An analytical optimal calibration framework of bonded particle model for rock strength envelop modelling.

When employing bonded discrete element models (DEMs) to model rocks, a fundamental problem is how to determine the micro parameters to accurately simulate the rock strength characteristics. One promising way to improve calibration efficiency is to fully utilize the underlying relationship between DEM micro parameters and the macro strengths of rocks. This paper developed an analytical-optimal calibration framework to automatically determine DEM bond strength parameters. Extensive parametric analysis was first conducted to obtain the relationships between DEM micro-parameters and macro strengths. Bond tensile strength, cohesion and local internal friction angle were identified as independent variables for calibration. The automatic calibration method is divided into two stages. Firstly, the rough estimations of the bond tensile and cohesion were obtained by successively performing a direct tensile simulation test and a uniaxial compression simulation test, while the local internal friction angle was estimated by an empirical formula about the Hoek-Brown parameter m(i). In the second stage, a finite difference gradient optimization method was used to further approximate the optimal bond parameters. A simplified gradient calculation is proposed based on the sensitivity analysis of macro strengths and DEM parameters. Adaptive moment estimation (Adam) was chosen as the iterative optimization algorithm to avoid the vanishing gradient problem. The advantage of the proposed calibration method is that the relationship between macro strengths and DEM parameters is fully exploited in both the initial estimation of DEM micro parameters and the optimization process. Moreover, the optimization method is a single-solution algorithm without the need to perform a large number of numerical simulations simultaneously. The proposed framework was demonstrated by calibrating the Bukit Timah granite, and a high calibration accuracy was achieved with a few iterations and a small number of simulation runs. Its applicability was also verified by the calibration results of various types of rocks.