failure), thecalibrated value of EM will appear large because of thesmaller instantaneous closure behaviour.

The behaviour of the rock in the secondary phase ofcreep is described by the Maxwell viscosity M. It is clearfrom the table that this value for the in situ measurements ismore than an order of magnitude smaller for the quartzitespecimen and two orders smaller than the lava specimen.Similarly, Kranz and Estey31 found that the viscosity valuescalculated in a deep hard rock mine are two orders smallerthan those for unfractured granite slabs. There musttherefore be another mechanism dominating the time-dependent behaviour of the rockmass surrounding stopes.

Following the work of Hodgson15 and Adams andJager17 described above, the rheological properties of thefracture zone, and particularly time-dependent fractureformation, must play a prominent role in the undergroundtime-dependent behaviour. This is in agreement with otherworkers (Tan and Kang32; Schwartz and Kolluru33).Realistic modelling of the time-dependent rock behaviourtherefore needs to simulate the rheological behaviour ofdiscontinuities and the interaction between these disconti-nuities. To address this problem, Napier and Malan34developed a time-stepping solution scheme to solve multipleviscous discontinuities in a boundary element code. Thisframework was used by Malan and Spottiswoode35 toimplement a viscoplastic displacement discontinuity interfacemodel with time-dependent strength properties. This model(Appendix A2) is used in the next section to simulate thetime-dependent fracture processes surrounding a deep stope.

Mn

A=

1

3

Mn

QRTA e

=

( ) 1

1 33 .

=

3 M


Figure 11Dependence of the viscosity coefficient M on the appliedstress magnitude

.

.

Incremental mining of a tabular stope: Numericalresults

Stope modelling was undertaken by covering the problemspace by a random mesh of viscoplastic discontinuities.Figure 13 shows a typical distribution used. This distri-bution should be considered as potential fracture surfacesas they are initially intact with a prescribed strengthdetermined by the failure criteria of the model. Mining wasundertaken in an incremental fashion allowing theprogressive evolution of the fracture zone. Due to computermemory limitations, the number of elements is limited. Theobject of this modelling should therefore be seen asstudying the effect of the time-dependent fracture processand not to replicate observed fracture patterns.

Figure 14 illustrates the typical development of thefracture zone following a series of mining steps. Thediscontinuities shown are all those mobilised up to thatparticular point in time. Due to the low density of the initialtessellation, this fracture pattern is at best only a coarseapproximation of that observed underground. This isespecially notable in the immediate area of the stope faceswhere the density of fracturing is much lower than expectedfor underground stopes. The model has nevertheless provedto be useful for simulating the time-dependent processes in

the rock. An important consequence of the prescribedviscoplastic behaviour is that the additional fracturingcaused by a sudden increase in stress occurs in a time-dependent fashion. After a mining increment, the existingdiscontinuities surrounding the stope are subjected to anincrease in mining- induced stress. Those discontinuitiessubjected to stresses above the yield surface relax in a time-dependent manner according to the constitutive model. Thisrelaxation process causes a stress transfer to the solid rockat the edge of the fracture zone. New fractures then form inthese positions as a time-dependent process. For theexample given, the increase in cumulative fracture length asa function of time after a blast is illustrated in Figure 15. Itshould be emphasised that there are no changes in theexcavation dimension during this time period. Similarly toAdams and Jagers17 observations, the majority of newfractures formed within a short period after the blast, andthe rate of fracturing then diminished until the next blast. Acomparison between this numerical time-dependent fractureprocess and cumulative seismicity after blasting can befound in Malan and Spottiswoode35. A good fit wasobtained illustrating the applicability of the model.



Figure 12The Burgers convergence model fitted to undergroundmeasurements

Figure 13Initial random distribution of potential fracture planessurrounding the reef

Figure 14Development of the fracture zone 24 hours after the 9thmining increment. The stope is represented by the thick black line

Figure 15Increase in cumulative fracture length after the 9th miningincrement


The time-dependent fracture process leads to the typicalstope closure profile illustrated in Figure 16. As expectedthe highest rate of closure occurs after blasting time andthis decays until the next blast takes place. Whencomparing this with underground observations (e.g. Figure12, and Leeman14) it is clear that similar closure trends arepredicted by the model.

