https://papers.acg.uwa.eu.au/p/574_29_tarasov/ B.G. Tarasov A.V. Dyskin School of Civil an Resource Engineering The University of Western Australia The paper analyses a phenomenon of rock behaviour - the embrittlement uner the ect of confining pressure an ynamic impact. The increase in confining pressure an strain rate generally makes the post-peak behaviour of rocks more uctile. Some rocks however are capable of increasing their post-peak stiffness at a certain (critical) range of confining pressures or strain rates. There are reasons to believe that the cause of embrittlement in both cases is the same: the specific change in the failure mechanism. Within the critical range the failure localises along a single plane subsequently the failure process is characterise by relatively low energy consumption resulting in a stiff post-peak branch. Outsie the critical range the failure pattern is more isperse the process is more power-consuming which softens the post-peak branch. The paper introuces a possible mechanism of rock embrittlement an iscusses the ect of this phenomenon on the loss of stability in rockmass surrouning an unergroun excavation. It is shown that this phenomenon can cause such types of instability as burst fracture an rockburst of remote origin. 1 INTRODUCTION The paper presents results of an investigation of an abnormal rock behaviour associate with embrittlement inuce either by increase in confining pressure or ynamic loaing. This phenomenon was reporte earlier (Santarelli an Brown 1989; Stavrogin an Tarasov 2001). Increase in confining pressure an strain rate generally makes the post-peak behaviour of rocks more uctile. Some rocks however are capable of increasing their post-peak stiffness at a certain (critical) range of confining pressures or strain rates. It is reasonable to suppose that the abnormal rock embrittlement observe in laboratories can also manifest itself in rockmass conitions (Santarelli an Brown 1989; Stavrogin an Tarasov 2001). For instance in certain cases this phenomenon can initiate the loss of the excavation stability in areas where rocks with the normal behaviour are regare as stable. Therefore ignoring this phenomenon coul lea to a consierable unerestimation of the risk of rock failure. Despite the experimental iscovery of the phenomenon it is still not clear what features of rock microstructure provie such material behaviour an what the mechanism of the failure localization is. The paper aims at iscussing possible mechanisms of the embrittlement an presents some recent experimental results. These results are obtaine using a stiff triaxial static ynamic testing machine (see escription in Appenix). 2 ROCK EMBRITTLEMENT BY CONFINING PRESSURE AND THE OPENING STABILITY The olerite that has been teste belongs to the type of rock with abnormal behaviour. The results shown in Figures 1 an 2 illustrate this. At confining pressures = 0 (uniaxial compression) an 10 MPa the failure process is characterise by the evelopment of many cracks some of which are oriente along the specimen axes an some are incline (see the photograph in Figure 1). The formation of such a system of cracks requires relatively large amount of energy. Graphically the total energy absorbe by the cracks is represente by the total area uner the stressstrain curve. An important point is that the total absorbe energy here is the sum of the energy accumulate within the specimen at the peak strength an the energy aitionally supplie by the loaing system in the post-peak region. In this case the post-peak moulus M of the material is negative an the failure process is controllable by a sufficiently stiff loaing machine. At confining pressures = 30 an 50 MPa the failure mechanism is ifferent. Here the failure localises along a single shear plane. The total energy consumption associate with the formation of this plane is smaller than the amount of elastic energy accumulate within the specimen at the peak strength. Graphically this energy is represente by the area locate between pre-peak an post-peak parts of the stress-strain curve. The post-peak part of the curve in this case is characterize by the positive value of moulus M. In the present tests we manage to obtain only the initial parts of the post-peak curves espite the very high stiffness an moern servo-control of the loaing machine. The further failure process was uncontrollable an violent. The release energy in this case is emitte by both the specimen an the loaing system. Differential stress (σ 1 - ) MPa FIG. 1 M < 0 = 10 MPa = 0 Axial strain Controllable failure Stress-strain curves an failure pattern of olerite at = 0 an 10 MPa 311
