Modeling Two‐Phase Debris Flows With Grain‐Fluid Separation Over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan

Abstract

Landslides or debris flows usually arise in mountainous areas and slide over a rough topography. As the flow body is typically a mixture of particles and interstitial fluid, this paper aims at developing a binary mixture model and its numerical implementation for shallow debris flows on rugged topography. The mathematical formulation of this saturated solid‐fluid mixture is developed with respect to a terrain‐fitted coordinate system. Employing the thin layer assumption, a system of depth‐integrated equations is derived, where the interstitial fluid is supposed to be a viscous Newtonian fluid and the granular material is treated as a frictional Coulomb‐like continuum. At the basal surface, the Coulomb sliding condition for the granular constituent and Navier slip for the fluid phase are applied. The interaction between granular material and interstitial fluid is depicted by the buoyancy and a drag force induced by the velocity difference of both the phases. Numerical investigations are performed for studying the features of the proposed model, where a shock‐capturing nonoscillatory scheme is employed. A thorough parameter study of flows over three idealized terrain geometries illustrates the distinct impacts of the applied material parameters on the flow dynamics and deposit shapes. The phase separation such as the solid‐phase‐dominated flow front and how this changes with parameter values are presented. The simulation of the Hsiaolin landslide successfully retraces the approximate flow path recognized in satellite images as well as the measured deposition given in Kuo et al. (2011, https://doi.org/10.1029/2010JF001921).

Landslide Scarp Assessments by Means of an Ellipse-Referenced Idealized Curved Surface

“…The historical event is the Hsiaolin landslide occurred in 2009 in southern Taiwan. As a representative event in Taiwan, it has received significant research interests and we would refer the readers for details to the relevant literature, such as the work of Dong et al (2011), Kuo et al (2011), Tai et al (2019, and Tai et al (2020). In application to the Hsiaolin landslide, we only consider the main scarp area, marked by HL-1 as shown in Figure 5, which consists of more than 94% landslide mass as given in the work of Kuo et al (2011) and Tai et al (2019).…”

“…In addition to searching the most appropriate ICS, numerical simulations are performed with the ICSs determined in various scenarios to investigate the impacts on the flow paths when the landslide takes place (e.g., hazard assessment). As a large portion of the hazardous landslides in Taiwan are triggered by heavy rainfall, the two-phase model for non-trivial topography (Tai et al, 2019) is employed here. In addition, the code has been reprogrammed and implemented for CUDA-GPU highperformance computation (MoSES_2PDF, see the work of Ko et al, 2021).…”

“…In addition, the code has been reprogrammed and implemented for CUDA-GPU highperformance computation (MoSES_2PDF, see the work of Ko et al, 2021). For minimizing the uncertainty and for a unique reference, all the parameters are set identical to the ones used in the work of Tai et al (2019). We refer readers to the work of Tai et al (2019) and Ko et al (2021) for details of the model equations and the applied GPU techniques used in the simulation tool, respectively.…”

Application Assessments of Using Scarp Boundary-Fitted, Volume Constrained, Smooth Minimal Surfaces as Failure Interfaces of Deep-Seated Landslides

“…All these landslides have areas larger than 10 ha, maximum depths over 10 m and, according to the definition from the Taiwanese government, are classified as deepseated landslides. Among them, the sites labeled with HLIN prefixes are the scarps associated with the Hsiaolin landslides (Kuo et al, 2011;Tsou et al, 2011;Tai et al, 2019). The landslides are defined by using the 2005 and 2010 LiDAR 1 m resolution digital elevation maps (DEMs).…”

“…Because of this limitation, the analysis may not provide sufficient information for deep-seated landslides in estimating landslide-influenced areas. For this purpose, the 3D scarp depth distribution of the slide mass, for example, is one of the essential quantities required to estimate the runout and spread of the landslide, and it is particularly important for rapid large-scale avalanches, whose motion can be largely influenced by the topographic conditions of the terrain (Kuo et al, 2011;Luca et al, 2016;Tai et al, 2019), and the references therein.…”