Yih-Chin Tai

Shock waves, dead zones and particle-free regions in rapid granular free-surface flows

Shock waves, dead zones and particle-free regions form when a thin surface avalanche of granular material flows around an obstacle or over a change in the bed topography. Understanding and modelling these flows is of considerable practical interest for industrial processes, as well as for the design of defences to protect buildings, structures and people from snow avalanches, debris flows and rockfalls. These flow phenomena also yield useful constitutive information that can be used to improve existing avalanche models. In this paper a simple hydraulic theory, first suggested in the Russian literature, is generalized to model quasi-two-dimensional flows around obstacles. Exact and numerical solutions are then compared with laboratory experiments. These indicate that the theory is adequate to quantitatively describe the formation of normal shocks, oblique shocks, dead zones and granular vacua. Such features are generated by the flow around a pyramidal obstacle, which is typical of some of the defensive structures in use today.

Shock-capturing and front-tracking methods for granular avalanches

Shock formations are observed in granular avalanches when supercritical flow merges into a region of subcritical flow. In this paper we employ a shock-capturing numerical scheme for the one-dimensional Savage-Hutter theory of granular flow to describe this phenomenon. A Lagrangian moving mesh scheme applied to the nonconservative form of the equations reproduces smooth solutions of these free boundary problems very well, but fails when shocks are formed. A nonoscillatory central (NOC) difference scheme with TVD limiter or WENO cell reconstruction for the conservative equations is therefore introduced. For the avalanche free boundary problems it must be combined with a front-tracking method, developed here, to properly describe the margin evolution. It is found that this NOC scheme combined with the front-tracking module reproduces both the shock wave and the smooth solution accurately. A piecewise quadratic WENO reconstruction improves the smoothness of the solution near local extrema. The schemes are checked against exact solutions for (1) an upward moving shock wave, (2) the motion of a parabolic cap down an inclined plane, and (3) the motion of a parabolic cap down a curved slope ending in a flat run-out region, where a shock is formed as the avalanche comes to a halt.

Flow of dense avalanches past obstructions

Abstract One means of preventing areas from being hit by avalanches is to divert the flow by straight or curved walls or tetrahedral or cylindrical-type structures. Thus, there arises the question how a given avalanche flow is changed regarding the diverted-flow depth and flow direction. In this paper a report is given on laboratory experiments performed for gravity-driven dense granular flows down an inclined plane obstructed by plane wall and tetrahedral wedge. It was observed that these flows are accompanied by shocks induced by the presence of the obstacles. These give rise to a transition from super-to subcritical flow of the granular avalanche, associated with depth and velocity changes. It is demonstrated that with an appropriate shock-capturing integration technique for the Savage-Hutter theory, the shock formation for a finite-mass granular flow sliding from an inclined plane into a horizontal run-out zone is well described, as is the shock formation of the granular flow on either side of a tetrahedral protection structure.

The landslide stage of the Hsiaolin catastrophe: Simulation and validation

[1]xa0Typhoon Morakot struck southern Taiwan in the summer of 2009, causing the most severe flooding since the 1950s. In the early morning of August 9, rainfall triggered the Hsiaolin landslide, and the resulting debris avalanche covered the township of Hsiaolin Village, Kaohsiung. Around five hundred people were buried alive. Reconstruction of the runout of the debris avalanche would increase understanding of the large-scale avalanches for future hazard mitigation purposes. Simulation of the debris avalanche runout can provide valuable information for this purpose. A new continuum shallow-water model is applied to flow over general topography. The Coulomb friction law is adopted; the friction coefficient is initially determined by high pressure rotary-shearing tests and subsequently fine-tuned by an iterative procedure to minimize the difference between the simulation and the measurement. The friction coefficients measured by laboratory tests are found to be in reasonable agreement with the best-fit result of the simulation. In addition, Voellmy rheology is applied, but it is found that the role of the fluid viscous drag is insignificant. The simulation result in the village area is further corroborated by near-surface magnetic surveys. These indicate that the northern part of the village is dislocated, while the artifact structures of the southern part are buried near their original locations. By comparing the landslide front and the flow direction of the simulation, we are able to confirm, as also described by survivors, that the landslide swept the northern part of the village into the Cishan River, while the southern part was flooded subsequently by the debris from a dam breach about 20 min after the landslide.

Dense Granular Avalanches: Mathematical Description and Experimental Validation

Snow avalanches, landslides, rock falls and debris flows are extremely dangerous and destructive natural phenomena. The frequency of occurrence and amplitudes of these disastrous events appear to have increased in recent years perhaps due to recent climate warming. The events endanger the personal property and infra-structure in mountainous regions. For example, from the winters 1940/41 to 1987/88 more than 7000 snow avalanches occurred in Switzerland with damaged property leading to a total of 1269 deaths. In February 1999, 36 people were buried by a single avalanche in Galtur, Austria. In August 1996, a very large debris flow in middle Taiwan resulted in 51 deaths, 22 lost and an approximate property damage of more than 19 billion NT dollars (ca. 600 million US dollars) [18]. In Europe, a suddenly released debris flow in North Italy in August 1998 buried 5 German tourists on the Superhighway “Brenner-Autobahn”. The topic has gained so much significance that in 1990 the United Nations declared the International Decade for Natural Disasters Reduction (IDNDR); Germany has its own Deutsches IDNDR-Komitee fur Katastrophenvorbeugung e.V. Special conferences are devoted to the theme, e.g., the CALAR conference on Avalanches, Landslides, Rock Falls and Debris Flows (Vienna, January 2000), INTERPRAEVENT, annual conferences on the protection of habitants from floods, debris flows and avalanches, special conferences on debris flow hazard mitigation and those exclusively on Avalanches.