Laboratory Testing an Experiments (1) Differential stress (σ 1 - ) MPa FIG. 2 = 30 MPa = 50 MPa Violent failure Axial strain M > 0 Stress-strain curves an failure pattern of olerite at = 30 an 50 MPa Figure 3 schematically illustrates the ifference in the energy reistribution in the tests iscusse above. Diagrams ABC in Figure 3(a) an (b) represent stress-strain curves for the material teste at low an high confining pressures corresponingly. (These iagrams o not take into account the variation in peak strength an resiual strength at ifferent confining pressures. They show only the ifference in the energy release cause by the change in sign of the postpeak moulus M.) Stress A a) FIG. 3 B F Strain C (D) Stress A b) C B F Strain Schematic illustration of the energy release in the tests iscusse above Assume that at low confining pressure the characteristics of stiffness for the material in the post-peak region (BC) an for the loaing system (BD) are equal. In this case the failure process in the post-peak region shoul be stable. All elastic energy accumulate at the peak strength both within the material (energy W m represente by area ABF) an within the loaing system (energy W l represente by area FBD) will be absorbe by the crack formation process. The absorbe energy W ab is represente by shae area ABC. Hence the release energy that can be transforme in ynamic forms of energy W in this case can be assume to vanish. W = W s + W l W ab = 0 [1] At high confining pressures the situation is completely ifferent. Here the failure process absorbs only a portion of elastic energy store within the material. The absorbe energy W ab correspons to shae area ABC. Elastic energy of the loaing system transforms entirely into the ynamic forms of energy. The white area CBD represents the release energy emitte from the material an the loaing system. This energy etermines the violence of the failure process. W = W s + W l W ab = area CBD [2] D For rock uner consieration the abnormal embrittlement was observe within the range of confining pressure 30 MPa 100 MPa. Outsie of this range the rock behaviour is conventional. The range of confining pressures (or minor stresses) where the rock embrittlement takes place will be calle here a critical pressure range. Experiments show that for ifferent rocks the critical pressure range can be very ifferent. The rock embrittlement inuce by confining pressure iscusse above poses a number of questions: i Which features of the rock microstructure are responsible for the embrittlement? ii What is the mechanism of failure localization? iii Can the embrittlement take place in rockmass or it is a feature of rock behaviour in the laboratory conitions? These questions can only be answere after comprehensive investigation of rocks collecte from ifferent mining areas qualifie as both hazarous an nonhazarous with respect to rockburst. Before that we can only iscuss the role of the rock embrittlement in the rockmass behaviour an in the stability of unergroun openings. However if we accept the hypothesis that the embrittlement is an intrinsic feature of some types of rock an that it can be observe in a range of scales (from specimen to rockmass) we can analyse the rockmass stability taking into account this important feature an propose some aitional explanation to specific types of rockmass behaviour. The following example illustrates this possibility. Ortlepp (1997) escribes in etail the shear rupture mechanism observe in eep mines. Many photographs presente in the book an concomitant analysis proof that the source mechanism of a major form of rockburst is the shear fracture. Ortlepp writes: The repetitive an cyclic nature of these fractures argues strongly for a process whereby mining-inuce stress increases in a zone ahea of an below the longwall face to a critical level at which failure occurs violently. This failure rives a new rapture along a more-or-less plane surface whose attitue an extent is etermine by the prevailing stress fiel. During this failure process a very large amount of energy is suenly an violently emitte from somewhere in the semi-infinite rock-space surrouning a mine to express itself as a large rockburst. In his analysis Ortlepp notes that the burst ruptures being typical for some eep mines are selom or never encountere in others. He explains this fact by features of mining circumstances an geoical nature of the rockmass surrouning the mining area. However taking into account the existence of two types of rock the first type exhibiting the normal behaviour an the secon type exhibiting the abnormal embrittlement we can look at this fact from another point of view. Figure 4 schematically illustrates a situation aroun an opening locate in rockmass exhibiting the embrittlement within a certain critical range of the values of minor stress. A qualitative iagram stress vs. istance from the opening shown in the picture inicates the critical pressure range within which the material acquires high brittleness. A shae zone (zone 2) surrouning the opening where the value of is critical represents rockmass being in the state of abnormal behaviour. This zone is locate between zone 1 an zone 3 where rock is in the normal state. If the mining-inuce stress σ 1 reaches the rock strength level within zone 2 a shear rupture will spontaneously erupt here an than propagate towars zones 1 an 3. 312
