Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects (1304.4895v1)

Abstract: A micro-hydromechanical model for granular materials is presented. It combines the discrete element method (DEM) for the modeling of the solid phase and a pore-scale finite volume (PFV) formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the DEM-PFV coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions.

• The paper presents an advanced micro-hydromechanical model combining the Discrete Element Method (DEM) and Pore-scale Finite Volume (PFV) to simulate fluid-particle interactions and poromechanical effects in granular materials.
• Model validity is demonstrated through simulation of an oedometer test, showing close alignment with Terzaghi's solution and coherence between microscale analysis and effective stress.
• The model effectively simulates both static (consolidation) and dynamic (deposition, phase transition) scenarios with improved computational efficiency, offering implications for geomechanics and environmental processes.

Pore-scale Modeling of Fluid-Particles Interaction and Emerging Poromechanical Effects

The paper presents an advanced micro-hydromechanical model specifically designed for granular materials, integrating discrete and continuous methods to capture the intricate poromechanical effects inherent in such systems. This model melds the Discrete Element Method (DEM) for the representation of solid particles with a Pore-scale Finite Volume (PFV) approach for simulating fluid flow within the pore spaces. The integration of these methodologies allows for a nuanced consideration of fluid-solid interactions at a scale that aligns well with Biot's poroelasticity theory under specific constraints, notably in scenarios involving incompressible phases.

Model Overview

• Discrete Element Method (DEM): This method is leveraged to model granular materials at the particle level, offering insights into the intricate mechanical interplays between individual particles. The DEM provides microscopic perspectives on granular behavior, traditionally applied to dry systems, which are extended herein to account for fluid interactions.
• Pore-scale Finite Volume (PFV) Method: The PFV method addresses fluid flow within the granular structure's pore spaces. It conceptualizes the pore network as a series of connected spaces, where each fluid element can be modeled with a size comparable to the solid particles. This intermediate scale is crucial for capturing local fluid velocity vectors and pressure gradients without relying on phenomenological assumptions typical of larger scale continuum approaches.
• Coupling Equations: The coupling between DEM and PFV establishes a strong framework to evaluate poromechanical effects. The solution of an oedometer test, included in this paper, demonstrates the capability of this model to effectively capture the consolidation process akin to classical poroelasticity.

Numerical Validation and Results

The proposed model's validity is demonstrated through the simulation of an oedometer test—a classical problem in soil mechanics. The numerical results align closely with Terzaghi's analytical solution for one-dimensional consolidation, highlighting the model's robustness. Moreover, microscale definitions of stress and strain enable further verification, linking the simulations back to fundamental principles of effective stress.

• Microscale Explorations: The definition and use of microscale stress and strain tensors allow for a granular-level analysis that bridges micro and macro behaviors, exhibiting coherence with Terzaghi's effective stress concept.
• Dynamic Scenarios: In addition to static problems, the research extends to simulate dynamic processes such as granular deposition, elucidating complex transitions between liquid and solid states due to phase changes or fluid-solid interactions.

Implications and Future Prospects

The implications of this model are substantial for both theoretical and practical advances in geomechanics and related fields. By achieving a precise simulation of fluid-particle interactions and capturing phase transitions, this approach provides a foundational tool for exploring soil consolidation, liquefaction mechanics, and other critical phenomena sensitive to poroelastic effects.

• Computational Efficiency: The model significantly reduces computational overhead compared to complete Navier-Stokes simulations, making it feasible for larger systems without sacrificing detail at the particle scale.
• Beyond Current Capabilities: The ability to simulate both saturated conditions and phase transitions opens pathways for further research into erosion, landslide initiation, and other complex environmental processes. There is potential for extending this method to dynamic, inertial regimes, further broadening its applicability.

Overall, this integration of DEM and PFV methodologies presents a robust framework for advancing our understanding and prediction capabilities concerning fluid-particle interactions in granular media. This research paves the way for more sophisticated models and simulations that could reshape approaches in civil engineering, subsurface analysis, and beyond.