A numerical simulation-based ANN method to determine the shear strength parameters of rock minerals in nanoscale

Rock is a heterogeneous material composed of multiple minerals, whose microscopic mechanical properties have a significant impact on the macroscopic mechanical properties of rocks. The elastic modulus and hardness of minerals could be measured by nanoindentation tests. However, determination of shear strength parameters (e.g., the cohesion and friction angle) of minerals in nanoscale is still a challenging work. In this paper, an elasto-plastic numerical model with Drucker-Prager failure criterion is established to simulate the nanoindentation tests. Uniform design is adopted to generate typical input parameters (e.g., elastic modulus, cohesion and friction angle) for the numerical model, by which the indentation load-penetration depth curve (P-h curve) corresponding to the typical input parameters are calculated. The artificial neural network (ANN) is trained to quantify the relationship between the input parameters and the P-h curve with high efficiency and accuracy. With a proposed optimization algorithm, the optimal input parameters such as the cohesion and friction angle, that achieve the minimum error between the simulated P-h curve by the ANN and the measured P-h curve by nanoindentation tests, could be determined. The proposed method is applied to determine the cohesions and friction angles of quartz, feldspar, and mica in granite. The results show that quartz exhibits the highest mechanical strength among the three minerals, and mica shows a greater discreteness. The results of this study will provide an effective method to obtain the microscopic mechanical properties of minerals and help to study the macroscopic mechanical properties of rock from microscopic perspective in the future.