FIG. 4 Illustration of a situation aroun an opening locate in rockmass with the abnormal behaviour The shear rupture irection an its extent are etermine by the prevailing stress fiel. Three of many possibilities of the shear rupture location are shown in the picture. The evelopment of the fracture is accompanie by a relaxation of the stress concentration in this area. The very large amount of elastic energy that can be release in such events is cause by two factors: i) high rock brittleness within zone 2 an ii) position of the maximum concentration of stress σ 1 in the same zone 2. The release energy transforms in such forms of ynamic energy as ynamic movement of rockmass seismic oscillation an in some cases in kinetic energy of flying rock fragments. The phenomenon of embrittlement in rockmass can only take place below a certain critical epth. Figure 5 explains this statement. A vertical opening here is shown by otte lines. Graphs minor stress vs. istance from the opening illustrate the stress situation near the opening at ifferent epths. Shae areas on these graphs represent the critical stress range within which the rock becomes abnormally brittle. At epths where the minor stresses reach values corresponing to the critical stress range the ect of embrittlement can take place if the major stresses σ 1 initiate the failure process. Hence we can conclue that accoring to the iscusse mechanism shear rupture can be initiate in rockmass surrouning an opening if three conitions are satisfie: i) the rock exhibits embrittlement at confine conitions; ii) the minor stresses are within the critical stress range; iii) the major stress in the zone of rock embrittlement reaches the rock strength. In eep mines where these conitions are not satisfie completely the occurrence of rockburst associate with the shear rupture is unlikely. 3 ROCK EMBRITTLEMENT IN DYNAMIC LOADING Usually the increase in strain rate increases the rock strength an uctility both in pre an post-peak regions. Such change in rock properties is similar to that generally inuce by confining pressure. However some rocks exhibit abnormal behaviour in ynamic loaing associate with the ecrease in strength or embrittlement in the post-peak region. FIG. 5 Depths of rock embrittlement aroun the opening Critical epth Critical stress range Graphical estimation of the critical epth below which the abnormal rock embrittlement can take place An important point is that the same rock can show both normal an abnormal behaviour epening on the loaing conitions. Results obtaine on rock salt (Figure 6) an sanstone (Figure 7) illustrate this feature Stavrogin an Tarasov (2001). In these figures the vertical axis correspons to the shear strength τ s = (σ 1 - )/2; the horizontal axis 313
Laboratory Testing an Experiments (1) correspons to the arithm of strain rate ε* 1. Data points on each graph represent rock strength at ifferent levels of strain rate. Rock salt was teste in uniaxial compression within the total range of strain rates 10-8 10 2 s. Within the range 10-8 10-6 s the material behaviour is usual. The increase in strain rate here causes the increase in strength. At greater strain rates we can observe significant egraation of the rock strength with increasing of ε* 1. The maximum strength egraation in the iscusse range of strain rates is about 40%. Sanstone was teste in uniaxial compression an confine ( = 100 MPa) compression within the same total range of strain rates. This rock also exhibits both strength egraation an strengthening in ifferent ranges of strain rate. Unlike the rock salt the sanstone ecreases its strength at low strain rates an shows strengthening within the range of high strain rates. At confine conitions this ect is more significant an the strength egraation amounts 25%. Some rocks can exhibit abnormal behaviour at a certain level of confining pressure while at other confine conitions their behaviour is normal. Sometimes together with the increase in strength at ynamic loaing the significant embrittlement takes place in the post-peak region. Experiments show that ynamic loaing can cause the failure localization even at high confining