Evaluation of slope stability along NH-7 in India based on Hoek–Brown failure criterion using physics-informed neural networks

This article deals with modeling the slope stability along the NH-7 in India based on the Hoek–Brown failure criterion using physics-informed neural networks within a Python framework. The geodynamic nature of the Himalayan region makes the terrain prone to slope failure. In the present work, eight debris slopes (L1, L2, L3, L4, L5, L6, L7, and L8) in Uttarakhand are considered between Rishikesh and Kaudiyala. The engineering parameters (Young’s modulus, Poisson’s ratio, cohesion, friction angle, and unit weight) of the slope-forming materials are used for the stability analysis. Field photographs of the slopes are used to develop sliding surfaces. The surfaces are meshed with the finite element generator in Gmsh. A CSV file is generated with the mesh considering the defined boundary conditions. The Hoek–Brown failure criterion is implemented for assessing the slope stability, and physics-informed neural networks are used to incorporate the physical laws directly into the training process with the Adam optimizer (epochs = 1,000) to improve the accuracy and efficiency. The displacements, stresses, strains, principal stresses, principal strains, and shear strengths are calculated with this model for each slope, and the status is plotted (1: elastic, 2: plastic/failure). OriginPro (2025b) is used for visualizing the displacements, stresses, and other relevant parameters through the contour plots. The results showed that the slope materials are mainly comprised of well-graded sands, gravelly sands, with little or no plasticity and display no clay activity along with moderate cohesion (19.5–31.6 kPa) and internal friction angle ( 26.2 4 0 to 38.4 5 0 ). The slopes with the highest height and dip angle (L4 and L6) are critically stable with a strength reduction factor less than 1.0. Based on the above results, it is evident that the slope geometry has a more significant effect on the stability conditions of the slopes than the activity of swelling clay minerals. Finally, to increase the stability of the slopes, it is suggested that the installation of retaining/gabion walls along the toe, planting grass on the slope surface, and excavation at the crown part of the slope are possible stabilization measures.