As mentioned in the introduction, McGarr18 investigatedthe stope closure rate throughout the week at East RandProprietary Mines (Figure 17). The closure is given duringsix-hour intervals with the value at the middle of a givensix-hour period plotted in the Figure 17. The experimentaldata have been averaged over 30 weeks. Results obtainedfrom numerical modelling illustrates similar trends. Themodel parameters used are = le-8 MPa1s1m, Sp =20MPa, Sr = 0 MPa, = 0.005 s1, = 0.005 s1, p = 30, r= 20 (See Appendix A2). The highest rate of closure occursduring the six-hour interval that includes the times of faceadvance. The rate also increases throughout the week untilSunday when no blasting takes place and the rock isallowed to relax further. There is however a weak fitbetween the experimental data and numerical results for theperiods of decreasing rate of closure after the blast. This iscaused by the low density of fracturing ahead of the faces inthe numerical model. Mining in this unfractured stressedrock results in relatively higher increase in convergence forthe period which includes the blast. The peak values of themodelling results also show some erratic behaviour becauseof the discontinuous nature of the model. As the density offractures in the tessellation is low, the rate of convergenceis still strongly influenced by the measurement position andthe orientation of the new fractures activated by eachmining step. If fractures with a favourable orientation areactivated in a particular step, higher rates of convergenceare suddenly experienced. That this erratic behaviouralmost follows the same trend as the peak values of theunderground measurements is purely accidental. Othertessellation patterns and measurement positions will givedifferent peak values for each step. Work is currentlyundertaken to increase the number of potential fractureplanes in the tessellation to alleviate this problem.

Conclusions

In deep level hard rock mining, the rheological behaviour ofthe rock is important as time-dependent aseismic processescan lead to a stable dissipation of energy reducing violentoutbursts. Underground closure measurements, observationsof time-dependent fracture formation and seismic dataindicate that the rock in deep South African gold minesshows notable time-dependent behaviour. The objective ofthis work was to quantify the time-dependent rock behaviourfor laboratory specimens and underground conditions.

Laboratory creep experiments of quartzite and lavaspecimens indicate that these rocks undergo measurablecreep strain at stress values below the failure strength. Thecreep curves illustrate the typical primary and secondarybehaviour. The strain rate in the secondary creep phase isstrongly dependent on the stress level for both rock types.This dependence can be successfully modelled with a stresspower law. The quartzite specimens are however prone tomore significant creep than the lava samples. For the type ofquartzite and lava tested, comparable creep rates areobtained if the stress in the quartzite is approximately one-third of that in lava.

The time-dependent rock behaviour observed for deeplevel stopes is much more significant than what can beexpected of the creep of intact rock. A Burgers viscoelasticmodel fitted to the creep of intact laboratory specimens andin situ closure measurements, indicates viscosity values twoorders smaller for rock on a mining scale. Observations andnumerical modelling indicate that underground behaviour isgoverned mainly by rheological behaviour of the fracturezone and the resulting time-dependent formation of newfractures. After a blast, the existing fractures surrounding thestope are subjected to an increase in mining induced stress.The fracture zone relaxes in a time-dependent fashiontransferring stress to the more solid rock. New fractures thenform in these positions as a time-dependent process. Themajority of the fractures however form within a short periodof the blast. Numerical modelling showed that this processcan be simulated by a large assembly of discontinuities eachbehaving in a viscoplastic fashion. Of significance, is that thecontinuous closure profiles observed can be simulated and


Figure 16Numerical stope closure as a function of time. Blasting tookplace at 0, 24, 48, 72 and 96 hours

Figure 17Numerical and experimental rate of closure as a function oftime. The experimental data are from East Rand Proprietary Mines(after McGarr18, see text)

therefore explained by this delayed fracture model. Almost no experimental data on the time-dependent

behaviour of fractures and other discontinuities subjected toshear is available however. Therefore, this study is currentlydirected towards a laboratory investigation to determine theapplicability of the time-dependent constitutive model andparameters for discontinuities. Further comparison withunderground observations and closure measurements is alsorequired.

