A two‐phase SPH model for debris flow propagation

Abstract

Summary This paper presents a model which can be used for fast landslides where coupling between solid and pore fluid plays a fundamental role. The proposed model is able to describe debris flows where the difference of velocities between solid grains and fluid is important. The approach is based on the mathematical model proposed by Zienkiewicz and Shiomi, which is similar to those of Pitman and Le and Pudasaini. The novelty of the present work is the numerical technique used, the smoothed particle hydrodynamics (SPH). We propose to use a double set of nodes for soil and water phases, the interaction between them being described by a suitable drag law. The paper presents both mathematical and numerical models, describing the main assumptions and their limitations. Then, the model is applied to (1) a simple case where shocks and expansion waves appear, (2) a dam break problem on a horizontal plane with a frictional soil phase, and (3) a debris flow which happened in Hong Kong. The main conclusions that can be drawn from the applications are: Debris flows having 2 phases with important relative mobility present a rich structure of shocks and rarefaction waves, which has to be properly modeled. Otherwise, the model will have numerical damping or dispersion. Dambreak exercises provide interesting information in simple and controlled situations. We can see how both phases move relative to each other. Real debris flows can be simulated with the proposed model, obtaining reasonable results.

Simulation of mixed‐mode fracture using SPH particles with an embedded fracture process zone

“…Given an incremental displacement jump du c , the predictor can be calculated using Equation 44. The trial yield function f trial based on the elastic traction predictor is then computed by using Equation 48. If the trial yield function f trial < 0, no further action is required, and the trial traction is accepted to be the correct one.…”

“…One example of mesh-free methods is the smoothed particle hydrodynamics (SPH) method. Invented by Gingold and Monaghan 36 and Lucy, 37 SPH has been successfully applied to a wide range of engineering applications such as large deformation and failure of geomaterials, [38][39][40] slope failures, [41][42][43] granular flows and landslides, [44][45][46][47][48][49] soil-structure interaction, [50][51][52][53][54] coupled soil-water problems [55][56][57] and among many others. 49 SPH combined with a traditional constitutive model such as elastoplastic or coupled elastoplastic and damage models has also been extended to rock fractures in literature.…”

A depth average SPH model including μ(I) rheology and crushing for rock avalanches

“…Savage and Hutter proposed in 1989 their much‐celebrated 1‐D lagrangian model. Since then, it has been extended to more general conditions, including pore pressure dissipation in saturated materials and two‐phase materials . The limitations of the Savage‐Hutter model have been presented in Hutter et al…”

“…Since then, it has been extended to more general conditions, including pore pressure dissipation in saturated materials and two-phase materials. 4,[27][28][29][30][31][32][33][34][35] The limitations of the Savage-Hutter model have been presented in Hutter et al 36 Depth-integrated equations are obtained by integration along depth of the balance equations. We will use the reference system depicted in Figure 2.1, where the axis X 2 is perpendicular to the paper and points inwards.…”

WCSPH with Limiting Viscosity for Modeling Landslide Hazard at the Slopes of Artificial Reservoir

“…Even if this field is rather explored with SPH method [37][38][39], this work represented the first attempt to apply the Kinetic Theory of Granular Flow to simulate, at the slope of an artificial basin, the fast dynamics of a complex landslide undergoing large deformation and involving a sediment volume comparable to the stored water volume.…”