Homogeneity Equation for the Effective Elastic Properties of Heterogenous Rocks Developed From Machine Learning

Abstract This study develops an artificial neural network (ANN) model designed to estimate the effective elastic properties of heterogeneous rocks with inclusions. The ANN addresses the limitations of traditional effective medium models by avoiding theoretical assumptions, such as low inclusion percentages, and it incorporates the effects of inclusion length, spacing and orientation. This approach enables the accurate calculation of an equation that links dimensionless geometrical and physical features of rocks to their equivalent Young's modulus and Poisson's ratio. A two‐dimensional finite element model is employed to calculate, through dynamic loading, the effective Young's modulus and Poisson's ratio of an elastic matrix with properties comparable to sandstones and shales that has ellipsoidal inclusions representing cracks. While this study focuses on a single matrix and inclusion type, the results demonstrate that the method can be extended to any combination of matrix and inclusion elastic properties. The numerical model is validated against experimental and analytical solutions for simple geometries and then used to generate the training data, with inputs including crack length, crack density, aspect ratio, and distances between cracks. The ANN, though dependent on the numerical model for training and testing, operates much faster and can be applied to a broader range of scenarios. By training a single‐layer neural network, an accurate homogeneity equation is derived, relating effective elastic properties to dimensionless inclusion parameters. This approach to obtain a homogeneity equation has applications in rock mechanics, geophysics, and composite materials.