Granular flows are present in many processes in manufacturing, chemical and metallurgical industries. They are also present in many natural processes like landslides, mudflows, and sediment transport, among others. Common to all these examples is the fact that granular flows are very complex dynamic problems, involving multiple phases, physics, and large deformations of the domain under analysis. The latter aspect poses difficulties to conventional numerical approaches reliant upon continuum mesh-based methods such as the Finite Element Method (FEM) due to mesh distortion. Continuum meshless methods are an appealing alternative and, in particular, the Smoothed Particle Hydrodynamics (SPH) method has achieved a degree of maturity in the geomechanics community. In our work we developed a Lagrangian formulation for simulating the continuum hydrodynamics of dry granular flows based on multiplicative elastoplasticity theory for finite deformation calculations. The formulation is implemented within the SPH method along with a variant of the usual dynamic boundary condition. We have performed some benchmark simulations on dry sands to validate the model, which included: (a) a set of plane strain collapse tests, (b) a set of 3D collapse tests, and (c) a plane strain simulation of the impact force generated by granular flow on a rigid wall. Comparison with experimental results suggests that the formulation is sufficiently robust and accurate to model the continuum hydrodynamics of dry granular flows in a laboratory setting.
Figure 1: Runout evolution and impact forces on a rigid wall of a granular flow. Top left: experimental setup; top right: impact forces obtained experimentaly, and numerically by Moriguchi et al. (2009) and with our SPH code; bottom: runout snapshots.
After validating the framework with laboratory-scale tests, we developed a 3D mechanistic model for a real-life test slope in Switzerland named Ruedlingen, and conduct numerical simulations of the flow kinematics using the framework. Two main simulations explore the impact of changes in the mechanical properties of the sediment on the ensuing kinematics of the flow. The first simulation models the sediment as a granular homogeneous material, while the second simulation models the sediment as a heterogeneous material with spatially varying cohesion. The variable cohesion is meant to represent the effects of root reinforcement from vegetation. By comparing the numerical solutions with the observed failure surfaces and final free-surface geometries of the debris deposit, as well as with the observed flow velocity, duration of flow, and hotspots of strain concentration, we provide insights into the accuracy and robustness of the SPH framework for modeling debris flow. The results also suggest the potential of the formulation for modeling more complex, field-scale scenarios characterized by more elaborate geometry and multiphysical processes. To our knowledge, this is the first time the multiplicative plasticity approach has been applied to granular flows in the context of the SPH method. The proposed framework can be extended to accommodate multiphase flows and different constitutive models, and it will be available as an open source code.
Moriguchi, S., Borja, R.I., Yashima, A., Sawada, K. (2009) Estimating the impact force generated by granular flow on a rigid obstruction. Acta Geotech, 4, pp 57-71.