Hitherto unknown shear rupture mechanism as a source of instability in intact hard rocks at highly confined compression

Highlights

• Physical motivation of a fan-shaped shear rupture mechanism is presented.

• It creates faults in intact rocks at shear stresses below the frictional strength.

• It makes rock failure inevitably spontaneous and violent.

• Physical and mathematical models of the mechanism are developed.

Abstract

Today, frictional shear resistance along pre-existing faults is considered to be the lower limit on rock shear strength for confined conditions corresponding to the seismogenic layer. This paper introduces a recently identified shear rupture mechanism providing a paradoxical feature of hard rocks — the possibility of shear rupture propagation through the highly confined intact rock mass at shear stress levels significantly less than frictional strength. In the new mechanism, the rock failure associated with consecutive creation of small slabs (known as ‘domino-blocks’) from the intact rock in the rupture tip is driven by a fan-shaped domino structure representing the rupture head. The fan-head combines such unique features as: extremely low shear resistance, self-sustaining stress intensification, and self-unbalancing conditions. Due to this the failure process caused by the mechanism is very dynamic and violent. This makes it impossible to directly observe and study the mechanism and can explain why the mechanism has not been detected before. This paper provides physical motivation for the mechanism, based upon side effects accompanying the failure process. Physical and mathematical models of the mechanism presented in the paper explain unique and paradoxical features of the mechanism. The new shear rupture mechanism allows a novel point of view for understanding the nature of spontaneous failure processes in hard rocks including earthquakes.

Introduction

It has been observed in field and laboratory conditions that failure of intact hard rocks at highly confined compression can be accompanied by abnormal violence. In both of these conditions the failure process is associated with shear rupture development. David Ortlepp, who acquired more than 40 years of experience in the study of shear rupture rockbursts in deep and ultra-deep South African mines, emphasised this phenomenon (Ortlepp, 1997, Ortlepp et al., 2005): “All rockbursts, by definition, involve sudden and often violent displacement of rock. Occasionally however, larger incident cause damage of such intense violence that it seems that our knowledge of the mechanism of damage is completely inadequate.” Special field studies (Gay and Ortlepp, 1979, McGarr et al., 1979) have revealed that shear ruptures causing abnormally violent rockbursts are created in intact rock (dry quartzite). An important feature is that they nucleate in zones of highly confined compression that are some distance away from excavation (close to the excavation the minor stress is low). It was shown that these mine tremors and earthquakes share the apparent paradox of having failure at low shear stresses, while laboratory measurements indicate high material strengths (McGarr et al., 1979).

Recent laboratory studies of post-peak failure of hard rocks (characterised by uniaxial compressive strength above 250 MPa) at highly confined compression (σ₁ > σ₂ = σ₃ when σ₃ > 50 MPa) support Ortlepp's idea about inadequate understanding of the failure mechanism at these loading conditions (Tarasov, 2008, Tarasov, 2010, Tarasov and Randolph, 2008, Tarasov and Randolph, 2011). Some observed abnormalities which cannot be explained on the basis of conventional approach are presented in Fig. 1, Fig. 2.

Fig. 1 shows two sets of generic stress–strain curves for different levels of confining pressure σ₃. Fig. 1a represents the conventional (well-studied) rock behaviour associated with increasing post-peak ductility with rising σ₃. To clearly show the character of variation of the post-peak curves they are indicated by dotted lines. Fig. 1b represents the unconventional type of rock behaviour. Here increasing σ₃ can lead to a contradictory variation of post-peak properties. In fact, rock behaviour can be changed from Class I to extreme Class II and then to Class I again. Class I is characterised by negative post-peak modulus M = dσ / dε, while Class II by positive (Wawersik and Fairhurst, 1970). At extreme Class II values of post-peak modulus M and elastic modulus E = dσ / dε can be very close indicating extremely small post-peak rupture energy (compare shaded areas in Fig. 1a and b for σ₃ = σ₃₍₄₎).

