A genetic programming model for estimating the rock mass deformation modulus based on analytical parameters and in situ stress

Abstract

The estimation of the rock mass deformation modulus (${\text{D}}_{\text{f}}$) has a history of nearly half a century with empirical models. However, reliable estimation of ${\text{D}}_{\text{f}}$ has been a challenging task due to the theoretical background of input parameters and data analysis methods. Analytical models present the principal input parameters; however, according to this study, the concept of principal input parameters (PIP) was developed with an emphasis on in situ stress. A review of seventy empirical models revealed that the majority of existing models suffer from a lack of PIP. Moreover, based on the geological strength index, confined Young’s modulus, and shear and normal joint stiffness at specified normal stress, the deformation modulus is forecasted by a new multigene genetic programming (MGP) as an optimal mathematical relationship in terms of fitness functions. A comparison of the estimated deformation modulus with several existing empirical models based on the same database, seventy-nine valid data sets of different rock types, shows the superiority of the new MGP in terms of residual average and fitness function (RMS and ${\text{R}}^{\text{2}}$). Furthermore, the Earth’s crust stress impact on ${\text{D}}_{\text{f}}$ was numerically simulated through 3DEC, based on a plate jacking test, in which only the azimuth of the main horizontal in situ stress changed consecutively to achieve the calculated deformation modulus based on the model’s displacement at the extensometer anchor points. The integration of PIP’s concept with the MGP model improves the global acceptability of empirical models in analytical and numerical stability analyses.