Modeling the Slump-Type Landslide Tsunamis Part I: Developing a Three-Dimensional Bingham-Type Landslide Model

Abstract

This paper incorperates Bingham and bi-viscosity rheology models with the Navier–Stokes solver to simulate the dynamics and kinematics processes of slumps for tsunami generation. The rheology models are integrated into a computational fluid dynamics code, Splash3D, to solve the incompressible Navier–Stokes equations with volume of fluid surface tracking algorithm. The change between un-yield and yield phases of the slide material is controlled by the yield stress and yield strain rate in Bingham and bi-viscosity models, respectively. The integrated model is carefully validated by the theoretical results and laboratory data with good agreements. This validated model is then used to simulate the benchmark problem of the failure of the gypsum tailings dam in East Texas in 1966. The accuracy of predicted flood distances simulated by both models is about 73% of the observation data. To improve the prediction, a fixed large viscosity is introduced to describe the un-yield behavior of tailings material. The yield strain rate is obtained by comparing the simulated inundation boundary to the field data. This modified bi-viscosity model improves not only the accuracy of the spreading distance to about 97% but also the accuracy of the spreading width. The un-yield region in the modified bi-viscosity model is sturdier than that described in the Bingham model. However, once the tailing material yields, the material returns to the Bingham property. This model can be used to simulate landslide tsunamis.

Modeling the Slump-Type Landslide Tsunamis Part II: Numerical Simulation of Tsunamis with Bingham Landslide Model

“…The boundary conditions are free-slip boundary conditions on the domain boundaries, except for the ceiling boundary, which is a pressure Dirichlet (P = 0) boundary condition. The dynamic viscosities of water and air are 10 −3 Pa s and 10 −5 Pa s respectively, whilst the yield viscosity of the slump is µ B = 50 Pa s. The slump un-yield viscosity µ A is 10 10 Pa s as addressed in Part I [42]. The yield stress of the slump suggested by Assier Rzadkiewicz [16] is τ y = 1000 Pa.…”

“…As for the comparisons of the slump shape, Part I [42] presents the 3D validation of the slump slide on the dry land for the detailed comparisons and discussions on the rheology parameters. In Part II, the simulated results are compared with the laboratory data as shown in Figure 2 at t = 0.4 s and 0.8 s. The simulated slump shape is very close to the laboratory data at t = 0.4 s. This indicates that the yield stress of the slump suggested by Assier Rzadkiewicz [16] performs very well at the initial stage of the slump slide.…”

“…While dealing with a landslide problem, the role of un-yield viscosity µ A is to stop the landslide deformation, which is discussed in Part I [42]. Figure 6 shows the free-surface profiles of four different un-yield viscosities: µ A = 10 2 , 10 4 , 10 6 , 10 10 Pa s. The yield viscosity µ B = 50 Pa s and the yield stress τ y = 1000 Pa are kept the same.…”

“…The interfaces between the air, water, and slump are tracked by the volume of fluid (VOF) method. The detailed numerical algorithm can be found in Part I [42].…”

Landslide tsunamis: Comparison between depth-averaged and Navier–Stokes models

“…In Kim et al (2020), the authors question the applicability of 2DH models to landslide tsunamis, suggesting that 3D models taking into account the vertical acceleration would produce more accurate results. Over the past two decades, several 3D models based on Navier-Stokes equations have been developed, among them, THETIS (Abadie et al 2008), FLUENT (Biscarini 2010), Fluidity (Davies et al 2011), NHWAVE (Ma et al 2013), TSUNAMI3D (Horrillo et al 2013), Splash3D (Wu et al 2020) and OpenFOAM (Lee et al 2016, Si et al 2018, Romano et al 2020, Lee & Huang 2021. However, an extensive comparison between 2D and 3D models for landslide tsunamis generation is, to the knowledge of the authors of this present study, not available.…”