Numerical modelling of intact and flawed rocks : effects of specimen size, stress, rate, and temperature

Abstract

In geological engineering, it is essential to assess the strength and failure behavior of rock masses, which consist of intact rock blocks separated by natural discontinuities. These underground rock masses are usually subjected to a true triaxial stress state and quasi-static loading ranging from 1e−7/s to 1e−3/s. Besides, rock masses in deep geological disposal can experience long-term heating up to 400°C by radioactive waste under sustained loading. These influences may lead to crack growth and rock weakening, which have long been studied indirectly through laboratory-scale tests on intact and flawed rocks. However, conducting laboratory tests under true triaxial compression, very low strain rates, or long-term heating with temperatures exceeding 200°C can be challenging. Alternatively, this research selects a continuum method, double-phase-field method (DPF), and a discontinuum method, discrete element method (DEM), to investigate the interplay of effects of stress, time, and temperature on rock masses. The research begins by investigating size effects on flawed crystalline rocks to bridge observations of fracturing processes across scales. A grain-based model in DEM is selected to reproduce the mineral microstructure and perform compression tests on geometrically similar flawed specimens, varying from 0.5 to 3 times the laboratory standard specimen. Strength decreases with increasing sizes, and the micro-mechanism is attributed to the increased likelihood of including more inter-grain cracking paths in larger specimens. Further work investigated size effects from a macroscopic perspective based on DPF. As the size increases, the softening behavior within fracture process zone becomes less evident. Corresponding cracking patterns also change from those observed in quasi-brittle rocks to those in highly brittle materials and the strength size effect qualitatively resembles Bažant’s size effect law. The research then investigated the effects of intermediate principal stress σ2 on cracking behavior of flawed specimens using DPF. σ2 loading direction exerts more control over the cracking pattern than the flaw inclination angle. The peak stress becomes lowest when σ2 is parallel to the flaw. Also, the effects of σ2 magnitude are more significant when σ2 becomes more oblique to the flaw plane. By incorporating a stress corrosion model in DEM, the research investigated the micro-mechanisms of rock rate dependency with strain rates ranging from 1e−7/s to 1e−3/s. Stress corrosion is the unify mechanism for creep behavior and rate dependency of rocks. The uniaxial compressive and direct tensile strength increase with rate as fewer subcritical cracks propagate due to the shorter stress-corrosion reaction time. Triaxial compressive strength is less rate-dependent because subcritical crack growth is suppressed at higher pressures. Finally, the research investigated thermal effects on rocks by considering thermal grain expansion in short term and temperature-dependent stress corrosion in long term. As the temperature increases, the strength first increases due to compacted microstructures. However, after 200°C, the strength decreases due to increased thermal-induced cracks. Besides, the time-to-failure decreases by 2-3 orders of magnitude and stress thresholds decrease significantly from 70% to 44% of UCS with increasing temperature. This comprehensive study suggests significant strength reduction under the influence of size, stress, rate, and temperature.