Abstract:  Fractures, as major storage spaces and transport channels within underground media, play a significant role in oil and gas reservoir exploration as well as in the storage and migration of carbon dioxide. Additionally, the movement and friction between subsurface fractures are closely related to geological hazards such as earthquakes and landslides. Therefore, identifying fractures and continuously monitoring their stress and movement are of substantial research significance. Compared to the classical stress-strain relationships in rock deformation, research on nonlinear elasticity in rocks demonstrates that, even under relatively small stress, the stress-strain relationship of rocks shows nonlinear characteristics due to their complex internal structure. Studying the nonlinear elastic properties of rocks will help us understand the mechanisms of small-scale structural changes within rocks under stress, thereby developing new exploration methods to improve exploration resolution rate or long-term monitoring of underground structural movements to prevent geological disasters. Fractures have a crucial impact on the nonlinear elastic characteristics of rocks. This experiment investigates the influence of cracks on nonlinear elastic characteristics using polymethyl methacrylate (PMMA) and sandstone. The PMMA material contains almost no internal microstructures and has a uniform material density distribution, giving it characteristics of approximate linear elasticity.  This  eliminates the interference of complex internal structures of  rocks on the experimental results. Sandstone, a common rock type in oil and gas reservoirs, is of significant research importance in the fields of oil and gas exploration and well logging. It contains numerous pores and fractures  internally, exhibiting obvious nonlinear elastic characteristics. Experimental results from two different materials with varying numbers of cracks confirm that cracks enhance the nonlinear elastic characteristics of solid materials. This study improves the model for cracks under normal stress by reflecting the increase and decrease of crack space under tensile and compressive strains, successfully explaining the phenomenon of periodic strain leading to the enhancement and weakening of material nonlinear elasticity.

Key words:  , nonlinear elasticity of rocks, fracture, PMMA, sandstone, reservoir, strain