<p><span>In Tai et al. (2020), the concept of idealized curved surface (ICS) is proposed to mimic the failure surface, and the application to a large-scale landslide yields good agreement with the satellite image for the post-failure flow paths. The ICS consists of two constant curvatures in the down-slope and cross-slope directions, respectively. Hence, it is convenient to evaluate the stability based on the moment of momentum with respect to the plausible ICS. In this study we are going introduce a new formula for the stability analysis, in which the balance of angular momentum is employed, so that the local failure thickness (above the ICS) and the local ground water level can be taken into account. That is, the depth distribution of the landslide body may also have significant impacts on the slope stability.</span></p><p><span>Motivated by the similarity between landslide and granular avalanches, the periodic sand avalanches on a heap are investigated by means of the snap shots of high-speed camera, where the sand is accumulated up to a specific volume before sliding down. It is found that the first failure takes place near the toe of the avalanching body and the rupture surface develops and moves upwards. The ICS and the associated stability analysis can well explain the initial failure near the toe. This concept can also be applied to the mystery of the Hsiaolin landslide, taking place in southern Taiwan in 2009, where the released volume is up to more than 22 Mm</span><sup><span>3</span></sup><span> but the mean slope is around 21 degrees. In spite of a 2D analysis, it can be found that, with a reasonable groundwater level, the first failure could be suspected to develop around the toe part. Therefore, we speculate that the plausible state of the landslide is the rainfall induced rise of groundwater level, inducing the sequential landslides and resulting the resultant large-scale landslide event.</span></p>

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For the investigation of landslide mass movement scenarios through numerical simulation, a well-defined released mass and a precise initial source area are required as prerequisites. In the present study, we present a genetic algorithm-based approach for preliminarily assessing the landslide scarp when the local field data are limited, using an ellipse-referenced idealized curved surface (ER-ICS)—a smooth surface constructed with respect to an ellipse. According to a specified depth at the center, there are two distinct curvatures along the major and minor axes, respectively. To search for the most appropriate ICS, the reference ellipse is translated, rotated, and/or side-tilted to achieve the optimal orientation for meeting the best fitness to the assigned condition (delineated area or failure depths). The GA approach may significantly enhance the efficiency, by reducing the number of candidate ICSs and notably relaxing the searching ranges. The proposed GA-ER-ICS method is examined and shown to be feasible, by mimicking the source area of a historical landslide event and through application to a landslide-prone site. In addition to evaluating the fitness of the ICS-covered area with respect to the source scarp, the impacts of various ICSs on the flow paths are investigated as well.

We present a grain-fluid mixture for debris flows moving on a rugged (non-trivial) topography, where entrainment and deposition may take place. The model equations are derived with respect to a terrain-following coordinate system, which is constructed based on the topographic surface. The coordinates are fixed in space, and a “subtopography” is added on the coordinate surface to account for the variation in the local topography when entrainment or deposition takes place. Numerical implementation is made based on a GPU-accelerated simulation tool, into which the entrainment-deposition mechanism is integrated accordingly. Two numerical examples are assigned to investigate the key features of the proposed model. One is on a horizontal plane, on which a finite mass of grain-fluid mixture is released from the state of rest. In this example, debris flow deposits significantly impact the post-event} morphology and the associated flow behaviors. The other concerns a moving mass down an inclined chute merging into a horizontal deposition plane, where the levee formation is reproduced. At the end, the model is validated against a debris flow experiment to evaluate its applicability.

The importance of scenario investigation in landslide-related hazard mitigation planning has long been recognized, where numerical simulation with physics-based models plays a crucial role because of its quantitative information. However, a plausible failure surface is a prerequisite in conducting the numerical simulation, but it often has a high degree of uncertainty due to the complex geological structure. The present study is devoted to proposing a methodology to mimic the plausible landslide failure surface (with some uncertainty) for investigating the consequent flow paths when failure takes place. Instead of a spherical shape, an idealized curved surface (ICS) is used, where two constant curvatures are, respectively, assigned in the down-slope and cross-slope directions. A reference ellipse is introduced for constructing the associated ICS with a specified failure depth regarding these two curvatures. Through translating, rotating, or side-tilting the reference ellipse, the most appropriate ICS is figured out with respect to the assigned constraints (failure area, volume of released mass, depth of sliding interface, etc.). The feasibility and practicability of this ellipse–ICS method are examined by application to a historical landslide event and one landslide-prone area. In application to the historical event, the fitness versus the landslide scarp area and its impacts on the consequent flow paths are investigated. For the landslide-prone area, five scenarios are arranged based on the surface features and the records of gaging wells. The most plausible failure scenario is therefore suggested as the prerequisite for mimicking the consequential flow paths.