JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 90, NO. B4, PAGES 3105-3125, MARCH 10, 1985 Compression-Induced Microcrack Growth in Brittle Solids' Axial Splittingand ShearFailure H. HORII AND S. NEMAT-NASSER Department of Civil Engineering, The Technological Institute, Northwestern University Evanston, Illinois Micromechanisms of rock failure (axial splittingand shearfailure) are examined in light of simple mathematical modelsmotivated by microscopic observations. The elasticityboundary value problem associated with cracks growing from the tips of a modelflaw is solved. It is shown that under axial compression, tensioncracks nucleateat the tips of the preexisting model flaw, grow with increasing compression, and become parallel to the directionof the maximumfar-field compression. When a lateral compression also exists, the crack growth is stableand stops at somefinite crack length. With a small lateral tension,on the other hand, the crack growth becomes unstable after a certain crack length is attained. This is considered to be the fundamentalmechanism of axial splitting observed in uniaxially compressed rock specimens. To model the mechanism of shear failure, a row of suitablyoriented model flaws is considered and the elasticity boundary value problem associated with the out-of-plane crack growth from the tips of the flaws is solved. It is shownthat for a certain overall orientationof the flaws the growth of the out-of-plane cracks may become unstable, leadingto possible macroscopic faulting. On the basisof this model the variations of the "ultimate strength"and the orientation of the overall fault plane with confining pressure are estimated, and the results are compared with published experimental data. In addition, the results of a set of model experiments on plates of Columbia resin CR39 containing preexisting flaws are reported.These experiments are specifically designed in order to show the effectof confining pressure on the crack growth regime. The experimentsseem to support qualitatively the analytical results. 1. INTRODUCTION Brittle solidssuch as rocks, by their nature, contain numer- ous flaws, cavities,inclusions, and other inhomogeneities. Ma- terials of this kind fail under axial compression by axial split- ting when the confining pressure is zero or very small and by faulting or (macroscopic) shear failure when the confining pressure is moderate but still below the brittle-ductile transi- tion value. The strength,the orientation of the macroscopic failure plane, the dilatancy, and other mechanical features are greatlyaffected by the confining pressure. Nucleation,growth, and interaction of microcracks are considered to be the domi- nant, controlling micromechanisms of macroscopic failure; see, for example, Paterson [1958, 1978], Griggs and Handin [1960], Brace [1964], Gramberg [1965], Fairhurst and Cook [1966], Mogi [1966], Scholz [1968], Friedman et al. [1970], Hoshino and Koide [1970], Wawersik and Brace [1971], Peng and Johnson [1972], Hallbauer et al. [1973], Olsson and Peng [1976], Tapponnier and Brace [1976], Holzhausen [1978], Holzhausen and Johnson [1979], Wong [1982a, b], and Kranz [1983]. For reviews and references, see Paterson [1978] and Kranz [ 1983]. Models of microcracking havebeen postulated based on the idea that frictional slidingalong preexisting cracksresults in the formation of tension cracks at the tips of the preexisting cracks,and experiments on glass and photoelasticplates have been performedto illustrate this process [Brace and Bornbol- akis, 1963; Hoek and Bieniawski, 1965; Bornbolakis, 1968]. In addition, model calculations have been made in order to quantify the microfracturing and the associated dilatancy and other macroscopic manifestations[McClintock and Walsh, 1963; Holcornb, 1978; Ingraffea and Heuze, 1980; Dey and Wang, 1981; Kachanov, 1982a, b; Moss and Gupta, 1982; Nernat-Nasser and Horii, 1982]. Copyright 1985by the AmericanGeophysical Union. Paper number 4B5089. 0148-0227/85/004B-5089505.00 Since about 1970, the use of high-resolution scanningelec- tron microscopes has produced a considerable amount of in- formation on the sources of microcracks and their growth in response to applied loads [Brace et al., 1972; $prunt and Brace, 1974; Dengler, 1976; Tapponnier and Brace, 1976; Kranz, 1979; Wong, 1982b]. It has beenobserved that isolated preexisting, Griffith-type cracks are seldom seen to be the major source of microcracking, and many sources (or stress concentrators), other than the preexisting cracks, have been identified. In Westerly granite, for example, Tapponnierand Brace [1976] report that sets of grain boundary, low-aspect ratio cavities, as well as suitably oriented interfaces of two different minerals(biotite often being involved),produce most of the microcracks. For marble, Olsson and Peng [1976] ob- serve, with the aid of optical microscopy,cracks forming at the intersections of inclined (relative to maximum axial com- pression) lamellae (or slip bands [Cottrell, 1953]) and grain boundaries. More recently, Wong [1982b] has made a detailed microscopic observation of the fracture process in Westerly granite at high pressures and temperatures. Wong confirms many early observations. In addition,he reports for prefailure loadings the presence of microcracks at high angles (15ø-45 ø) relative to the axial compression, which can slip by over- coming the frictionalresistance alongtheir surfaces. It is essential that the developmentof analytic models for microcracking be guided by these physical observations. A model of this kind is considered in section 2, and its relation to the microscopically observed deformation processes is dis- cussed. It is concludedthat although preexisting, frictional microcracks are seldom observed to be the source of micro- cracking, the shearcrack model proposed by Brace and Bom- bolakis [1963] still presents a reasonable idealization, if it is properlyinterpreted as a "microflaw" associated, for example, with a set of grain boundary cavities, a soft inclusion,a clea- vage, a slip band, or evenwith a high-angle frictional crack.A microflaw of this kind may have frictional resistance, cohesive shear resistance (due to its in-plane plastic deformation), or 3105