Particulate DEM Simulation of Thermal Effect on Fracture Toughness of Rock

This study relates to thermal effect on fracture toughness of rock. Fracture toughness is a parameter of geo-materials that describes its ability to resist fracturing. This parameter is fundamentally important to rock and reservoir engineering applications, for example hydraulic fracturing for geothermal energy, oil and gas extractions (especially in the tight and low permeable formations), as well as wellbore stability assessment.

Although fracture toughness is often deemed as an intrinsic property of rock, it still can with factors including geological anisotropy (e.g., Chandler, 2016), temperature and confinement (e.g., Funatsu et al., 2014), experimental setup and loading conditions (e.g., Shang et al., 2018a). Chong and Kuruppu (1987) experimentally investigated the fracture behvaiour of layered oil shale, where semi-circular bend (SCB) specimens (later suggested by ISRM) containing different proportions of organic matter were prepared. It was found that organic-rich shale specimens had a higher fracture toughness than leaner specimens. Chandler et al. (2016) reported fracture toughness measurements on Mancos shale in three principal crack orientations (i.e., arrester, divider and short-transverse) using a short-rod method, and found that fracture toughness of the divider oriented specimens was much higher (increased by a factor of 3.4) than that measured using the short-transverse oriented specimens. Temperature can be another important factor that affects fracture toughness of rock, especially in the deep underground. It is well accepted that fracture toughness of a rock material can increase under elevated temperatures until it reaches an elasto-plastic transition phase (Mahanta, 2016), after which a decrease in fracture toughness can be seen. The transition phase is rock type- and temperature-dependent, which is probably due to the variations in mineral composition leading to various thermal dilations, as well as due to mineral grain interactions at microscale. This paper reports a particulate DEM study on the thermal influence on mixed-mode fracture toughness of a clay-rich sandstone, where a fully coupled thermal-mechanical model was used.

In the study, a series of semi-circular bend (SCB) specimens with the ISRM-suggested dimensions were numerically manufactured using the Particle Flow Code (PFC) to measure the fracture toughness of rock under elevated temperatures (up to 600°C). Fig.1 shows a representative numerical sample used in the study, where main minerals in the Midgley Grit Sandstone (MGS, Shang, 2016) were differentiated by assigning particles with different thermal expansion coefficients (i.e. quartz, 24.3×10⁻⁶K⁻¹; feldspar, 8.7×10⁻⁶K⁻¹; biotite, 1.0×10⁻⁶K⁻¹; clay, 3.6×10⁻⁶K⁻¹) (Fei, 1995; Zhao, 2016). Thermal strains can be produced in the sample by accounting for the thermal expansion of the particles as well as the bonds which act as thermal pipes (only apply to parallel bond). Specific heat of each particle and thermal expansion per unit length were 1.0e³ J/kg°C and 0.3°C/Wm, respectively. The DEM samples used in the study were first heated to desired temperatures up to 600°C, followed by three-point bending tests (without cooling phase) as shown in Fig. 1. It is worthwhile mentioning that a group of particles (green particles in Fig. 1) contacting the loading bar and the two supporting bars was generated and these particles were not heated (thus, no thermal expansion) so as to eliminate stress concertation which can be due to the different contact conditions arising from different expansion coefficients of the particles. Sample dimensions are shown in Fig. 1, in which sample radius R (50 mm), span length 2s (55 mm), thickness t (30 mm), and crack length a (25 mm) are constants, and the crack angle β varied from 0° to 46° to allow a complete modes of fracture toughness to be measured (Shang et al. 2018a). Table 1 shows the micro-parameters used in the study which have been calibrated by Shang et al. (2017).