Investigation on the evaluation method and influencing factors of cross-scale mechanical properties of shale based on indentation experiment

Low-cost, fast and accurate acquisition of multi-scale mechanical properties of shale is essential to realize the complex hydraulic fracture network and the optimization of multi-scale fracture efficiency of bottom hole rock. The macro-scale indentation test is used to study the mechanical parameters of the meso-scale across the scales. The rapid evaluation method of the shale mechanical parameters across the scales is established, which can be used as a method to obtain the mechanical parameters of shale quickly and accurately. The macro-indentation test experiment is carried out through the elastic contact hypothesis, the macro-micro mechanics theory, and the grid indentation experiment method. Considering the coupling effects of peak indentation fluctuations, contact stiffness(S), and the ratio of elastic work to total work (Wu/Wt), the cross-scale distribution characteristics of shale hardness(H) and elastic modulus(E) are studied. The results showed that the elastic modulus and hardness showed a normal distribution on the whole, and the macroscopic indentation process of the rock was accompanied by the meso-scale indentation. For Longmaxi shale, the elastic modulus and hardness have large discreteness and heterogeneity. The kernel density values of elastic modulus and hardness were studied by using kernel density analysis method. Different factors have different effects on the fluctuation amplitude of elastic modulus and hardness. The fluctuation range of the S is the largest, and the fluctuation range of Wu/Wt is the smallest. At the meso-scale, the dispersion of hardness peak value is larger, and the dispersion of elastic modulus peak value is smaller than that of valley value. The S-Wu/Wt-E-H coupling response law presents a "striped" characteristic. The S-Fm-E-H coupling response law presents a "multi-point" distribution. The Fm-Wu/Wt-E-H coupling response law shows a "wave-like" distribution. The hardness of vertical bedding indentation is greater than that of parallel bedding. There is a good linear correlation between the elastic modulus and hardness. With the increase of the elastic modulus, the hardness increases. The research results are helpful to determine the parameters in the actual design of hydraulic fracturing and improving the rock breaking efficiency.