Simulating time-dependent rockfall initiation by progressive sub-critical crack growth

Progressive brittle fracture plays an important role in rockfall initiation. Although the magnitude of in situ stress near the surface of a slope may be low relative to the strength of intact rock, gravitational stresses become concentrated near the tips of pre-existing discontinuities, promoting the slow process of subcritical crack growth. Over time, subcritical crack propagation reduces the size of intact rock bridges that interrupt an incipient failure surface, increasing the stress intensity at the advancing crack front. Eventually the stress intensity reaches a critical threshold where the fracture toughness of intact rock is exceeded, causing a rapid acceleration of crack growth and sudden failure.

This paper demonstrates a modified fracture mechanics model for time-dependent subcritical crack growth, applied using the bonded block discrete element method. A series of conceptual numerical models are developed based on the geological environment of Blue Mountains National Park in New South Wales, where the Triassic sandstone formations of the Narrabeen Group outcrop in cliffs up to 200 m high. The landscape of the Blue Mountains has been shaped by stream incision and escarpment retreat processes that now are dominated by gravity-driven slope failures, including rockfalls that vary in magnitude from discrete minor block falls up to rock mass scale cliff collapse events. This investigation first explores a simplified model for progressive failure of an overhanging sandstone slab, driven by time-dependent propagation of a vertical rear release joint. The methodology is then extended to consider collapse of a sandstone cliff by undermining failure of a weaker underlying shale layer. The models demonstrate how the time required for rockfall initiation varies depending on the geometry and persistence of pre-existing discontinuities and the intact rock bridges that must fail for an incipient rockfall block to detach. When combined with empirical methods for estimating rockfall magnitude-frequency relationships, the proposed methodology can help to improve the temporal estimates of rockfall probability that form a critical input to rockfall risk assessment.