Evaluating the impact of eccentric loading on strip footing above horseshoe tunnels in rock mass using adaptive finite element limit analysis and machine learning

The present study investigates the ultimate bearing capacity (UBC) of a footing subjected to an eccentric load situated above an unlined horseshoe-shaped tunnel in the rock mass, following the Generalized Hoek-Brown (GHB) failure criterion. A reduction factor (R_f) is introduced to investigate the impact of the tunnel on the UBC of the footing. R_f is determined using upper and lower bound analyses with adaptive finite-element limit analysis. The study examines the influence of several independent variables, including normalized load eccentricity (e/B), normalized vertical and horizontal distances (δ/B and H/B) of the footing from the tunnel, tunnel size (W/B), and other rock mass parameters. It was found that all these parameters significantly affect the behavior of tunnel-footing interaction depending on the range of varying parameters. The findings of the study indicate that the critical depth (when R_f is nearly 1) of the tunnel decreases with increasing load eccentricity. The critical depth is found to be δ/B ≥ 2 for e/B ≤ 0.2 and δ/B ≥ 1.5 for e/B ≥ 0.3, regardless of H/B ratios. Additionally, the GHB parameters of the rock mass significantly influence the interaction between the tunnel and the footing. Moreover, this study identifies some typical potential failure modes depending on the tunnel position. The typical potential failure modes of the footing include punching failure, cylindrical shear wedge failure, and Prandtl-type failure. This study also incorporates soft computing techniques and formulates empirical equations to predict R_f using artificial neural networks (ANNs) and multiple linear regression (MLR).