Compression‐induced microcrack growth in brittle solids: Axial splitting and shear failure

Micromechanisms of rock failure (axial splitting and shear failure) are examined in light of simple mathematical models motivated by microscopic observations. The elasticity boundary value problem associated with cracks growing from the tips of a model flaw is solved. It is shown that under axial compression, tension cracks nucleate at the tips of the preexisting model flaw, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. When a lateral compression also exists, the crack growth is stable and stops at some finite 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 fundamental mechanism of axial splitting observed in uniaxially compressed rock specimens. To model the mechanism of shear failure, a row of suitably oriented 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 shown that for a certain overall orientation of the flaws the growth of the out-of-plane cracks may become unstable, leading to possible macroscopic faulting. On the basis of 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 effect of confining pressure on the crack growth regime. The experiments seem to support qualitatively the analytical results.

[1]  Arvid M. Johnson,et al.  Crack growth and faulting in cylindrical specimens of chelmsford granite , 1972 .

[2]  Kevin K. Lo,et al.  Analysis of Branched Cracks , 1978 .

[3]  S. Nemat-Nasser,et al.  Compression‐induced nonplanar crack extension with application to splitting, exfoliation, and rockburst , 1982 .

[4]  G. Holzhausen.  Sheet structure in rock and some related problems in rock mechanics , 1977 .

[5]  S. Peng,et al.  Stresses within elastic circular cylinders loaded uniaxially and triaxially , 1971 .

[6]  L. Dengler.  Microcracks in Crystalline Rocks , 1976 .

[7]  S. Murrell,et al.  The Effect of Triaxial Stress Systems on the Strength of Rocks at Atmospheric Temperatures , 1965 .

[8]  Y. Gupta,et al.  A constitutive model describing dilatancy and cracking in brittle rocks , 1982 .

[9]  M. Kachanov,et al.  A microcrack model of rock inelasticity part II: Propagation of microcracks , 1982 .

[10]  Arvid M. Johnson,et al.  ANALYSES OF LONGITUDINAL SPLITTING OF UNIAXIALLY COMPRESSED ROCK CYLINDERS , 1979 .

[11]  W. Olsson,et al.  Microcrack nucleation in marble , 1976 .

[12]  W. Brace,et al.  Direct observation of microcavities in crystalline rocks , 1974 .

[13]  Peizhen Zhang,et al.  Research on the geometry of shear fracture zones , 1984 .

[14]  R. Kranz.  Microcracks in rocks: a review , 1983 .

[15]  A. Gerasoulis.  The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type , 1982 .

[16]  Sia Nemat-Nasser,et al.  Energy-Release Rate and Crack Kinking Under Combined Loading , 1981 .

[17]  Paul Tapponnier,et al.  Development of stress-induced microcracks in Westerly Granite , 1976 .

[18]  M. Paterson,et al.  EXPERIMENTAL DEFORMATION AND FAULTING IN WOMBEYAN MARBLE , 1958 .

[19]  Bhushan Lal Karihaloo,et al.  On crack kinking and curving , 1982 .

[20]  Robert E. Jackson,et al.  Porosity dependence and mechanism of brittle fracture in sandstones , 1973 .

[21]  D. Pollard,et al.  Formation and interpretation of dilatant echelon cracks , 1982 .

[22]  A. Cottrell,et al.  Dislocations and plastic flow in crystals , 1953 .

[23]  C. Fairhurst,et al.  The of Maximum Phenomenon of Rock Splitting Parallel to the Direction Compression In the Neighbourhood of a Surface , 1966 .

[24]  W. R. Wawersik,et al.  Post-failure behavior of a granite and diabase , 1971 .

[25]  W. F. Brace,et al.  A note on brittle crack growth in compression , 1963 .

[26]  S. J. Green,et al.  Observation of brittle-deformation features at the maximum stress of westerly granite and solenhofen limestone , 1970 .

[27]  R. Kranz,et al.  Crack-crack and crack-pore interactions in stressed granite , 1979 .

[28]  A. Ingraffea,et al.  FINITE ELEMENT MODELS FOR ROCK FRACTURE MECHANICS , 1980 .

[29]  C. H. Scholz,et al.  Experimental study of the fracturing process in brittle rock , 1968 .

[30]  N. Cook,et al.  Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests , 1973 .

[31]  E. G. Bombolakis.  Photoelastic study of initial stages of brittle fracture in compression , 1968 .

[32]  J. Gramberg,et al.  The axial cleavage fracture 1 Axial cleavage fracturing, a significant process in mining and geology , 1965 .

[33]  Paul Segall,et al.  Mechanics of discontinuous faults , 1980 .

[34]  Z. T. Bieniawski,et al.  Brittle fracture propagation in rock under compression , 1965 .

[35]  D. Holcomb.  A quantitative model of dilatancy in dry rock and its application to westerly granite , 1978 .

[36]  R. Martin,et al.  The effect of dilatancy on velocity anisotropy in Westerly granite , 1978 .

[37]  Hsi-Ping Liu,et al.  Dilatancy and precursory bulging along incipient fracture zones in uniaxially compressed westerly granite , 1976 .

[38]  Chi‐yuen Wang,et al.  SOME MECHANISMS OF MICROCRACK GROWTH AND INTERACTION IN COMPRESSIVE ROCK FAILURE , 1981 .

[39]  W. G. Knauss,et al.  II – On the Problem of Crack Extension in Brittle Solids Under General Loading , 1978 .

[40]  J. C. Jaeger.  Brittle Fracture Of Rocks , 1966 .

[41]  Chien H. Wu.  Elasticity problems of a slender Z-crack , 1978 .

[42]  Teng-fong Wong,et al.  MICROMECHANICS OF FAULTING IN WESTERLY GRANITE , 1982 .

[43]  Kiyoo Mogi,et al.  Pressure Dependence of Rock Strength and Transition from Brittle Fracture to Ductile Flow. , 1966 .

[44]  M. Kachanov,et al.  A microcrack model of rock inelasticity part I: Frictional sliding on microcracks , 1982 .

[45]  J. Handin,et al.  Chapter 13: Observations on Fracture and a Hypothesis of Earthquakes , 1960 .

[46]  Teng-fong Wong,et al.  Effects of temperature and pressure on failure and post-failure behavior of Westerly granite , 1982 .

[47]  E. Silver,et al.  Cracks and Pores: A Closer Look , 1972, Science.

[48]  J. Rice,et al.  Slightly curved or kinked cracks , 1980 .