Modeling Geomechanical Behavior under Very Large Deformation with the Material Point Method

MPoint

Overview

Geotechnical problems involving large deformation, such as slope failures, landslides, and dam breaches, can be difficult to simulate using conventional numerical methods. These traditional approaches, when available in large strain, often encounter fatal mesh distortions in scenarios that undergo significant displacement. The result is a modeling gap after the initiation of failure and what happens as deformation continuese to evolve.

The Solution

ITASCA has developed MPoint, for both 3D and 2D simulations, to address this challenge directly. Built on the Material Point Method (MPM), MPoint combines the advantages of continuum mechanics, suited for a wide variety of material behaviors, with a numerical approach specifically designed for extreme deformation scenarios.

Rather than relying on a mesh that deforms with the material, MPoint tracks material points moving through a fixed computational background grid. This allows simulations to advance from the onset of failure, through extreme deformations, and the consequence of failure in one continuous model.

The outcome is a practical solution for modeling geomechanical problems that tend to encounter mesh distortions under severe material deformation, including:

Bulk material flow behavior
Landslide runout
Tailings dam failures
Embankment and levee breaches
Slope instability

Validation Process

To verify the accuracy of ITASCA’s MPM numerical framework, the MPoint development team validated the methodology against several established continuum solutions.

Dynamic Verification Problem

Results from MPoint (in both 2D and 3D) were compared with equivalent FLAC2D and FLAC3D finite-volume models in an example problem of free oscillation of an unstressed elastic body subjected to gravitational loading with no damping. Results showed near-exact agreement between the two methods for both dimensions (Figure 1), demonstrating accurate implementation of the mechanical governing equations and interpolation procedures.

Figure 1. Comparison of oscillation responses in 2D and 3D, with nearly exact agreement.

Slop Runout Verification Problem

To demonstrate MPoint’s effectiveness in a geomechanical scenario, a slope runout analysis involving the excavation of a block, forming two 90-degree walls, in a Mohr-Coulomb material with zero tensile/cohesive strength and a 30-degree friction angle was dynamically simulated using a local damping of 0.2. The scenario was modeled in FLAC3D, MPoint3D, and in a coupled FLAC3D-MPoint3D model, and the performance of each modeling method was compared.

All models are initially made up of zones, brought to equilibrium under gravity, and then a quarter block of material was removed. For the material points only model, all zones were converted to material points (8 per hexahedral zone) after equilibrium. For the coupled model, zones were set to automatically convert into material points as needed (e.g., specified strain limit or onset of poor zone geometry).

As shown in Figure 2, the zone-based (FLAC3D) model, in large-strain mode, encountered bad zone geometry early on with excessive deformations. In contrast, both the MPoint3D only and coupled FLAC3D-MPoint3D approaches were able to simulate the entire slope failure successfully. It is worth noting the contact interaction and merging of the material from each excavation face. The coupled solution demonstrates continuity between finite volume FLAC3D zones and MPM material points, illustrating the capability of this hybrid modeling approach.

Figure 2. Comparison of total displacement for: (a) large-strain FLAC3D zones, (b) MPoint3D material points only, and (c) coupled FLAC3D-MPoint3D models.

After excavation, there were 109,375 zones or 875,000 material points, for case (a) and case (b), respectively. At the end of simulation in case (c), 89,800 material points had been generated from zones. A notable advantage of the coupled approach is the computational savings, with case (c) running about 4.7x faster than case (b) made up of material points only.

Conclusion

Verification testing of MPoint confirms the accuracy of the Material Point Method for large-deformation geomechanical simulation for scenarios where traditional mesh-based approaches fall short. Both MPoint and the coupled MPoint-FLAC3D models were able to capture the continuation of large deformation behavior that could not be represented using the traditional mesh-based modeling method alone.

The studies demonstrate that MPoint:

Accurately reproduces benchmark continuum responses.
Efficiently models large-strain deformation without remeshing, as would be required in other continuum methods.
Offers computational efficiency when coupled with FLAC2D/FLAC3D.

Material Point Method modeling with MPoint offers a pathway for practical simulation of geotechnical systems under extreme deformation, with more complex modeling capability possible through coupling MPoint with ITASCA’s other trusted software solutions, such as FLAC2D and FLAC3D.