Predicting rock strength anisotropy using a sensitivity-driven evolutionary polynomial regression

Abstract

The strength of anisotropic rocks remarkably depends on the orientation of stresses with respect to existing directional features in rocks such as foliation, bedding planes, and cleavages. While rock strength anisotropy is crucial for engineering design, experimental tests to obtain peak strengths of samples with several degrees of anisotropy and confining stresses are time-consuming and costly. Reliable and high-fidelity models derived with soft computing techniques can be applied to estimate rock strength anisotropy. Using a data set containing samples from 15 transversely isotropic rocks, this work developed a sensitivity-driven evolutionary polynomial regression (EPR) model to predict transverse isotropic strength. The model computes the peak strength, $$\:{\sigma\:}_{1}$$ , as a function of confining stress, $$\:{\sigma\:}_{3}$$ , orientation angle, $$\:\beta\:$$ , degree of anisotropy, $$\:R$$ , and parameters of the Hoek-Brown strength criterion, $$\:{m}_{i}$$ and $$\:{\sigma\:}_{ci}$$ . The developed model showed parsimony (lower number of parameters and input variables), good predictive capability (accurately tracks observed peak strengths) and generalization ability (physical meaning). Sensitivity analysis revealed that the model can adequately simulate the U-shaped anisotropy curves and capture non-linear relationships between $$\:{\sigma\:}_{1}$$ and other inputs ( $$\:{\sigma\:}_{3}$$ , $$\:\beta\:$$ , $$\:{m}_{i}$$ and $$\:{\sigma\:}_{ci}$$ ), but it is less sensitive to $$\:R$$ . Moreover, our modeling approach benefits from Monte Carlo simulations to explore the uncertainty involved in the input–output relationships. Comparison of simulated peak strengths with results of recent models published in the literature further supported the ability of our optimal EPR model structure. The proposed model could be a useful approach for estimating the strength of transversely isotropic rocks.

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