Phenomena and theoretical analysis for the failure of brittle rocks

Jourmal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (4): 331- -337Journal of Rock Mechanics and Geotechnical EngineeringJournal online: www.rockgeotech.orgPhenomena and theoretical analysis for the failure of brittle rocksFaquan Wu', Jie Wu2*, Shengwen Qi'Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China2 Engineering College, China University of Geosciences, Wuhan, 430074, ChinaAbstract: Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineeringfor more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulombtheory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena ofrockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffththeory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensilefailures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energyin the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) theunderstanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control,i.e. from keeping the reduction in initial compressive stress σ, to restricting the creation of secondary tensile stress.Key words: failure of britte rock; tensile-shear fracture; Griffith criterion; released strain energy; kinetic energysandstone with a uniaxial compressive strength (UCS)1 Introductionover 60 MPa.(3) Excavation. In the recent decades， manyRockburst, an unstable failure of brittle rocks, isunderground engineering projects are encountered withlarge scale excavations. Taking Xiaowan hydropowerfrequently encountered in ground and undergroundstation as an example, the height of cut slope at theengineering projects in Southwestern China recently,dam site reaches 680 m, and the thickness of excavatedand it has brought forward a difficulty in engineeringrock exceeds 90 m; and for Jinping I hydropowergeology and rock mechanics. The factors concernedstation at Yalong River in Sichuan Province, thewith rockbursts are commonly considered as follows:(1) High crustal stress. It is well known thatgeometry of underground powerhouse is 28.9 m inSouthwestern China is feathered with complexwidth, 73 m in height, and 277 m in length.Studies on rockburst have a long history since 7geological structure and topography. Active tectonicaccidents occurred in the gold mines of South Africa inmovement induces high crustal stress and a series of1908. After that, rockbursts happened frequently inzones are found with concentrated geological stress.deep mines in South Africa, Germany, Russia, Poland,Lots of measured in-situ stresses, σ , exceed 20 MPa,England, Chile, Canada, and United States and otherand the maximum value even reaches 57.27 MPa at thecountries/regions. The earliest record of rockburst indam site of Xiaowan hydropower station that is locatedChina is a coal burst in Shengli coal mine in Fushun,at Lancang River in Yunnan Province.(2) Hard rock. Most of key structures are hosted inNortheastern China in 1933. Since then, rockbursts inmines, diversion tunnels, highways, railways, under-hard rock, such as granite, gneiss, martble or hard thickground powerhouses， etc.， have been frequentlyreported. The most remarkable rockbursts are thoseDoi: 10.3724/5PJ.1235.2010.00331recorded in Erlangshan highway tunnel, Qinling*Corresponding author. Tel: +86- 10-82998216;E-mail: wj867 16@ hotmail.comrailway tunnel中国煤化工of Jinping IISupported by the National Natural Science Foundation of China (4 1030749),hydropower stMHCNMHGMinistry of Railways (2009G005-A) and Chinese Academy of Sciences(KZCX2-YX-109).Great progress nas been made on theoretical.Faquan Wu et al. 1 Journal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (4): 331-337researches during the past decades. A series of criteriacontrol.and evaluation methods for evaluating occurrence andintensity of rockbursts have been proposed, including2 Typical fracture phenomena ofHoekmethod,Turchaninov method,Kidybinskibrittle rocks in excavationmethod, Russense criterion, Gu method, Xu-Wangcriterion, Hou criterion, and Tao criterion, etc. [1]. .In this section, we briefly introduce some ruptureHowever, most criteria or methods are based on aphenomena of rock masses induced by excavationcommon concept， i.e. ratio of stress