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

Abstract

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.

An Alternative to Conventional Rock Fragmentation Methods Using SCDA: A Review

“…This frictional influence of adjacent microcolumns on the failure of rock was therefore considered by Renshaw and Schulson [95] and found a twofold lesser failure stress compared to Horii and Nemat-Nasser [93] Ashby and Hallam [97] models. However, crack growth in all of these studies has been arrested at similar crack lengths when compressive forces normal to the crack growth direction present.…”

“…Nemat-Nasser and Horii [93] conducted uniaxial compression on plates of a brittle material to investigate the behaviour of a preexisting planar crack set when it at different orientations to the major principal stress (σ1). The frictional sliding (τ) between the faces was found to produce wing cracks at crack tips, which deviate sharply from the sliding plane and continue to grow steadily towards the axis of major principal stress with increasing compressive strength (see Figure 13).…”

Numerical simulation of failed zone propagation process and anomalies related to the released energy during a compressive jog intersection

“…The vertical failure zones outside the jog, which are observed in the present numerical results, are especially similar to splitting cracks from a slip interface in the simplified model of [Ewy and Cook 1990]; see Figure 7(d). Wing fractures originating from a preexisting fracture were also observed in many experiments [Horii and Nemat-Nasser 1985;Shen et al 1995;Dyskin et al 1999;Saimoto et al 2003]. Using a displacement discontinuous method, Shen and Stephansson found that a stiff contact condition (high normal fracture stiffness and high shear fracture stiffness) produces straight wing fractures similar to the present vertical failure zones, while a noncontact condition (zero normal fracture stiffness and zero shear fracture stiffness) leads to curved wing fractures analogous to the present wing failure zones.…”

An empirical model for estimating fracture toughness using the DCDC geometry

“…1). Symmetric cracks initiated at the crown and base of the hole propagate along the axis of the specimen in the direction of the applied compression (Horii and Nemat-Nasser 1985). The test is stable when the compression required to grow the cracks increases with crack length.…”