<p>The movement of a debris flow is channelized by the mountain topography. It slows down and begins to deposit, forming the so-called debris-flow fan, when the slope is gentle. Since the flow body is composed of solid grains with interstitial fluid, the solid fraction may vary and plays a crucial role in the deposition process. In the present study, an entrainment-deposit law together with the two-phase model for grain-fluid flows (Tai et al., 2019) is proposed for describing the development of a debris flow fan. The model equations are derived in a terrain-following coordinate system, in which the coordinates are in coincidence with the topographic surface and the deposition/erosion is treated as the sub-topography. Numerical validation is performed against flume experiments (Tsunetaka et al., 2019), where the sediment-water mixture is released from a channel and merging into a gentle inclined flat plain via a steady water inflow. In this study, we shall illustrate the impacts of the sediment concentration on the evolution of the debris-flow fan, such as the location, distribution, geometry of debris-flow fan as well as the flow paths. </p>

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<p>An Idealized curve surface (ICS) with two constant curvatures was proposed in Tai et al. (2020) for mimicking the plausible landslide failure surface in numerical simulation.  For ease of illustrating the ICS, Ko et al. (2021) suggested the concept of a reference ellipse for constructing the associated ICS, i.e. the ellipse-ICS method. Hence, with respect to a landslide-prone area, the most appropriate ICS can be figured out by translating, rotating and side-tilting the reference ellipse.</p><p>In the present study, the criteria for the searching the most appropriate ICS consist of the terrain characteristics (cracks, scarps, erosion gullies) and the data of the gauging station (inclinometer and groundwater indicators), where the terrain characteristics indicate the plausible boundary of the failure area, the records of inclinometer help to identify the (local) depth of sliding surface. Since the inclinometer and groundwater indicators provide the local data only, the proposed ellipse-ICS method is employed as an efficient tool to construct the plausible ICS and to investigate the impacts of the groundwater distribution on the slope stability.</p><p>The ellipse-ICS method is therefore applied to two potential large-scale landslide areas in Taiwan, i.e., the T003 at Yanping Township in eastern Taiwan and the T002 at Fuxing District in northern Taiwan. The ICSs are identified with respect to the failure depths measured by inclinometer, where the safety factors are estimated. Together with the numerical approach given in Tai et al. (2019), the subsequent flow paths of post-failure can be estimated and may serve as useful information for hazard assessment.</p><p> </p><p>Keywords:</p><p>ellipse-ICS, inclinometer, groundwater level, safety factors, flow paths</p><p> </p><p>References</p><ul><li>Tai, Y. C., Heß, J., & Wang, Y. (2019). Modeling Two‐Phase Debris Flows with Grain‐Fluid Separation over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan. <em>Journal of Geophysical Research</em>: <em>Earth Surface</em>, <strong>124(2)</strong>, 305-333.</li> <li>Tai, Y. C., Ko, C. J., Li, K. D., Wu, Y. C., Kuo, C. Y., Chen, R. F., & Lin, C. W. (2020). An idealized landslide failure surface and its impacts on the traveling paths. <em>Frontiers in Earth Science</em>, <strong>8</strong>, 313.</li> <li>Ko, C. J., Wang, C. L., Wong, H. K., Lai, W. C., Kuo, C. Y. & Tai, Y. C. (2021). Landslide Scarp Assessments by Means of an Ellipse-Referenced Idealized Curved Surface. <em>Frontiers in Earth Science</em>, <strong>9</strong>,862.</li> </ul>