to strength, .during the construction of a large-scale hydropowerindicating that rockburst is formed in a compressivestation in Southwestern China.rupture mode. As a necessary condition, researchers2.1 Rupture phenomena in the dam foundationattempt to use the Coulomb theory to analyze theexcavation of Xiaowan hydropower stationcauses of the phenomena of rockbursts, to predict theXiaowan hydropower station is built on Lancangextent of damage, and to seek possible engineeringRiver in Yunnan Province. It is a double-curvature archcontrol measures. However, they have encountereddam with a height of 292 m. The maximum height ofserious theoretical difficulties. The difficulties irthe vertical excavation of foundation is 90 m. The damCoulomb theory when predicting rockburst mainlyfoundation is hosted on gneiss with a UCS of 95- -170exist in the following aspects:MPa, internal friction angle of 50° -57° and elastic .(1) The Coulomb theory is mainly used to studymodulus of 34 42 GPa. The principal stress σcompressive and shear failure. But in fact, rockburst inmeasured at slope varies from 20 to 35 MPa and thebrittle rocks often takes place when the maximummaximum value of σ at a depth of 50 m below theprincipal stress σ is far less than its UCS.bottom of valley reaches 57.37 MPa. Rock cores(2) According to the Coulomb theory, rock ruptureintensely have a rupture in the shape of thin disks.angle θ, i.e. the angle between the fracture surfaceA series of rockburst phenomena can be seen at theand σ, can be expressed asexcavation surface. Besides, there are also onion-θ=45°-号(1)peeling and some other special failure modes. Figure 1shows that the rupture angle is extremely small, evenwhere φ is the internal friction angle of rock, usuallyless than 5°.less than 60°. Therefore, the rupture angle θ shouldbe theoretically larger than 15°. Unfortunately, it canoften be as small as 3°- 5° at excavation surface, whichcan be called “blade-like failure". On the sidewall ofunderground space, this angle can even be 0°, namely,plate fracture.Jaeger and Cook [2] tried to use the Griffith theoryto explain the failure mechanism of britle materials.However, the Griffith theory has not beenappropriately used to explain the phenomenon o26.1 1.2005fracture and guide disaster control in a rock mass. Thebasic reason is that the Griffith theory has been(a) Large plate-like fractural sheets.normally thought to be only applicable to themechanism of tensile or tensile-shear fracture. It isbelieved that most rock masses are under compressiveand compressive-shear stress states, and large value oftensile stress will not be formed in rock mass becausethe discontinuities within rock mass do not have tensilestrength. In fact, that is a misunderstanding.This paper, based on Griffith theory, attempts toanalyze the fracture phenomenon of brittle rock massesduring excavation, including the small rupture angle,中国煤化工005the mechanical mechanisms and the energy process,and tries to provide a theoretical basis for rock damage1HCNMHGim u unpucement..Faquan Wu et al. / Journal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (4): 331-33733(c) A broken arch fracture.(b) Sheet cleavage at the sidewall.Fig.2 Rupture of surrounding rock at the undergroundpowerhouse of Jinping I hydropower station.2.3 Common features of excavation-induced failureof brittle rock massesFeatures of excavation -induced failure of brittle rockmasses can be seen as follows:(1) Shape of fragments. Most of the fragmentspresent the shape of knife-like flakes, sheets and arch(d) Opening of the fracture surface in holes.fractures by squeezing. The shear rupture angle can beFig.1 Rockburst phenomena at the excavation surface of damas small as39- 5°. The rupture angle for sheet cleavagefoundation of Xiaowan hydropower station.at the sidewall is reduced even to 0°. These tinyfracture angles make the failure planes almost parallel2.2 Rupture of surrounding rock masses in a large-to the excavated surface (Fig.3).scale underground powerhouseJinping 1 hydropower station is built on YalongRiver, Sichuan Province with a dam height of 305 m.Underground caverns include main powerhouse,transformer chamber and a series of tunnels. The