Fatigue behaviour characteristics and life prediction of rock under low-cycle loading

Abstract

The fatigue characteristics of rock materials significantly impact the economy and safety of underground structures during construction. Hence, it is essential to conduct further investigation into the progressive damage processes of rocks under cyclic loading conditions. This research utilised both laboratory experiments and discrete element simulations to investigate how confining pressure and fatigue upper limit stress influence the mechanical behaviour and crack development of marble under low-cycle fatigue conditions. By introducing synthetic displacement and reasonable assumptions, the classical damage evolution law was updated, resulting in a fatigue life prediction formula applicable to various rock materials and loading conditions. The results indicate that lower fatigue upper limit stress can delay the accumulation of damage and extend the fatigue life of the rock, but it results in more severe ultimate failure. The damage variable’s correlation with the relative number of loading cycles for different fatigue load upper limits under the same confining pressure can be approximated by the same functional relationship. The modified damage evolution model provides an effective characterisation of this trend. The proposed fatigue life prediction method comprehensively accounts for different rock materials, confining pressures, loading frequencies, and initial damage, showing a close match with actual results.

1. Introduction

During the construction and use of underground spaces, such as tunnel excavation [1], resource extraction [2], and the storage and use of underground oil and gas reservoirs [3], rock masses are frequently exposed to cyclic loading. However, rock materials reveal significant sensitivity to stress paths. Under cyclic loading, the mechanical behaviour and failure modes differ significantly from those observed under monotonic loading conditions [4]. This unquestionably presents a significant threat to the safety of underground engineering, in addition to compromising its long-term stability and economic viability [5,6]. Consequently, undertaking further investigation into crack propagation and the associated progressive damage evolution in rock materials subjected to cyclic loading is both essential and imperative.

The fatigue behaviour of rock under cyclic loading has consistently been a prominent subject of research. Macroscopic experimental results show that the stress-strain behaviour of rock under cyclic loading demonstrates pronounced hysteresis characteristics [7]. Under cyclic loading with varying amplitudes, the secant modulus of rock initially rises before declining as loading progresses, whereas the generalised Poisson’s ratio initially exhibits a gradual increase, followed by a pronounced acceleration in growth [8]. The rock exhibits brittle failure at lower confining pressures, whereas at higher confining pressures, it transitions to ductile failure [9]. In the case of cyclic loading with fixed amplitude, Vutukuri et al. [10] identified a stress threshold for rock materials, termed the fatigue strength. When the maximum cyclic stress remains below this threshold, the rock does not fail, regardless of the number of cycles.