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Volume 114
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MPS simulation of dense granular flows using a gradient-expansion nonlocal μ(I) rheology
Akinkunmi Mumeen, Olalekan Rufai, Yee-Chung Jin *
Faculty of Engineering and Applied Science, University of Regina, Saskatchewan, S4S 0A2, Canada
10.1016/j.partic.2026.04.013
Volume 114, July 2026, Pages 186-206
Received 31 January 2026, Revised 1 April 2026, Accepted 13 April 2026, Available online 28 April 2026, Version of Record 4 May 2026.
E-mail: yee-chung.jin@uregina.ca
Highlights

• Energy evolution governed by static and dynamic friction contributions.

• Gradient expansion nonlocal μ(I) model within a meshfree MPS framework.

• Nonlocal fluidity diffusion capturing cooperative effect in transitions.

• Strength-based μ(I) friction limits providing consistent flow prediction.

• Basal stress redistribution and surge formation in downslope collapse.


Abstract

Dense granular flows are common in many natural and industrial processes; yet, capturing their transition between inertial motion and quasi-static arrest remains difficult within continuum frameworks. This study presents a Lagrangian numerical framework combining the Moving Particle Semi-implicit (MPS) method with a strength-based nonlocal μ(I) rheology. It employs a gradient-expansion approach in which fluidity diffuses via a stabilized Laplacian operator, allowing the model to simulate creeping motion, a finite shear-band thickness, and smooth transitions between flowing and static zones. Both static and dynamic friction coefficients are derived from geomechanical functions tied to the internal friction angle, eliminating the need for empirical calibration. Validation against granular column-collapse experiments on flat and inclined beds accurately predicts the front propagation, internal velocity fields, and deposit shape across different aspect ratios and slopes. The nonlocal formulation addresses the cooperative effects deficiency of the local μ(I) model, particularly during the transition from inertial spreading to arrest. Energy analyses indicate that the dynamic friction coefficient governs post-yield mobility and runout, while the static coefficient primarily influences flow initiation. The framework offers a physically grounded, numerically robust tool for dense granular flows, eliminating the need for parameter calibration and enhancing predictive consistency.


Graphical abstract
Keywords
Gradient expansion model (GEM); μ(I)rheology; MPS method; Granular flow; Strength parameter
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