sizeof the main powerhouse is 277 mx 73 mx 28.9 m. The .UCS of the surrounding rock, thick layered marble,varies from 50 to 129 MPa. Elastic modulus is 20- 45GPa, and internal friction angle is 45°- -56°. Thea)b)maximum initial principal stress σ around the plantFig.3 Orientation of fracture planes and its relations with theis about 35.7 MPa. Ruptures during excavation ofexcavated surface.underground spaces mainly cover the following twotypes: (1) flake fracture by extrusion at the foot of top(2) The way of movement. Apparent opening andarch or the position with a bigger curvature; and (2)shear displacement of the failure fragments reflect thesheet cleavage at the sidewall (Fig.2).features of tensile or tensile- shear movement. They canalso verify the existence of secondary tensile stressstate near the excavation surface.(3) The last type of rock damage is usually accom-panied by the fast release of the restored strain energy.3 Mechanism of failure for brittlerocks induced by excavation中国煤化工(a) Flake fracture by extrusion at the foot of top arch or the position with a3.1 The 0CCN M H Gstate duringbigger curvature.excavation.MYH.334 .Faquan Wu et al. 1 Jourmal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (4): 331-337It is commonly accepted that excavation may lead toWe can see, from Fig.5, that the rock mass will notthe occurrence of tensile stress, and it has been verifiedfail when the point (σ3，σ) is located at the rightby theoretical solutions and numerical simulations.side of the strength curve in the coordinate system ofUsually，tensile stress appears at some parts olσ and σ3. Once the stresses reach the critical state,excavated surfaces with small curvature, such as theor even cross the curve, the rock mass will be broken.sidewall of underground structures. For instance,So if the minimum principal stress in the rock mass iscalculation ilustrates that a tensile stress of 1.127 MPaσ3=-σ，whatever the value of σ| is, the rock massis induced at the straight wall in the main powerhousewill be damaged in a tensile mode; while under theof Jinping I hydropower station (Fig.4) [3]. In fact,conditionsof σ3≥-σ and 3σ, ≤σ≤8σ, the pointFigs.1 and 2 have shown a series of rupture pheno-track of (σ3,σ) can fit the curve well, and rock mass .mena, indicating the existence of tensile stress. Thiwill possibly suffer from tensile- shear failure, i.e.possibly allows us to use the Griffith theory to analyzeσ≥σ3 +4σ +4Jσ,(σ, +σ3)4)the britle fracture phenomena caused by excavation.Equation (4) infers that the rock mass can be brokenFLIC3D210under the conditionof σ1 <σ。, and σ doesn't needto have a high value because the tensile strength of theock mass is relatively lower. Taking the damfoundation of Xiaowan hydropower station as anCelm 4312example, the UCS of fresh gneiss is 168 MPa, internalfriction angle φ = 56.6*, and its tensile strength is 8.85MPa. In accordance with the brittle fracture theoryreferred above, the maximum principal stress σwhich leads to tensile-shear failure of rock, rangesfrom 26.55 to 70.8 MPa. We can imagine that, for apure tensile failure，σ can be much lower. AccordingFig.4 Elastic stress fieldround Jinpingundergroundto the Coulomb theory, σ can be written aspowerhouse (unit: Pa) [3].1+ sinφ3.2 Analysis of rock brittle fracture based on1-sinP.σ3+σ。5)Griffith theoryIt is clear that σ= 69.59 MPa at least is required(1) Failure stress conditionsfor the fracture of the rock when considering theAs we know, the Griffith theory is applicable to theoccurrence of the secondary tensile stress caused byanalysis of tensile and tensile-shear ruptures. Theexcavation, i.e. σ3≥-σ . However, such a large valuecriterion can be expressed in the form of principalof σ is almost impossible to occur near thestress (taking compression as positive):excavated surface of the dam foundation. That is whyσ=σ (3σ; +σ≤0)it is difficult to explain the failure of the rock mass(σ→σ3) =8σ{(σ1+σ3) (3σ3+σ>0) .