Explicit meshfree solution of the dynamic Biot formulation at large strain

Area of Science:

• Geotechnical Engineering
• Computational Mechanics
• Pore Water Pressure Dynamics

Background:

• Simulating saturated soils under dynamic loads requires robust numerical methods capable of handling large deformations.
• Traditional methods often face high computational costs or limitations in accuracy for complex geomechanical problems.
• Understanding the coupled behavior of solid and fluid phases is crucial for accurate soil dynamics analysis.

Purpose of the Study:

• To introduce an efficient and robust methodology for simulating saturated soils under low-to-medium frequency dynamic loadings.
• To address the challenges of large deformation regimes in geomechanical simulations.
• To develop a computationally less expensive yet accurate numerical approach for dynamic soil analysis.

Main Methods:

• Utilizing a dynamic reduced formulation of Biot's equations to solve the coupled solid-fluid phases (solid displacement - pore water pressure).
• Employing an explicit two-steps Newmark predictor-corrector time integration scheme for accurate large strain analysis.
• Implementing Local Maximum Entropy shape functions within the Optimal Transportation Meshfree framework for numerical solutions.

Main Results:

• The proposed methodology efficiently simulates saturated soils under large deformation dynamic loadings.
• The explicit Newmark scheme provides accurate solutions at large strains, avoiding the high costs of implicit methods.
• Numerical simulations demonstrate the effectiveness of the Local Maximum Entropy and Optimal Transportation Meshfree framework in fluid-saturated porous media.

Conclusions:

• The developed methodology offers an efficient and robust solution for simulating complex geomechanical problems involving saturated soils.
• This approach significantly reduces computational expense while maintaining high accuracy for large deformation dynamic analyses.
• The study highlights the potential of advanced meshfree methods and explicit integration schemes in geotechnical engineering.