pressures where at static conitions the material behaviour is absolutely plastic. Figure 8 illustrates this feature. Basalt specimens were teste at confining pressure = 200MPa in static (ε* 1 = 10-5 s ) an ynamic (ε* 1 = 8 s ) regimes. The static stress strain curve shows that at these conitions the material behaviour after the achievement of the yiel stress is plastic. The macroscopic irreversible eformation here occurs along many shear planes uniformly istribute within the specimen boy. The traces of these planes are seen on the specimen surface. Results obtaine in the ynamic loaing emonstrate a significant strengthening ect (about 40%) the absence of resiual strain before the peak strength an failure localization along the only plane. The material behaviour in ynamic loaing has a relatively brittle character in comparison with the static loaing. Thus rocks exhibit many types of abnormal behaviour inuce by the strain rate change. The rock strength egraation an embrittlement observe in the laboratory conitions give groun to suggest the anaous behaviour of rockmass in the fiel. In this case the ynamic pulses from explosions or other kins of ynamic events can provoke the loss of the opening stability that can exhibit itself as a rockburst of remote origin. The mechanisms of the abnormal rock behaviour in ynamic loaing are still not clear. However the anay with rock embrittlement associate with the post-peak failure localisation observe both in confine an ynamic tests suggests the similarity in failure mechanisms that take place in these two cases. On the basis of this anay we can assume that rocks exhibiting embrittlement uner the ect of confining pressure can show the same behaviour in ynamic conitions. ε* 1 s = 0 τ s 15 MPa 10 10 8 10 6 10 4 10 2 0 10 2 5 ε* 1 s FIG. 6 Shear strength τ s versus arithm of axial strain rate ε* 1 for rock salt teste at = 0 ε* 1 s = 100 MPa = 0 τ s MPa 300 200 100 10 8 10 6 10 4 10 2 0 10 2 ε* 1 s FIG. 7 Shear strength τ s versus arithm of axial strain rate ε* 1 for sanstone at = 0 an 100 MPa Dynamic Static 4 A POSSIBLE MECHANISM OF ROCK EMBRITTLEMENT The mechanism of the phenomenon of embrittlement escribe in the previous sections is obviously relate to the mechanism of post-peak softening of rocks. Shear failure observe in triaxial loaing with confining pressure below brittle-uctile transition suggests that the mechanism of post-peak softening is base on crack growth (e.g. Berry 314 FIG. 8 Stress-strain curves an failure patterns for basalt at = 200 MPa in static an ynamic regimes
1960; Cook 1965; Kemeny an Cook 1986; Dyskin et al. 1994) which must be unstable uner the peak loa (otherwise the crack growth cannot be maintaine in ecreasing stress in the post-peak region). Three issues arise with respect to this mechanism. Firstly while the unstable propagation of a crack uner uniform loaing in tension is well establishe an unerstoo the mechanism of propagation of a shear fracture still poses a challenge since as irect experiments emonstrate incline cracks in compression o not propagate in their own plane but rather kink. As a consequence neither the formation of a shear fracture nor their unstable growth at the critical loa can be explaine. Seconly the analysis unertaken uner the assumption that conitions exist that make the shear fracture propagate in its own plane shows that if the post-peak softening is cause by the growth of a single crack the latter must alreay be of a size (pre-existing or grown) comparable with the sample imensions (Berry 1960; Dyskin et al. 1994). The question is then what is the mechanism of formation of such a large crack prior to the peak given that the multiple crack growth in the post-peak region is neither observe nor possible since the first crack that starts growing brings the sample to the escening branch the corresponing stress reuction preventing the other cracks from growth. Thirly what is the mechanism of embrittlement uner the increase of the lateral pressure given that the in-plane shear crack propagation in the postpeak region can be formulate in terms of ective shear stress an strain an hence qualitatively insensitive to the lateral pressure? This section proposes a mechanism that aresses these issues. The mechanism is base on the influence of ilation in a shear crack cause by the interaction of rough surfaces Figure 9. Consier a crack with rough surfaces subjecte to an ective shear stress τ = (3) τ σ tanϕ where τ an σ n are the remote shear an normal stress acting in the crack plane ϕ is the friction angle relate to the geometry of the crack surfaces the cohesion is neglecte. FIG. 9 τ σ sh n σ il Dilation Shear an ilation of a crack with rough surfaces uner the ective shear stress (3): σ sh is the major principal stress associate with concentration of shear stress; σ il is the major principal stress associate with ilation Shearing of such a crack causes two types of tensile stress concentration at a istance from the crack tip associate with the size of non-elastic zone (Dyskin an Galybin 2001): σ sh >σ il. The conventional major principle stress σ sh woul cause kinking however further growth of the kink woul be suppresse by the ambient compression. In the situation when the out-of-plane crack growth is suppresse the only mechanism of its growth is associate with the major principle stress σ il cause by ilating crack opening. This stress prouces a straight (in-plane) crack growth. For the sake of simplicity in orer to emonstrate the main iea we express the conitions of crack growth as follows: 2 (4) τ r /π = K IIc where the crack is assume to be penny-shape of raius r an K IIc is an ective fracture toughness expresse in terms of shear stress concentration. The post-peak region prouce by such a crack is expresse through the Griffith locus Figure 10 which comprises the points at which conition (4) is satisfie. The Griffith locus is escribe by the equation relating the ective shear stress an shear strain relate to the crack plane τ γ + G π K 3 6 IIc 5 12VGτ = (5) where V is the sample volume an G is the shear moulus. The tip of the Griffith locus correspons to the minimum strain γ e : γ = G 6 1 e 5 τ e = ( 12 V ) 1/ 6 τ e K IIc π 5 (6) This point correspon to the crack size which is of the orer of the sample size τ r< r e r> r e r e 0.335V1/3 (7) γ=τ /G Griffith locus (τ e γ e r e ) FIG. 10 Griffith locus in coorinates (γ τ ) Subsequently the post-peak behaviour epens upon the size r of the crack at which criterion (4) is satisfie Figure 10: only if the crack raius is alreay quite large r>r e the postpeak branch will have negative slope which correspons to the situation shown in Figure 1 otherwise if r<r e the postpeak branch will have positive moulus which correspons to the situation shown in Figure 2. If one exclues the possibility of a large pre-existing crack in the sample (such a sample woul likely be broken on the stage of extraction or machining) the situation of r>r e is only achievable when there exist a consierable phase of stable crack growth before the peak loa is reache. If the crack growth is governe by equation (4) the only parameter that can ensure the stable crack growth is the increase in the ective fracture toughness K IIc as the crack size r increases. A possible mechanism that hampers growth of large cracks such that the fracture toughness increases with the shear crack size is its arrest on tensile microcracks intersecting its path Figure 11a. These microcracks can be forme in compressive loaing by local stress concentrators (e.g. wing cracks) or by spatial stress fluctuations (see Dyskin 1999). These cracks can be small as shown in Figure 11a or large as shown in the photograph on Figure 1. γ 315
Laboratory Testing an Experiments (1) A tensile microcrack intersecting the crack path causes its offset Figure 11b (Galybin an Dyskin 2004). This offset increases the ective fracture toughness. Now it is clear that the particular form of the post-peak behaviour epens upon the concentration of tensile microcracks. If the concentration is low the probability of intersecting the path of the ilating shear crack is low. Therefore the fracture toughness will not increase sufficiently to prevent the unstable crack growth from the very beginning an hence the post-peak branch of the Griffith locus will start at a branch with positive slope proucing the situation shown in Figure 2. Only when the concentration of the tensile microcrack is sufficiently large the frequent intersections will make the fracture toughness sufficiently increase to ensure the shear crack enlargement in a stable moe to a size exceeing r e an thus activating the Griffith locus at a negative slope. Concentration of the tensile microcracks is strongly affecte by both lateral pressure an the loaing rate. Since these microcracks are primarily oriente vertically the lateral pressure reuces their concentration by reucing the number an size of the microcracks by suppressing their growth. The concentration of the tensile microcracks can also be reuce by the increase in strain rate because at high loaing rate there is not enough time for the microcracks to evelop. Subsequently the increase in the lateral pressure or the loaing rate reuces the microcrack concentration an thus removes the stabiliser of the shear crack growth. This leas to positive slope of the post-peak branch which manifest itself as violent failure associate with embrittlement. Dilating shear crack (a) Tensile cracks Dilating shear crack Tensile crack (b) Continuation of shear crack characterise by relatively low energy consumption resulting in a stiff post-peak branch. Outsie the critical range of confining pressures or loaing rates the failure pattern is more isperse the process is more power-consuming which softens the post-peak branch. In rockmass the embrittlement can be responsible for generation of unstable shear fractures at a istance from the excavation (where the confining pressures are high) causing remote rock burst. The phenomenon of embrittlement cause by confining pressure (minor stress) in rockmass can only take place below a certain epth where the minor stresses are within the critical stress range. ACKNOWLEDGMENT The authors acknowlege the financial support through a 2004 UWA Research Grant. REFERENCES Berry J.P. (1960) Some kinetic consierations of the Griffith criterion for fracture. Parts I II. J. Mech. Phys. Solis 8 pp. 194 216. Cook N.G.W. (1965) The failure of rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 2 pp. 389 403. Dyskin A.V. (1999) On the role of stress fluctuations in brittle fracture. Intern. J. Fracture 100 pp. 29 53. Dyskin A.V. an Galybin A.N. (2001) Solutions for ilating shear cracks in elastic plane. Int J. Fracture 109 pp. 325 344. Dyskin A.V. Germanovich L.N. an Ustinov K.B. (1994) Post-peak softening of brittle geomaterials in tension. In: Computer Methos an Avances in Geomechanics. Proc. Eighth Int. Conf. of the Association for Computer Methos an Avances in Geomechanics IACMAG 1 pp. 567 573. Galybin A.N. an Dyskin A.V. (2004) Simulation of crack trajectories in materials with weak interfaces. Proc. Intern. Conference on Structural Integrity an Fracture (SIF2004) (in print). Kemeny J.M. an Cook N.G.W. (1986) Effective mouli non-linear eformation an strength of a cracke elastic soli. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 23 No. 2 pp. 107 118. Ortlepp W.D. (1997) Rock fracture an rockburst. The South African Institute of Mining an Metallurgy. Johannesburg 98 pages. Santarelli F.J. an Brown E.T. (1989) Failure of three seimentary rocks in triaxial an hollow cyliner compression test. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 26 No. 5 pp. 401 413. Stavrogin A.N. an Tarasov B.G. (2001) Experimental physics an rock mechanics. Balkema 356 pages. FIG. 11 A mechanism of size-epenent ective fracture toughness: (a) ilating shear crack arreste by tensile microcracks; (b) offset of the crack path after passing through a tensile microcrack as a mechanism of fracture toughness increase 5 CONCLUSIONS An important phenomenon that can control the stability of rockmass an remote rockbursts is the anomalous rock embrittlement inuce by confining pressure or ynamic impact when the post-peak branch of the loaing curve becomes steeper as confining pressure or loaing rate increase within a certain critical range of confining pressures or strain rates. A possible mechanism of the embrittlement is the suppression of the accumulation of wing cracks because either the confining pressure hampers their growth or they simply o not have time to grow at high loaing rates. In the absence of sufficient amounts of wing cracks the probability that they cross the path of the shear fracture is low an hence the unstable phase of the shear fracture growth can start at smaller lengths proucing in accorance with the Griffith locus steep post-peak branch. As a result the failure localises along a single plane subsequently the failure process is 316
APPENDIX Stiff Triaxial Static-Dynamic Testing Machine The experiments referre to in the paper (Figures 1 2 8) were conucte using a special loaing machine recently built an commissione at the UWA (ARC RIEF Grant 2000). The general view of the machine is shown in Figure 12. The machine provies a wie range of testing conitions incluing a high variation in confining pressure (0 200 MPa) an strain rates (10-7 - 10 +2 s ) as well as ifferent kins of cyclic loaing. High stiffness an moern servo-controlling allow stuying the rock behaviour in the post-peak region. One of the features of the machine is that the ynamic loaing can be applie at any stage of the preliminary static loaing. In aition the machine contains precise flow measuring systems in orer to measure open porosity rock permeability an to investigate the ect of fracturing on the permeability evelopment. The machine provies servo-controlling of strain or stress rate confining an pore pressure supply. Specimen sizes for the pressure cell are 36-38 mm in iameter an 76 mm in length. Uner uniaxial compression the specimen sizes can be up to 100 mm in iameter an 200 mm in length. FIG. 12 General view of the rock testing machine 317