Acknowledgements

This work forms part of the rockmass behaviour researchprogramme of Rock Engineering, CSIR Division of MiningTechnology. The authors acknowledge the financialassistance and support received from the Safety in MinesResearch Advisory Committee (SIMRAC). D.F. Malan isworking towards a Ph.D. degree at the University of theWitwatersrand and the work described here also forms partof that study. The authors would like to thank Dr J.A.L.Napier, Dr M.F. Handley and an anonymous referee forreviewing the manuscript and making several usefulcomments.

Appendix

A1: Burgers viscoelastic convergence solution for a tabularparallel-sided panel in isotropic ground

If it is assumed that the rock behaves elastically inhydrostatic compression and as a Burgers model (see Figure9) in distortion, Malan30 showed that the incrementalviscoelastic convergence Sz(x,t) for a stope with faceadvance of 1 at one side only can be written as

[A1]

where

[A2]

and

[A3]

[A4]

[A5]

[A6]

[A7]

[A8]

[A9]

[A10]

and

[A11]

[A12]

[A13]

[A14]

[A15]

[A16]

L = half span of the stopex = distance from the centre of the stope (origin of co-

ordinate system) = specific weight of the rock H = depth below surfacek = ratio of horizontal to vertical stress = dip of the reef = angle between x-axis and the dipK = bulk modulus

The z-axis is perpendicular to the plane of the excavationand points towards the footwall. The two-dimensional sectionis taken parallel to a plane normal to the y-axis (See FigureA1). This model is however only applicable to stopes withouttotal closure in the back area and where the geometry is suchthat the assumption of plain strain is possible.

A2: Formulation of a viscoplastic displacementdiscontinuity model

Figure A2 illustrates a discontinuity with the shearcomponent Ds and normal component Dn. Malan andSpottiswoode35 showed that if the discontinuity behaves in aviscoplastic fashion (Perzyna36 ) the incremental increase indiscontinuity components for a small timestep t, can be

dH

=

sin cos

W k kz = +( ) + ( )[ ] cos H2 1 1 2

q vE

M K

K2

1=

+( ) q M1 =

pv

E EK M

M K2

21=

+( )

pv E E E

E EK M M K M M

K M1

1=

+( ) + +( )

h Kp qKp q

=

+

+1 1

2 26

f qq

=1

2

cq q

Kp q Kp q q Kq81

22

2 2 1 1 12

26 2 2=

+( ) +( )

cq Kp q Kp q q q

b Kp q Kp q q Kq71

22 1 1 2 1 2

2 22

1 1 12

2

12 62 6 2 2

=

+( )+( ) +( )

cK p q p q q q

q Kp q q Kq62 1

21 1 2 2

2

2 1 1 12

2

22 2

=

+( )+( )

cKq

Kp q q Kq51

1 1 12

2

22 2

=

+

g Kp q q KqKq1

1 1 12

2

12

2 24

=

+

bKp q K Kp q

Kp q=

+( ) +( )+( )

6 24 64 6

1 12

2 2

2 22

F t g

c t c e c eftht

( ) =

+ + + ( )

1

5 6 712 sinh cosh bt + c bt8

S x t W dx F t

L x L x

z z,

( ) = + ( )

+

4 12

12

12

2 22 2




given as

[A17]

where is the dilation angle, ' is the discontinuityfluidity constant with units Pa-1s-1m and l assumes thevalue -1 or +1 depending on the direction of the shearstress. F is the yield function and assumes a value of 0 ifthe stresses are below the shear strength of the discon-tinuity.