Small post-peak rupture energy in turn indicates high post-peak brittleness. A special brittleness index was developed to characterise unambiguously the post-peak brittleness at any type of rocks behaviour (see details in Tarasov and Potvin, 2013). The index K = dW_r / dW_e = (M − E) / M is based on the ratio between the post-peak rupture energy dW_r and elastic energy dW_e withdrawn from the material during the failure process. The index K characterises the capability of the rock for self-sustaining failure due to the elastic energy available from the failing material. Fig. 1c shows variation of the brittleness index K with rising confining pressure σ₃ for rocks exhibiting the conventional and unconventional behaviours. In contrast to the conventional behaviour where rising σ₃ is accompanied by a monotonic decrease in post-peak brittleness, the brittleness variation for unconventional behaviour follows a typical pattern of initially increasing, reaching a maximum and then ultimately decreasing. The harder the rock, the greater the effect of embrittlement. Experiments (Tarasov, 2010) showed that some rocks at high confinement became hundreds of times more brittle compared to uniaxial compression.

Fig. 2 illustrates abnormal violence of hard rock failure at extreme Class II behaviour. Experiments conducted on an extremely stiff and servo-controlled testing machine based upon the loading principles are described in Stavrogin and Tarasov (2001). Fig. 2a shows a set of stress–strain curves for dolerite (uniaxial compressive strength of 300 MPa) obtained at different levels of σ₃. At σ₃ < 60 MPa the total post-peak control was provided for both Class I and Class II behaviours. Dotted lines here indicate general orientation of post-peak curves. At σ₃ ≥ 60 MPa control was only possible at the start of the post-peak stage, after which spontaneous and violent failure took place. Dotted lines here indicate orientation of post-peak curves at the moment of instability start. In this case M is close to E, post-peak rupture energy is vanishingly small and post-peak brittleness approaches the absolute brittleness (extreme Class II). This question will be discussed in detail in section 2.4.

To demonstrate the difference in violence at spontaneous failure for Class II at low σ₃ (where post-peak control is possible) and for extreme Class II at high σ₃ (where post-peak control is impossible), some special experiments were conducted. At low σ₃ the spontaneous failure was generated at the peak stress due to the absence of post-peak servo-controlling. During failure at all levels (low and high) of σ₃ the differential stress variation with time was recorded by a load cell adjoining the tested specimens (Fig. 2b). Two different modes of rock behaviour were distinguished. Fig. 2c shows a stress–time curve typical for σ₃ < 60 MPa, while Fig. 1d shows a stress–time curve typical for σ₃ ≥ 60 MPa.

It should be emphasised that for the presented two curves obtained at σ₃ = 30 and 60 MPa the stress drop Δσ (the difference between the stress of the instability start σ_A and the residual strength σ_f) was practically the same: Δσ₍₃₀₎ = 310 MPa and Δσ₍₆₀₎ = 340 MPa. Points of instability are marked by asterisks on the stress–strain curves in Fig. 2a and stress–time curves in Figs. 2c and d. Despite the fact that elastic energy available from the specimen-loading machine is comparable for both experiments, the shape of the curves differs dramatically. For σ₃ = 30 MPa the failure was followed by a conventional stress oscillation around the residual strength. For σ₃ = 60 MPa an extraordinary post-failure stress shock was generated, after which the equilibrium condition was reached at a stress level significantly below the residual (frictional) strength σ_f. Identical stress shocks were observed in all experiments conducted at σ₃ ≥ 60 MPa (Tarasov and Randolph, 2008).

The observed features of hard rocks, such as the dramatic post-peak embrittlement with rising confining pressure σ₃; the abnormal failure violence within a certain range of σ₃; and the huge post-failure stress shock cannot be explained with the basics of common understanding of shear rupture mechanisms. This paper shows that the observed abnormalities are generated by a recently identified shear rupture mechanism (fan-mechanism) which is activated in hard rocks (uniaxial compressive strength above 250 MPa) at highly confined compression. The fan-mechanism combines such unique features as: extremely low shear resistance, self-sustaining stress intensification, and self-unbalancing conditions. Due to this the shear rupture can propagate through the medium with negligible resistance causing abnormal violence. This makes it impossible to directly observe and study the mechanism and can explain why the mechanism has not been detected before.

This paper provides physical motivation for the mechanism, based upon side effects accompanying the failure process. This mechanism can operate in small laboratory specimens and in field conditions generating shear rupture rockbursts and earthquakes. Natural faults normally have very complicated multi-hierarchical segmented structure. First we will discuss features of the fan-mechanism operation in primary ruptures (thin continuous formations) and then in complex faults. Physical and mathematical models of the mechanism presented in the paper explain unique and paradoxical features of the mechanism. The new shear rupture mechanism allows a novel point of view for understanding the nature of spontaneous failure processes, which includes earthquakes.