Savage Hutter Type Research Articles

Dynamic process simulation with a Savage-Hutter type model for the intrusion of landslide into river

Natural damming of rivers by mass movements is a very common and potentially dangerous phenomena which has been documented all over the world. In this paper, a two-layer model of Savage-Hutter type is presented to simulate the dynamic procedure for the intrusion of landslide into rivers. The two-layer shallow water system is derived by depth averaging the incompressible Navier-Stokes equations with the hydrostatic assumption. A high order accuracy scheme based on the finite volume method is proposed to solve the presented model equations. Several numerical tests are performed to verify the realiability and feasibility of the proposed model. The numerical results indicate that the proposed method can be competent for simulating the dynamic process of landslide intrusion into the river. The interaction effect between both layers has a significant impact on the landslide movement, water fluctuation and wave propagation.

Numerical simulation of tsunamis generated by landslides on multiple GPUs

In this work we propose a two-layer Savage–Hutter type model that is the natural extension of the 1D system proposed by E. D. Fernández-Nieto et al in 2008 to simulate tsunamis generated by landslides. We describe a single GPU and a multi-GPU implementation of this model using MPI and the CUDA framework over structured meshes. The distributed implementation is tested for several artificial and realistic problems using up to 24 GPUs. We also propose a static and a dynamic load balancing algorithm in order to deal with the unbalanced computational load due to different amount of wet and dry areas among the subdomains. The validity of the model is tested by simulating the tsunami occurred in Lituya Bay, Alaska, in 1958. Numerical experiments show the efficiency of the multi-GPU solver, the usefulness of the load balancing algorithms and the validity of the model to simulate real tsunamis generated by landslides.

A two-layer model for simulating landslide dam over mobile river beds

Landslides can block mountainous streams and form landslide dams to threaten downstream residents. It is necessary for reliable methods to predict landslide dam dynamic for risk assessment. In this paper, we present a two-layer model of Savage-Hutter type to simulate the dynamic evolution of landslide dam which take account of the erosion of river bed. The two-layer shallow water system is derived by depth-averaging the incompressible Navier-Stokes equations with the hydrostatic assumption integrated of the erosion model of river bed. The effect of excess pore water pressure is considered in the erosion process. A high order accuracy scheme based on Roe-type solver is used to discretize the present model. Finally, several numerical tests are performed to verify the stability of the algorithm and reliability of the model. Numerical results indicate that the erosion effect enhances the huge destructiveness of landslide and increase the possibility of river blocked by landslides. The impact of excess pore water pressure on erosion process should be considered.

Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis

Two layer Savage–Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the resulting solution uncertainty (UQ) is a crucial task in geophysics. We propose a novel paradigm for UQ that combines the recently developed IFCP spatial discretizations with the recently developed Multi-level Monte Carlo (MLMC) statistical sampling method and provides a fast, accurate and computationally efficient framework to compute statistical quantities of interest. Numerical experiments, including realistic simulations of the Lituya Bay mega tsunami, are presented to illustrate the robustness of the proposed UQ algorithm.

Central-Upwind Scheme for Savage–Hutter Type Model of Submarine Landslides and Generated Tsunami Waves

Abstract. We develop a new central-upwind scheme for a one-dimensional Savage–Hutter type model of submarine landslides and generated tsunami waves. Our scheme exactly preserves physically relevant steady-states, preserves positivity of water depth, is insensitive to choice of discretization of nonconservative products, and properly incorporates friction inherent in the model. We apply our scheme to a variety of test problems and the numerical results clearly demonstrate a high accuracy and robustness of the proposed method.

Physically-based modelling of granular flows with Open Source GIS

Abstract. Computer models, in combination with Geographic Information Sciences (GIS), play an important role in up-to-date studies of travel distance, impact area, velocity or energy of granular flows (e.g. snow or rock avalanches, flows of debris or mud). Simple empirical-statistical relationships or mass point models are frequently applied in GIS-based modelling environments. However, they are only appropriate for rough overviews at the regional scale. In detail, granular flows are highly complex processes and physically-based, distributed models are required for detailed studies of travel distance, velocity, and energy of such phenomena. One of the most advanced theories for understanding and modelling granular flows is the Savage-Hutter type model, a system of differential equations based on the conservation of mass and momentum. The equations have been solved for a number of idealized topographies, but only few attempts to find a solution for arbitrary topography or to integrate the model with GIS are known up to now. The work presented is understood as an initiative to integrate a fully physically-based model for the motion of granular flows, based on the extended Savage-Hutter theory, with GRASS, an Open Source GIS software package. The potentials of the model are highlighted, employing the Val Pola Rock Avalanche (Northern Italy, 1987) as the test event, and the limitations as well as the most urging needs for further research are discussed.

