Assessment of the modulus of elasticity at a triaxial stress state for rocks using gene expression programming

Abstract

Rocks were subjected to the deformation test under five different confining stresses (0, 5, 10, 15, and 20 MPa) using the Hoek cell to determine changes in the elastic properties of the rocks under confining stress, and the results were evaluated based on density, porosity, Schmidt hardness, and compressive strength. A total of nine different rocks, two granites, two andesites, two limestones, one tuff, one diorite, and one marble, were used. When the confining stress was increased from 0 MPa to 5 MPa and from 5 MPa to 10 MPa, elasticity increased by approximately 20%. When the confining stress was increased from 10 MPa to 20 MPa, the increase was 7% in comparison with the previous value.<br />Then, to formulate the modulus of elasticity for rocks under the triaxial stress conditions, a new and intelligent approach to gene application, gene expression programming was utilized. The success of the model was thoroughly assessed based on measurable criteria such as the root mean square error, mean absolute percentage error, and coefficient of determination. Furthermore, the success of the model was comprehensively assessed based on the model testing, and 0.88 and 0.81 R2 values were obtained for training and validation, respectively. The performance of the gene expression programming-based formulation was compared with the formulae previously proposed in the literature. The gene expression method exhibited the best performance, and it was identified to calculate the modulus of elasticity under triaxial stress conditions more effectively.