Risk of shear failure and extensional failure around over-stressed excavations in brittle rock

Abstract

The authors investigate the failure modes surrounding over-stressed tunnels in rock. Three lines of investigation are employed: failure in over-stressed three-dimensional (3D) models of tunnels bored under 3D stress, failure modes in two-dimensional (2D) numerical simulations of 1000 m and 2000 m deep tunnels using FRACOD, both in intact rock and in rock masses with one or two joint sets, and finally, observations in TBM (tunnel boring machine) tunnels in hard and medium hard massive rocks. The reason for ‘stress-induced’ failure to initiate, when the assumed maximum tangential stress is approximately (0.4–0.5)σc (UCS, uniaxial compressive strength) in massive rock, is now known to be due to exceedance of a critical extensional strain which is generated by a Poisson's ratio effect. However, because similar ‘stress/strength’ failure limits are found in mining, nuclear waste research excavations, and deep road tunnels in Norway, one is easily misled into thinking of compressive stress induced failure. Because of this, the empirical SRF (stress reduction factor in the Q-system) is set to accelerate as the estimated ratio σθmax/σc >> 0.4. In mining, similar ‘stress/strength’ ratios are used to suggest depth of break-out. The reality behind the fracture initiation stress/strength ratio of ‘0.4’ is actually because of combinations of familiar tensile and compressive strength ratios (such as 10) with Poisson's ratio (say 0.25). We exceed the extensional strain limits and start to see acoustic emission (AE) when tangential stress σθ ≈ 0.4σc, due to simple arithmetic. The combination of 2D theoretical FRACOD models and actual tunnelling suggests frequent initiation of failure by ‘stable’ extensional strain fracturing, but propagation in ‘unstable’ and therefore dynamic shearing. In the case of very deep tunnels (and 3D physical simulations), compressive stresses may be too high for extensional strain fracturing, and shearing will dominate, both ahead of the face and following the face. When shallower, the concept of ‘extensional strain initiation but propagation’ in shear is suggested. The various failure modes are richly illustrated, and the inability of conventional continuum modelling is emphasized, unless cohesion weakening and friction mobilization at different strain levels are used to reach a pseudo state of yield, but still considering a continuum.