RESEARCH PAPER Investigating the physical characteristics of dense granular flows by coupling the weakly compressible moving particle semi-implicit method with the rheological model Luoyilang Ke 1 • Yee-Chung Jin 1 • Tibing Xu 2 • Yih-Chin Tai 3 Received: 28 November 2018 / Accepted: 26 November 2019 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract Mesh-free methods have recently been coupled with constitutive rheological models to model dynamics in dry granular flows. However, this approach has not yet been comprehensively validated in different configurations with regard to the pressure, velocity, shear stress, free surface, and friction factor. Therefore, this study applied the weakly compressible moving particle semi-implicit method (WC-MPS) coupled with the l(I) rheology model to investigate three different cases: flow on an inclined plate, 2D column collapse, and granular dam-break flow. In the simulations, the flow characteristics were successfully captured in each of the different flow scenarios. In the granular flow on an inclined plate, the coupled model reproduced a steady uniform zone, in good agreement with analytical solutions in terms of pressure, shear stress, friction factor, and velocity distribution. In the 2D column collapse and granular dam-break flow, the coupled model showed good performance in capturing dynamic features from experimental observations. The numerical results of the coupled model for the pressure, shear stress, and friction factor were analysed, and the coupled model was found to distinguish flow regimes in the granular flows according to the calculated pressure, stress, and friction factor. The numerical results showed nonlinear distributions with dramatic changes in the pressure and shear stress on the free surface. Thus, this study demonstrated that the WC-MPS method coupled with the l(I) rheology model can reflect granular flow characteristics. Keywords Friction factor  Granular flow  Mesh-free method  Model validation  Moving particle semi-implicit method (MPS)  Rheological model 1 Introduction Granular flows, such as rock falls, debris flows, and ava- lanches, widely occur in the course of natural and industrial processes and can result in risks to human safety and industrial efficiency. The understanding of granular flow characteristics has been an important research subject in geotechnical engineering. In many industrial processes, such as agricultural and pharmaceutical product transfers, understanding such flow behaviours is also important to improve the transfer efficiency. However, granular flow characteristics are difficult to predict because of the tex- ture, size, shape, heterogeneity, and density of the granular materials. Therefore, research on flow behaviours caused by these materials must be conducted so that precautionary measures can be taken to mitigate risks caused by the granular flows and to improve efficiency in industrial processes that involve granular materials. Granular flows are complex and granular materials can appear in both solid-like and liquid-like states [9, 11, 33]. When grains are sufficiently compacted, a fixed and/or stable structure is formed among the grains, which can limit grains’ movement, resulting in a solid-like state. In contrast, when a granular material is dominated by & Yee-Chung Jin yee-chung.jin@uregina.c 1 Faculty of Applied Science and Engineering, University of Regina, 3737 Wascana Parkway, Regina, SK, Canada 2 Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo, China 3 Department of Hydraulic and Ocean Engineering, National Cheng Kung University, 1 University Road, Tainan, Taiwan 123 Acta Geotechnica https://doi.org/10.1007/s11440-019-00905-8