PINNs-SlopeStability-MohrCoulomb

This repository implements Physics-Informed Neural Networks (PINNs) for slope stability analysis based on the Mohr-Coulomb failure criterion. The aim is to evaluate slope stability under various conditions, providing insights into critical parameters such as safety factors, displacement, and stress distribution.

Features

• Mohr-Coulomb Model: Implements the Mohr-Coulomb failure criterion for assessing slope stability.
• Physics-Informed Training: Utilizes PINNs to incorporate physical laws directly into the training process, improving accuracy and efficiency.
• Loss Function: A custom loss function that combines boundary conditions and physics-based constraints.
• Visualization Tools: Tools for visualizing displacement, stress, and other relevant parameters through heatmaps and contour plots.

Model Details

The PiNN is trained using:

• Physics equations: 2D linear elasto plastic using Mohr-Coulomb Model
• Material parameters:
  • Young's Modulus soil layer (E): 50000 kN/m² (for example) to compare with FEM from Plaxis2d
  • Poisson's Ratio (ν): 0.3
  • Cohesion = 3 kPa (for example) to compare with FEM from Plaxis2d
  • Friction angle = 13° (for example) to compare with FEM from Plaxis2d
  • Unit Weight (γ): 18 kN/m³ (for example) to compare with FEM from Plaxis2d
• Boundary Conditions: Fixed displacements on the bottom, left, and right sides.
• 

Result

-Safety factor from PiNNs = 1.54

-Safety factor from FEM = 1.876

• Requirements

• Python 3.x
• PyTorch
• NumPy
• Matplotlib
• Pandas

Installation

Install the necessary tools using:

pip install torch matplotlib numpy
pip install pandas
pip install pytorch