Analysis of run-up of granular avalanches against steep, adverse slopes and protective barriers

The purpose of this study was to determine whether run-up of rapid landslides or avalanches against protective dykes or walls placed perpendicular to the path can be predicted using a dynamic model based on shallow-flow assumptions. A series of laboratory experiments were carried out involving rapid flow of dry sand in a flume, arrested by a steep adverse slope. The barrier slope was varied and included a perpendicular wall. A curved transition of varying radius separated the path from the barrier. The dynamic internal and basal friction angles of the sand were determined by independent testing. The results were analysed using a Savage–Hutter type model. A shock wave was observed as the flow approached the barrier toe and the model had to be improved by an original velocity-smoothing algorithm to prevent numerical instability. The new model is capable of simulating the entire process of run-up of the leading edge against the barrier face, deposition of the sand behind the barrier, and backward migration of the shock wave. Comparisons between experiment and analysis results are presented. The model tends to overpredict the vertical run-up in cases where the barrier slope is steep. The results of traditional run-up formulas are also compared.

Numerical modeling of seismic triggering, evolution, and deposition of rapid landslides: Application to Higashi–Takezawa (2004)

AbstractA mathematical model is developed for the dynamic analysis of earthquake‐triggered rapid landslides, considering two mechanically coupled systems: (a) the accelerating deformable body of the slide and (b) the rapidly deforming shear band at the base of the slide. The main body of the slide is considered as a one‐phase mixture of Newtonian incompressible fluids and Coulomb solids sliding on a plane of variable inclination. The evolution of the landslide is modeled via a depth‐integrated model of the Savage–Hutter type coupled with: (a) a cyclic hysteretic constitutive model of the Bouc–Wen type and (b) Voellmy's rheology for the deformation of the material within the shear band. The original shallow‐water equations that govern the landslide motion are appropriately reformulated to account for inertial forces due to seismic loading, and to allow for a smooth transition between the active and the passive state. The capability of the developed model is tested against the Higashi–Takezawa landslide. Triggered by the 2004 Niigata‐ken Chuetsu earthquake, the slide produced about 100m displacement of a large wedge from an originally rather mild slope. The mechanism of material softening inside the shear band responsible for the surprisingly large run‐out of the landslide is described by a set of equations for grain crushing‐induced pore‐water pressures. The back‐analysis reveals interesting patterns on the flow dynamics, and the numerical results compare well with field observations. It is shown that the mechanism of material softening is a crucial factor for the initiation and evolution of the landslide, while viscoplastic frictional resistance is a key requirement for successfully reproducing the field data. Copyright © 2009 John Wiley & Sons, Ltd.

A new Savage–Hutter type model for submarine avalanches and generated tsunami

In this paper, we present a new two-layer model of Savage–Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e.g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature. We prove that the model verifies an entropy inequality, preserves water at rest for a sediment layer and their solutions can be seen as particular solutions of incompressible Euler equations under hydrostatic assumptions. Buoyancy effects and the centripetal acceleration of the grain movement due to the curvature of the bottom are considered in the definition of the Coulomb term. We propose a two-step Roe type solver to discretize the presented model. It exactly preserves water at rest and no movement of the sediment layer, when its angle is smaller than the angle of repose, and up to second order all stationary solutions. Finally, some numerical tests are performed by simulating submarine and sub-aerial avalanches as well as the generated tsunami.

On new erosion models of Savage–Hutter type for avalanches

In this work, we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations. This model has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system. It has physically relevant steady state solutions, and, for constant slope, it gives a particular exact solution to the incompressible hydrostatic Euler equations. Then, we propose a simplified model, for which the energy conservation holds only up to third-order terms. Its associated eigenvalues depend on the mass exchange velocity between the static and moving layers. We show that a simplification used in some previously proposed models gives a non-consistent energy equation. Our models do not use, nor provide, any equation for the moving interface, thus other arguments have to be used in order to close the system. With special assumptions, and in particular small velocity, we can nevertheless obtain an equation for the evolution of the interface. Furthermore, the unknown parameters of the model proposed by Bouchaud et al. (J Phys Paris I 4,1383–1410, 1994) can be derived. For the quasi-stationary case we compare and discuss the equation for the moving interface with Khakhar’s model (J Fluid Mech 441,225–264, 2001).

A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows

We introduce a new model for shallow water flows with non-flat bottom. A prototype is the Saint Venant equation for rivers and coastal areas, which is valid for small slopes. An improved model, due to Savage–Hutter, is valid for small slope variations. We introduce a new model which relaxes all restrictions on the topography. Moreover it satisfies the properties (i) to provide an energy dissipation inequality, (ii) to be an exact hydrostatic solution of Euler equations. The difficulty we overcome here is the normal dependence of the velocity field, that we are able to establish exactly. Applications we have in mind concern, in particular, computational aspects of flows of granular material (for example in debris avalanches) where such models are especially relevant. To cite this article: F. Bouchut et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).