# Bridging Macro-Microscopic Parameters: Correspondence and Calibration Approaches
## 5 Conclusions  
This research endeavors to establish a standardized method for calibrating the microscopic parameters of granular materials as a solution framework to address the parameter calibration issues encountered in numerical simulations. This calibration method is derived by analyzing the relationship between macroscopic and microscopic parameters of the particles, forming a stepwise, clear, and efficient approach. Through careful study and verification of practical calibration scenarios, the research elucidates the practical application of the fine particle calibration method and the optimization mechanisms for overcoming challenges in real-world simulations. Key insights derived from this study are the following:  
1. The fundamental experimental approaches for obtaining three types of microscopic parameters: inter-particle friction coefficient, particle-wall friction coefficient, and particle-wall rolling friction coefficient, are provided: interparticle friction experiment and friction angle experiment. These methods enable the determination of required microscopic parameters for numerical simulations in a relatively straightforward manner. 2. The \"facet\" method is proposed for numerical simulation of uniaxial compression experiments on sand samples. By varying the microscopic parameters \(k_{n}\) and \(k_{s}\) within certain ranges, a correlation between the macroscopic parameter \(E_{s}\) and the microscopic parameters \(k_{n}\) and \(k_{s}\) is established. It is observed that an increase in the normal stiffness \(k_{n}\) amplifies the effect of the tangential stiffness \(k_{s}\) on the particle elastic modulus \(E_{s}\). When \(k_{n}\) is less than or equal to \(1\times 10^{8}\), the influence of \(k_{s}\) on \(E_{s}\) is negligible; however, when \(k_{n}\) exceeds \(1\times 10^{8}\), the influence of \(k_{s}\) on \(E_{s}\) becomes positively correlated. Furthermore, it is noted that \(k_{n}\) generally exerts a greater influence on \(E_{s}\) compared to \(k_{s}\) under various conditions, leading to the derivation of an empirical formula relating the microscopic parameters \(k_{n}\) and \(k_{s}\) to the macroscopic parameter \(E_{s}\). 3. A method for calibrating the microscopic parameters of sandy soil samples, grounded on uniaxial compression tests and indoor direct shear tests, is proposed. This method commences with the numerical simulation of uniaxial compression and utilizes empirical formulas to initially calibrate the stiffness parameters. Subsequently, it undergoes further verification through the numerical simulation of direct shear at 100 kPa. The experiments are uncomplicated and the steps are lucid, enabling the calibration of granular microscopic parameters within a relatively short time frame. 4. The microscopic parameters of sand samples obtained via the calibration method in this paper can be effectively applied to the numerical simulations of direct shear and pile-up of sandy soil samples. In the numerical simulation of direct shear, the maximum shear stress and the curvature of the shear stress-shear displacement curve are in good accordance with the actual results. In the numerical simulation of pile-up of sandy soil samples, the simulated pile-up morphology and range are consistent with the actual circumstances. 5. The present study is subject to the following limitations: Firstly, while the macro-micro parameter analysis provides a standardized scientific method for calibrating the microscopic parameters of granular materials, the diversity of particle types and the complexity of the coupling effects of microscopic parameters present significant challenges to the efficiency and accuracy of calibration. In cases involving larger particle sizes or particles with viscous properties, the existing calibration methods still require the introduction of new conditions or modifications to the original ones.