Numerical Simulation of Slope Failures in 2D and 3D Using the Material Point Method

Resumo

Slopes are inclined surfaces used in civil engineering projects, primarily intended to ensure the stability of soil or rock masses. They are widely found in infrastructure projects such as highways, railways, and in urban or rural areas with natural hillsides. When subjected to anthropogenic interference—such as deforestation, unregulated construction, or poorly planned excavations—they become vulnerable to landslides, especially during periods of heavy rainfall. These events pose significant risks to human life, the integrity of structures, and the functionality of access routes, directly impacting the safety and well-being of communities. To understand and predict slope behavior under different conditions, modern geotechnical engineering relies on numerical modeling. Among the available methods is the Material Point Method (MPM), a hybrid technique that combines Eulerian and Lagrangian mesh approaches, making it well-suited for simulations involving large deformations. Using physical soil properties such as Young's modulus, density, Poisson's ratio, friction angle, and cohesion, it is possible to numerically represent the behavior of a slope and its response to external factors. The study will include simulations in both 2D and 3D to evaluate slope behavior under different geometries. Additionally, results will be compared with traditional limit equilibrium methods, such as Slope/W, to ensure consistency and validation of the numerical approach. Implemented in C++, MPM can be integrated with tools like Matlab for postprocessing analysis, including automated calculation of the factor of safety (FS) and identification of the maximum displacement of material points after failure. This approach enables the simulation of landslide reach, supporting the planning of mitigation measures. Additionally, probabilistic modeling can be incorporated into MPM to better represent the uncertainties inherent in soil properties, contributing to safer and more cost-effective designs. This integration of modeling, scientific programming, and statistical analysis marks a new level of advancement in slope engineering.