Estimation of the Elastic Modulus of Granite Under Uniaxial Compression at the Pre-Peak Stage Using the PROS Method for Approximating Experimental Data

This study investigates the application of the Pure Random Orthogonal Search (PROS) method, introduced in the literature in 2021, for approximating force and displacement measurement data obtained from rock specimen testing, using granite as a case study. The primary objective is to simplify the data approximation procedure and improve the accuracy of experimental data analysis by reducing the influence of subjective factors within a predefined protocol. The research focuses on determining the maximum value of the tangent modulus of elasticity during the pre-peak deformation stage of granite specimens under uniaxial compression. The study employs methods of mathematical modeling of rock mechanical behavior and experimental data analysis. To approximate the experimental data, a modified two-parameter S-curve equation is proposed. The optimal parameter values are determined using the PROS method, which reduces the problem to solving a two-dimensional objective function minimization task. The dimensionality of this optimization problem remains independent of the number of experimental data points, thereby enhancing computational efficiency. A systematic computational procedure is developed for the automated calculation of the approximating equation’s parameters and the determination of the maximum tangent modulus of elasticity. In the context of challenges associated with accurately measuring displacements using conventional testing machines, a numerical correction procedure is proposed and implemented to account for the compliance of the loading system. The results of the study are consistent with both the literature-reported experimental data and the data obtained in this work. The methodology and findings can be adapted for analyzing the properties of concrete as an artificial analog of natural rock materials.