An accurate shock-capturing finite-difference method to solve the Savage-Hutter equations in avalanche dynamics

Abstract The Savage-Hutter equations of granular avalanche flows are a hyperbolic system of equations for the distribution of depth and depth-averaged velocity components tangential to the sliding bed. They involve two phenomenological parameters, the internal and the bed friction angles, which together define the earth pressure coefficient which assumes different values depending upon whether the flow is either diverging or contracting. Because of the hyperbolicity of the equations, since velocities may be supercritical, shock waves are often formed in avalanche flows. Numerical schemes solving these free surface flows must cope with smooth as well as non-smooth solutions. In this paper the Savage-Hutter equations in conservative form are solved with a shock-capturing technique, including a front-tracking method. This method can perform for parabolic similarity solutions for which the Lagrangian scheme is excellent, and it is even better in other situations when the latter fails.

A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone

In this paper a detailed approach is proposed for the behavior of two-dimensional cohesionless granular materials moving down a confined inclined plane chute into the horizontal run-out zone, where the upslope propagating bore is treated as a growing deposition heap. It deals with the theoretical-numerical and experimental treatments. The depth-averaged field equations of balance of mass and linear momentum are described in moving coordinates for general topography as prescribed by Tai and Kuo [Acta Mech. 199, 71 (2008)]. A most simplistic approach to the erosion/deposition parameterization is proposed and the spatial coordinate coincides with the arc length of the variable basal surface. These equations describe the temporal evolution of the depth and velocity of the granular mass, especially the locations and shapes of the growing deposition heaps beneath the flowing layer. Experiments were carried out with different material supply rates and in two types of chutes, which differed by the bottom surface ...

Particle Size Segregation, Granular Shocks and Stratification Patterns

Large scale stratification patterns [1] are formed when a mixture of two grain sizes, or more, repeatedly avalanche downslope and are brought to rest by upslope shock wave propagation. The avalanches are generated by either surface deposition, basal erosion or rotation of the free surface. Provided each of these processes take place at sufficiently low rates the avalanches occur intermittently, due to the difference between the static and dynamic friction angles [2], [3]. Segregation of the particles takes place within the flowing avalanche by a process called kinetic sieving [4], [5]. An initially homogeneous mixture of grains is rapidly transformed into an inversely graded particle size distribution, in which the large particles overlie the smaller ones. The reason for this segregation is simple. As grains are sheared within the avalanche void spaces are continually being created and annihilated below each grain, and the smaller grains are more likely to fall into the available space than the large grains. For a bi-disperse granular material two segregated layers are rapidly generated within the avalanche, as shown in the photograph and schematic diagram in Fig. 1. An additional velocity shear through the depth of the avalanche transports the larger particles to the front and the smaller ones to the rear. This can also be seen in Fig.1.

NON-CARTESIAN, TOPOGRAPHY-BASED AVALANCHE EQUATIONS AND APPROXIMATIONS OF GRAVITY DRIVEN FLOWS OF IDEAL AND VISCOUS FLUIDS

When dealing with geophysical flows across three-dimensional topography or other thin layer flows, for the physical modelling and for computational reasons, it is more convenient to use curvilinear coordinates adapted to the basal solid surface, instead of the Cartesian coordinates. Using such curvilinear coordinates, e.g. introduced by Bouchut and Westdickenberg,3 and the corresponding contravariant components of vector and tensor fields, we derive in full generality the governing equations for the avalanche mass. These are next used to deduce (i) the thin layer equations for arbitrary topography, when the flowing mass is an ideal fluid, and (ii) the thin layer equations corresponding to arbitrary topography and to a viscous fluid that experiences bottom friction, modelled by a viscous sliding law.

Pressure Coefficient in Dam-Break Flows of Dry Granular Matter

AbstractThe propagation of dry granular flows, such as rock and snow avalanches, can be described by depth-averaged models. Different from classical shallow-water equations, these models take into account the anisotropy of normal stresses inside the flowing pile through using an earth pressure coefficient in the pressure term. A new regularization function for calculating the pressure coefficient in the Savage-Hutter-type models at the early stages of dam-break flows and collapses is proposed. In such circumstances the flow lines are significantly curved with respect to the basal surface and a special treatment of the earth-pressure coefficient is required for obtaining a satisfactory agreement with experimental data. The comparison between numerical simulations and laboratory experimental data shows an apparent improvement in describing the early stages of dam-break waves over rough beds. The comparison with experiments over smooth bed surface exhibits minor evidence of improvement. Nonetheless, in this ...