(3)with the Coulomb theory.where σ, is the tensile strength of rock. Equations (2)(2) Rupture angleand (3) can be plotted in Fig.5.Equation (3) can be expressed in the form ofσ-τ as follows:τ2=4σ,(σ, +σ)6)(σ1-σ3) =8σ,(σ +σ;)etT=τ2-4σ,(σ, +σ)7)Failure area8cand substitute σ and τ with the functions of σ，σ=σ3σ3 and a = 90°- β, the expression of a can bederived when T obtains its peak value. The shearrupture angle， β=g-a ，can then be written asσ=σ,一follows:中国煤化工Fig.5 Diagram for the Griffth theory.β= arccos-.MYHCNMH G8).Faquan Wu et al. 1 Journal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (4): 331-33735The geometrical relationship between the ruptureenergy u。and volumetric energy u, of a unit can beangle and shear strength curve is shown in Fig.6. Inwritten asFig.6, we can see that the rupture angle decreases whenu。_1+V[(σ.-σ2)° +(σ,-σ;)° +(σ2-σ;}] (12)the normal stress on the failure plane decreases. And6Ewhen the normal stress becomes tensile, rupture angle3(1-2v)(σ, +σ2 +σ,;)°(13)is gradually reduced to 0°. This is the mechanical2Emechanism for the appearances of knife-like ruptures,where v and E are the Poisson's ratio and the elasticsheet cracks and arch cracks.modulus, respectively.r2 =4σ(σ, +σ)On the other hand, multiplying both sides of Eq.(9)with (1 + v)/(6E), we can get a criterion in a form ofdistortion strain energy as follows:1+[(σ -σ,)° +(σ-σ;) +(σ2-σ;)}]=4(1+v)j(σ, +σ, +σ,)(14)Comparing Eq.(14) with Eqs.(12) and (13), we canget4/6(1+v)√/(1-2v)Eσu(15)Fig.6 Diagram for rupture angle.where Uc is the energy for the shear fracture of a rock.Meanwhile，as a reasonable extension, we canEnergy analysis of fracture forpropose a tensile fracture energy criterion based on thebrittle rocks by excavationpyramid tensile strength surface (Eq.(10)):un=uc，u2=uc，u3=uc(16)4.1 Failure stress condition in three dimensionswhere the parameters of uu，12，U3 are the strainMurrell (1963) extended the Griffith theory to aenergy for different principal stresses; and lUce is thethree- dimensional situation [2] ascritical energy for the tensile fracture of a rock.(σ-σ)°+(σ-σj) +(σ2-σ})°=According to the elasticity theory, the tensile stress-24σ,(σ +σ2 +σ3)(9)induced strain energy can be written asThis is a paraboloid with a symmetrical axis, i.e. theline of σ=σ2=σ3. A Griffith strength curved-(17)surface can be formed by the intersection of thiswhere σ; and ε; are the tensile stress and theparaboloid and the following tensile strength planes:related strain, respectively.(σ+σ)(σ2 +σ)(σ3 +σ)=0(10)Similarly, the critical strain energy of tensile fracture,namely, planes σ1=-σ,σ2=-σ and σ3=-σUe，can be written as lue =σ /(2E). This infers thatTaking the intersection curve between Eqs.(9) andthe Griffith criterion is not only a stress criterion, but(10) for example, an ellipse can be achieved in thealso an energy criterion.planeof σ,=-σ，asSimilar to the strength criterion (Eqs.(9) and (10)),σ-σσ2+σ?-1lo,(σ +σ2)+13σ?=0(11)the energy criterion is supposed to be the combinationThe ellipse， Eq.(11)， intersects with the planeof Eqs.(14) and (16). Namely, when any of the threeσ2=-σ atthe point (5σ， -σ，-σ).principal stresses reaches the tensile fracture condition,Considering the symmetry, the coordinates of threethe strain energy aroused by stresses will meet Eq.(16),points, which are created by the intersection betweenand the failure of rock mass will take placeparaboloid and three planes of the pyramid, arepreferentially. Otherwise, the distortion strain energy(5σ，-σ，-σ)，(-σ[, 5σ，-σ)，(-σ，-σ，criterion in Eq.(14) or (15) will be used for the5σ), respectively.judgement of tensile- -shear failure of rock masses.4.2 Three-dimensional strain energy criterion ofFurther anal中国煤化Inergy criteriafailureinfers that whilCNMHGmass,σ3( 12σ for a three-dimensional condition (Eq.(9)).Secondly, based on the calculated stress field of thein the basic thinking in rockburst control, i.e. fromsurrounding rock mass, the failure criteria can be usedkeeping the reduction of initial compressive stress σ3to restricting the creation of secondary tensile stress,to determine the range of rupture.Finally, reducing the secondary tensile stress iswhich may be a much more effective way.obviously an effective way for the control of rockburst.ReferencesResearchers usually try to avoid the fracture of thesurrounding rock mass by keeping the initial stress1] Zhang Jingjian, Fu Bingjun. 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