Effect of σ2 on All Aspects of Failure in Rocks from Granite to Sandstone

Abstract:

We have studied the effect of σ₂ on failure characteristics of two crystalline and three clastic rocks subjected to true triaxial stresses. Common to all rocks tested is the rise in both strain localization onset and σ₁ at failure (σ_1,peak) for a given σ₃, as σ₂ is elevated beyond its base level (σ₂ = σ₃). σ_1,peak reaches a maximum at some level of σ₂, beyond which it gradually declines, approaching its base magnitude when σ₂ nears its own maximum. Failure-plane angle with respect to σ₁ for a given σ₃ also increases with σ₂, at least until the maximum σ_1,peak is reached.

Westerly granite (Haimson and Chang, IJRMMS, 2000) and KTB amphibolite (Chang and Haimson, JGR, 2000), exhibited a dramatic σ₂ effect: at low σ₃ (20-30 MPa)_, higher σ₂ lifted σ_1,peak by up to 50% over its base level. At high σ₃, the increase in σ_1,peak was reduced, but even at σ₃ = 100 MPa, maximum σ_1,peak in both rocks was over 20% higher than its base level. Failure mode remained brittle throughout the stress range tested, but the onset of dilatancy rose with σ₂, as did the failure-plane (shear-band) angle (by up to 20°).

A gentler effect of σ₂ on σ_{1, peak} and failure-plane angle was observed in the clastics, and that effect subsided as porosity increased. In low porosity (φ = 7%) TCDP siltstone (Oku, et al, GRL, 2007), the maximum σ_1,peak at σ₃ = 25 MPa was about 30% larger than at σ₂ = σ₃ level, and only 12.5% larger at σ₃ = 100 MPa. Failure mode stayed brittle throughout, but shear-band angle increase with σ₂ was limited to about 10°, irrespective of σ₃ level. An even smaller σ₂ effect was observed in Coconino sandstone (φ = 17%) (Ma, PhD thesis, 2014). σ_1,peak reached a maximum of about 10% higher than at σ₂ = σ₃ level; failure-plane angle rise with σ₂ was less than 10°. The weakest σ₂ effect was found in the high porosity (φ= 25%) Bentheim sandstone (Ma, PhD thesis, 2014). Here σ_{1, peak} reached a maximum of well under 10% higher than its base magnitude, regardless of σ₃ level; average failure-plane angle rise with σ₂ was below 10°. Failure at σ₃ = 150 MPa was along a compaction band(s) normal to σ₁, regardless of σ₂. Both Coconino and Bentheim underwent dilatant failure at low σ₃, shifting to compactive failure at high σ₃ levels. But σ₂ also affected the failure mode: compactive failure at σ₂ = σ₃ gradually reverted to a dilatant mode as σ₂ was raised.