Monitoring of Primary and Secondary Creep in Granite Using Ultrasonic Monitoring and Digital Image Correlation
Authors: Imani Mehrdad , Walton Gabriel , Moradian Omid , Hedayat Ahmadreza 
Published: September 2023

ABSTRACT
Rocks exhibit time-dependent creep behavior under constant stress conditions. This can cause damage, instability, and failure of rocks depending on the applied stress levels. Creep behavior is defined by three stages: primary (decelerating), secondary (steady-state), and tertiary (accelerating) creep. In this study, damage monitoring during primary and secondary creep was performed using synchronized optical-geophysical systems. To investigate and characterize creep behavior, an unconfined constant stress test was conducted on a prismatic intact Stanstead granite (SG) specimen. During loading, mechanical deformation and damage evolution were tracked using two-dimensional digital image correlation (2D-DIC) and active ultrasonic monitoring. The SG specimen was loaded up to a stress approximately equal to crack damage stress (CD), and this stress was held constant to allow creep to occur. To characterize damage evolution during creep, accumulated tensile and shear damage were quantitatively estimated according to non-elastic components of total apparent tensile and shear strains obtained from 2D-DIC. In addition, the evolution of strain, new crack creation, and development were investigated during creep. The transmitted ultrasonic signals were recorded at various creep stages and showed great sensitivity to the formation and growth of cracks.

INTRODUCTION
Brittle failure in rocks commonly occurs by accommodation of deformation through cracking, and it usually takes place when there are sufficient microcracks to create a distinct fracture causing failure (Bieniawski, 1967; Scholz, 1968; Heap, 2009). Among many factors affecting brittle failure in rocks (confining pressure, temperature, pore fluid characteristics, etc.), time is the least well-understood parameter (Heap, 2009; Brantut et al., 2013 Sabitova et al., 2021). For this reason, the characterization of the time-dependent behavior of brittle rocks is fundamental to understating the behavior of underground excavations, earthquake rupture processes, and geothermal energy development (Main, 2000; Frenelus et al., 2022; Shabani and Kaviani-Hamedani, 2023). Brittle creep is a term used to describe the inelastic deformation of rocks sustained under a constant stress (below the short-time strength) over a long period of time. Creep behavior is typically described by three stages: (1) primary (or decelerating) creep, (2) secondary (or steady-rate) creep, and (3) tertiary (or accelerating) creep (Kranz, 1979; Scholz, 1968; Brantut et al., 2013; Zhou et al., 2022). The first stage (primary creep) is characterized by a high initial strain rate decreasing gradually to reach a quasi-linear secondary phase, which is typically considered as a stage of steady creep. Finally, after extended loading, the tertiary phase is reached with an accelerating strain rate resulting in macroscopic failures in rock specimens (Baud and Meredith, 1997; Amitrano and Helmstetter, 2006; Fabre and Pellet, 2006). It is commonly observed that macroscopic behavior and failure of rocks are closely linked to the microscopic (grain-scale) time-dependent cracking process, and this is a key aspect to understanding the brittle creep and fracturing process (Leckie, 1986; Brantut et al., 2012; Imani et al., 2017; Zafar et al., 2022).