When assuming a Mohr-Coulomb model, F can begiven by

F = | | Sc + n tan c [A18]where is the shear stress and Sc and c are the currentvalues of cohesion and friction angle respectively. Themobilised discontinuities can undergo a time-dependentreduction in strength (Malan and Spottiswoode35 )according to

[A19]

[A20]

where is the cohesion decay factor, is the friction decayfactor and Sr and r the residual values of cohesion andfriction angle. The time t is that accumulated for eachdiscontinuity which is loaded to within 80% or above ofthe shear strength.

References

1. GRIGGS, D. Creep of rocks. J. Geol. vol. 47, 1939. pp. 225251.

2. LAMA, R.D. and VUTUKURI, V.S. Handbook on mechanical properties of

rocksTesting techniques and results. Volume III. Trans Tech

Publications, Germany, 1978. pp. 209320.

3. DUSSEAULT, M.B. and FORDHAM, C.J. Time-dependent behavior of rocks.

Comprehensive rock engineering, vol. 3, Hudson, J.A. (ed.). Pergamon

Press, 1993, pp. 119149.

4. ROUX, A.J.A. and DENKHAUS, H.G. An investigation into the the problem of

rock bursts- An operational research project. J. Chem. Metall. Min. Soc. S.

Afr., vol. 55, 1954. pp. 103124.

5. DENKHAUS, H.G., HILL, F.G., and ROUX, A.J.A. A review of recent research

into rockbursts and strata movement in deep-level mining in South

Africa. Ass. Min. Mngrs. S. Afr., 1958. pp. 245268.

6. POMEROY, C.D. Creep in coal at room temperature. Nature. vol. 178, 1956.

pp. 279280.

7. POTTS, E.L.J. and HEDLY, D.G.F. The influence of time-dependent effects on

the design of mine pillars. Int. Bureau of Rock Mech. Proc. 6th Int. Conf.

Leipzig, 1964.

8. WIID, B.L. The time-dependent behaviour of rock: Considerations with

regard to a research programme. CSIR Report MEG 514, 1966.

9. KOVCS, I.K.A. An investigation of the time-dependent behaviour of solid

rock in uniaxial compression. CSIR Report MEG 1032, 1971.

10. Rock Mechanics Research Group, National Mechanical Engineering

Institute, CSIR. Report on the non-elastic properties of rock from borehole

number 3034 from Hartebeestfontein gold mine. CSIR Report MEG 563,

1963.

11. BIENIAWSKI, Z.T. Mechanism of brittle fracture of rockPart IIIFracture in

tension and under long term loading. Int. J. Rock Mech. Min. Sci., vol. 4,

1967. pp. 425430.

12. KING, R.G., JAGER, A.J., ROBERTS, M.K.C., and TURNER, P.A. Rock mechanics

aspects of stoping without back-area support. COMRO (Now CSIR

Miningtek) Research Report no. 17/89. 1989.

13. GRTUNCA, R.G. Results of a classified tailings monitoring programme at

Vaal Reefs. COMRO (Now CSIR Miningtek) Internal Report no. 614. 1989.

14. LEEMAN, E.R. Some measurements of closure and ride in a stope of the

East Rand Proprietary Mines. Pap. Ass. Min. Mngrs. S.Afr. vol.

19581959, 1958. pp. 385404.

15. HODGSON, K. The behaviour of the failed zone ahead of a face, as indicated

by continuous seismic and convergence measurements, C.O.M. Res. Rep.

31/61, Transvaal and Orange Free State Chamber of Mines Res. Org.

1967.

16. COOK, N.G.W., HOEK, E., PRETORIUS, J.P.G., ORTLEPP, W.D. and SALAMON,

M.D.G. Rock Mechanics applied to the study of rockbursts. J. S. Afr. Inst.

Min. Metall. vol. 66, 1966. pp. 435528.

17. ADAMS, G.R. and JAGER, A.J. Petroscopic observations of rock fracturing

ahead of stope faces in deep-level gold mines. J. S. Afr. Inst. Min. Metall.,

vol. 44, 1980. pp. 204209.

