Characterization and Monitoring of Damage Evolution in Brittle Rock During Primary, Secondary, and Tertiary Creep Phases
Authors: Imani M , Hedayat A , Walton G 
Published: August 2024

ABSTRACT:
Brittle creep in rocks involves the progressive degradation of mechanical properties over time; therefore, monitoring of the damage process is essential for the assessment of long-term behavior of structures in rocks. Numerous studies have explored the link between macroscopic behavior and rupture of rocks with the microscopic damage evolution of rock specimens. However, efforts to non-destructively monitor and characterize small-scale damage during brittle creep have been limited. This preliminary study focuses on evaluating damage evolution at varying levels of applied stress. Specifically, specimens of Stanstead granite were subjected to creep under uniaxial stresses of 115 and 120 MPa (approximately equivalent to 81% and 85% of the average UCS, respectively). We utilize two-dimensional digital image correlation (2D-DIC) and ultrasonic transmitted waves to characterize creep behavior and damage evolution by quantifying non-elastic strain components of minor principal and maximum shear strain obtained by 2D-DIC. The correlation between strain-based damage magnitude and transmitted waveform parameters shows the ultrasonic wave parameters (amplitude, frequency, and velocity) decreased as the small-scale damage magnitude increased during creep. Additionally, the evaluation of mean frequency shows precursor signals to the initiation of tertiary creep for all the ultrasonic image areas of both specimens.

1. INTRODUCTION
Time-dependent behavior of rocks (e.g., creep) plays a crucial role in the long-term stability of rock engineering projects such as open-pit mines, underground excavations, cut slopes, geothermal energy developments, and nuclear waste repositories (Heap et al., 2009; Zhao et al., 2019; Zhou et al., 2022). Creep is a term used to describe time-dependent deformation of materials subjected to constant loads. This phenomenon occurs through nucleation, interaction, and growth of microcracks during brittle creep and plastic deformation and dislocation motion during ductile creep (Grgic & Amitrano, 2009; Sone & Zoback, 2013; Zhao et al., 2019). Brittle creep is characterized by three stages: primary creep, secondary creep, and tertiary creep, defined based on macroscopic trends in strain over time. Over the past few decades, numerous studies have concluded that the accumulation of strain eventually leads to macroscopic failures during brittle creep, which is closely associated with smaller-scale micro-fracturing processes (Kranz, 1979; Lockner, 1993; Baud & Meredith, 1997; Imani et al., 2022; Zafar et al., 2022; Xue et al., 2023). Accordingly, many research investigations utilized various monitoring techniques such as scanning electron microscopy (SEM) (Kranz, 1979), computed tomography (CT) (Baoxian et al., 2012), acoustic emission (AE) (Ohnaka, 1983; Baud & Meredith, 1997; Zha et al., 2021; Zafar et al., 2022), ultrasonic monitoring (Ran et al., 2021; Zhou et al., 2022), and digital image correlation (DIC) (Tal et al., 2016; Zafar et al., 2022; Traore et al., 2023) to study the micro-fracturing process of brittle creep. Baud & Meredith (1997) applied different levels of constant stress on the Darley Dale sandstone to study the effect of load levels on the time-dependent brittle deformation by monitoring of axial strain, AE, and pore volume changes during creep experiments. They concluded that the onset of tertiary creep occurred at approximately the same levels of cumulative AE energy and accumulated axial strain regardless of the applied stress level. Baoxian et al. (2012) used CT to evaluate the microscopic damage evolution of coal rocks during brittle creep and showed that gradual formation of new cracks and ongoing propagation of existing major cracks dominate the failure process at later stages of creep. Zafar et al. (2022) used both AE and 2D-DIC to evaluate the evolution of damage during brittle creep of specimens with pre-existing macroscopic flaws and showed that damage during brittle creep is dominated by tensile fracturing. Zhou et al. (2022) monitored brittle creep using ultrasonic transmitted waveforms and found that wave velocity decreased as creep progressed at the given deviatoric stress.