A reduction law for cohesive crack model in large-scale quasi-brittle fracture simulation

Large-scale fracture simulation in rock engineering is vital in understanding the real geotechnical and geological behaviors. It has become increasingly important, as an enabling technique, when some emerging fields of underground exploration are being developed, e.g., geothermal energy, underground energy storage, faults and earthquakes, etc. Finite and Discrete Element Method (FDEM) based on cohesive crack model is a widely used simulation method for rock fracture propagation due to meaningful physical parameters and reliable algorithm implementation. However, in large-scale simulations, the cohesive element size often increases with the model scale and may become larger than the characteristic length of the fracture process zone (FPZ). It will cause significant errors or inaccuracy as the damage zone is insufficiently represented. This paper establishes a reduction law for fracture simulations when using relatively large element size. The size effect law of FPZ length is proposed by D-B model and Bazant size effect law. A series of three-point bending tests with Digital Image Correlation (DIC) technique and FDEM models are carried out to obtain FPZ length results and verify the size effect law. Worked examples on large-scale three-point bending tests and compressed air energy storage in rock caverns are demonstrated. This method can provide a useful and practical tool for low-cost simulation of large-scale rock fracture and failure, while not sacrificing the accuracy.