Size Dependence of Rock Fracture Toughness Obtained from Burst Experiments Predicted by Cohesive Zone Finite Element Simulations
Authors: Huang Y. , Bunger A. P. 
Published: September 2022

ABSTRACT:
Pressurizing a jacketed and notched borehole under confinement is a laboratory test used for the estimation of rock fracture toughness. The premise is that the fracture toughness can be calculated based on the critical burst pressure obtained by the experiments. Recent advances have shown that analysis based solely on linear elastic fracture mechanics (LEFM) can lead to misrepresentation of the fracture toughness, but that analysis using cohesive zone elements of experiments performed with varying hole sizes can allow characterization of the traction separation law for the rock. However, like all testing of the strength of rocks, it is likely these experiments exhibit size effect. The nature and possible impact of this size effect is studied here using cohesive zone finite element modeling, with rock properties calibrated to laboratory experiments for Kasota Valley Limestone. To this goal, different specimen sizes and notch lengths are simulated to generate a series of in silico experiments. Results for various specimen sizes, borehole sizes, and notch lengths show that the estimate for fracture toughness does not stabilize to a constant value with further size increase until the specimen is nearly two meters in diameter. This exceeds what is practically achievable in the laboratory. Additionally, the geometry that stabilizes in one in which detection of crack initiation is challenging. Hence, it is instead recommended to leverage this size dependence as an advantage, noting that the predicted size effect law is dependent upon cohesive zone properties. This opens the door for burst experiments with different geometries to provide a way to characterize the traction separation law for rocks under confined conditions.

1. INTRODUCTION
Rock fracture behavior in the deep underground is significant since this knowledge is widely applied across multiple domains including the oil and gas industry, mining, and geothermal energy. While some approaches are convenient and well-established for testing unconfined specimens, specialized tests are required in order to capture the impact of confining stresses. The so-called burst experiment (Abou-Sayed 1978) is one of the most popular among these specialized tests. It is a long-used technique applied to estimate the fracture toughness of rocks under confinement in the laboratory by pressurizing an internal and axially-notched borehole of a cylindrical specimen with radial confinement applied to the boundary the specimen simultaneously. As the test proceeds (following the detailed description available in Abou-Sayed, 1978), the external and internal pressure are proportionally increased, with the internal pressure typically ramping up with a slope that is six times greater than the external pressure, until a crack catastrophically grows, and a burst event occurs in the specimen that is detected in the pressure and flow rate records of the pump(s) that are controlling the internal and external applied pressures. Recently, Huang et al. (2022) proposed that, in some commonly-used geometries and loading combinations, there will be a misrepresentation of the fracture toughness for typical configurations lead by the analysis based solely on linear elastic fracture mechanics (LEFM), but the numerical analysis using cohesive zone elements can allow characterization of fracture toughness for the rock with a three parameter traction separation law for burst experiments conducted with varying borehole sizes and confining stress. The borehole size has also been demonstrated to have impact on the crack growth behavior of the burst experiments, but limited to experiments involving the same overall specimen size (Zhang 2019, Huang et al. 2022). However, other size effect also likely exists in these experiments.