18. MCGARR, A. Stable deformation near deep-level tabular excavations

J. Geophys. Res. vol. 76, no 29, 1971, pp. 70887106.

19. MALAN, D.F. A viscoelastic approach to the modelling of the transient

closure behaviour of tabular excavations after blasting. J. S. Afr. Inst.

Min. Metall., vol. 95, 1995. pp. 211220.

20. COOK, N.G.W. Seismicity associated with mining. Eng. Geol. vol. 10, 1976.

pp. 99122.

21. MCGARR, A. Dependence of magnitude statistics on strain rate. Bull. Seism.

Soc. Am., vol. 66, no. 1, 1976. pp. 3344.

22. STEWART, R.D. and SPOTTISWOODE, S.M. A technique for determining the

seismic risk in deep-level mining. Rockbursts and Seismicity in Mines.

R. P. Young, (Ed.). 1993. pp.123128.

S S S S e

e

c r p rt

c r p rt

= + ( )= + ( )

D F tD | D tan

s

n s

=

=

l|


Figure A1Co-ordinate system used for the Burgers convergencemodel

Figure A2Components of the displacement discontinuity vector

23. VAN ASWEGEN G. and BUTLER A.G. Applications of quantitative seismologyin South African gold mines. Rockbursts and Seismicity in Mines,R.P. Young (ed.). Balkema, 1993. pp. 261266.

24. MENDECKI, A.J. Management strategies and rockburst prediction. Proc.SIMRAC/SAIMM Symposium, Johannesburg, 1996.

25. MENDECKI, A.J. Real time quantitative seimology in mines. Keynote lecture.Rockbursts and Seismicity in Mines, R.P. Young (ed.). Balkema, 1993.pp. 287295.

26. VOGLER, U.W. Creep tests on argillaceous footwall quartzite. CSIR ReportEMA-C 9052. 1990.

27. VOGLER, U.W. and DRESCHER, K. Creep tests on Ventersdorp Lava. CSIRInternal Report. In preparation. 1996.

28. TAN, T-K. The importance of creep and time-dependent dilatancy, asrevealed from case records in China. Rock testing and site characteri-sation. Comprehensive Rock Engineering, vol. 3, J.A. Hudson (ed.). 1993.pp. 709744

29. HANDLEY, M.F. Personal communication, 1996.

30. MALAN, D.F. Discussion of reference 19. A viscoelastic approach to themodelling of transient closure behaviour of tabular excavations afterblasting. J. S. Afr. Inst. Min. Metall., vol. 96, 1996. pp. 159164.

31. KRANZ, R.L. and ESTEY, L.H. Listening to a mine relax for over a year at 10

to 1000 meter scale. Proc. 2nd North Am. Rock Mech. Symp: NARMS 96,

M. Aubertin, F. Hassani and H. Mitri, (eds.). Montreal, Jun. 1996.

pp. 491498.

32. TAN, T-K. and KANG, W. Locked in stresses, creep and dilatancy of rocks,

and constitutive equations. Rock Mechanics, vol. 13, 1980. pp. 522.

33. SCHWARTZ, C.W. and KOLLURU, S. The influence of stress level on the creep

of unfilled rock joints. Proc. 25th Symp. Rock Mech. 1984.

pp. 333340.

34. NAPIER, J.A.L. and MALAN D.F. Viscoplastic modelling of rock deformation

using an explicit displacement discontinuity formulation. Submitted to Int.

J. Rock Mech. Min. Sci. & Geom. Abstr., 1996.

35. MALAN, D.F. and SPOTTISWOODE, S.M. Time-dependent fracture zone

behaviour and seismicity surrounding deep level stoping operations.

Accepted for publication in Proc. 4th Int. Symp. Rockbursts & Seismicity

in Mines, S.J. Gibowitz (eds.). Krakow, Poland, Aug. 1997.

36. PERZYNA, P. Fundamental problems in viscoplasticity. Adv. Appl. Mech.,

vol 9, 1966. pp. 243377.



New software that will assist mining engineers in the designof safer underground workings has recently been developedby the Department of Mining Engineering at the Universityof Pretoria. A workshop was held to announce the computerprogram, known as JBlock. The program evaluates thepotential for rock falls in blocky rock often encountered inmining excavations. The program calculates the effect ofdifferent types and layouts of support on potential rock falls.This enables engineers to optimise the layout of support fortheir local rock conditions.

Rock falls are a major cause of accidents in undergroundmines. The falls are often caused by natural planes ofweakness in the rock being mined. In deep mines, stressfractures may also exist in the rock, further increasing thehazard of rock falls. Rock engineers require a designmethod to realistically model the types of rock block whichare formed by the intersection of these natural and stress-induced planes of weakness. They also need a method todetermine how the supports installed in the workings willinteract with the rock blocks. This need is addressed by theprogram JBlock.

JBlock was developed by Mr Essie Esterhuizen of theDepartment of Mining Engineering. The development wasinitially supported by Samancor. The program is nowcommercially available and has aroused much interest in the

rock engineering fraternity. The workshop was attended by40 persons from different South African mining groups.

* Issued by: Mr G.S. Esterhuizen, Dept. of MiningEngineering, University of Pretoria.

New software ensures safer mine environment*

Representatives from the mining industry who attended the launch. Mr Essie Esterhuizen

is on the extreme left


Twenty-three bursaries,valued at R161 000.00, havebeen awarded by the SouthAfrican Institute of ElectricalEngineers (SAIEE) this year.This three-fold increase offunds previously set aside forbursaries has been structuredto meet future demand forelectrical engineers andtechnicians. The SAIEEsHermann Broschk (right),responsible for the Institutesbursary loan scheme and a member of its education andtraining committee, says several innovative strategies wererecently adopted. Among these are that the Institute willadminister bursaries for companies without facilities to doso themselves, and will also administer bursaries to which

small companies can collec-tively contribute and whichwill bear the names of thecontributing companies assponsors. With Broschk areHT Aspinall bursars HansZacher of the University of theWitwatersrand (left) andDaniel van Niekerk of WitsTechnikon. The HT AspinallBursary Fund is administeredby the SAIEE and givespreference to Technikon

Witwatersrand and University of the Witwatersrandstudents.

* Issued by: Lynne Hancock Communications, P.O. Box 180Witkoppen, 2068.

Revamped SAIEE bursary scheme offers more than financial help*

Colliery Dust Control (CDC) of Springs has secured a majorcoal dust suppression systems contract with Matla Colliery.

The R1,7-million contract is for provision of dust sup-pression equipment for 12 continuous minersrepresentingabout 75% of the machines deployed in the mines three shafts.

The contract involves manufacture and supply ofscrubber boxes, water-powered air movers and spray fansystems operating together as an integrated system on eachof the continuous miners.

Matla Colliery, near Kriel in Mpumalanga, is one ofIngwe Coal Corporations collieries. The order is the firstmajor order by an Ingwe group colliery for CDC equipment.

Prior to the order being placed CDC made available threescrubber boxes to Matla Colliery to use on their continuousminers to assist them in assessing their requirements.

CDCs range of dust suppression equipment forcontinuous miners is backed by a 24-hours-a-day sparesand service operation and service exchange units, enablingmines to reduce their stockholding of key componentswithout adversely affecting machine availability.

The CDC scrubber box is the most important componentin the three-in-one integrated system which the companyprovides. A major feature of the scrubber box is its small-frame water-cooled motor which assures the reliability ofthe unit and virtually eliminates the risk of motor failuredue to low inertia and minimal thermal cycling.

* Issued by: J. Kraft Public Relations, P.O. Box 28552,Kensington 2101.

Matla awards R1,7-million dust suppression contract to CDC*

v097n03p135

Documents

time dependency

timedependentrock behaviour

observations of time

time factor

ratedependent behaviour

different types of time

elastodynamic behaviour

creep of rocks