LANDSLIDE - RUNOUT

Val Pola - Italy (1987)

The Val Pola landslide, Crosta et al., 2003, was the most destructive and expensive landslide occurred recently in Italy. The 28 July Val Pola landslide in Lombardy, northern Italy claimed 27 lives and total cost of about 400 million euros including destruction of villages, road closure, monitoring and warning systems, construction of permanent outlet tunnels and earth movements. Between June and July 1987, Valtellina was hit by an exceptional meteorological event. About four times the average rainfall for the area felt between the 15 and 22 of July, while the 0 grad isotherm remained between 3500 and 4000 m a. s. l. causing rapid glacier melting. On 28 July, a volume between 34 and 43 millions of cubic meters detached from the slope. It moved rapidly down the western valley flank to reach the valley bottom. Maximum avalanche deposit thickness was about 90m and the materials was characterized by hummock surface, lobate forms, large blocks at the deposit surface and fine grained materials within the accumulation body.

In our calculation the groundwater from reality was included. Initially the pore pressures follow from a specified phreatic level. When the sliding mass runs down, the groundwater is more or less entrapped and moves together with the sliding mass downwards. Due to consolidation effects the groundwater builds very high pressures at the point of changing inclination of the Val Pola hill ; these high groundwater pressures significantly influence the overall velocity of the sliding soil + water mass. The water pressure pictures below nicely show the build of of groundwater pressures.

Vajont - Italy (1963)

In the vajont landslide 300 million cubic meter soil volume slided into the Vajont river. A soft clay layer formed the principal sliding surface. Separate material layers in the landslide can be seen with different colors in the plots below. Please realize that our numerical scheme allows for such variations over the height of a sliding mass, as apposed to depth averaged methods which cannot take into account variations in depth direction. In the picture on the left, the initial layers can be seen. The picture on the right shows the slides layers, as settled in the end stage in the Vajont river.

Arvel - Switzerland (1922)

The analysis of the Arvel slide in Switzerland shows the capabilities of our numerical scheme to model erosion of a sliding mass on other soil layers. The picture below show this erosion process at separate time points. The downward moving slide erodes the initially loose deposit material at the bottom of the domain. To obtain realistic soil material properties we found it to be necessary to include plasticity softening in the sliding mass elasto-plasticity law.

Background information

Continuum models invoke the classical conservation equations of mass, momentum and energy. They have been frequently applied through a depth-averaged approach, where properties remain constant through material columns and no exchange or internal flow of the material is allowed. In general, the adoption of a continuum approach presents the advantage of representing the complex geometry of the avalanche (i.e. flow height, deposit size and geometry, runout length, velocity distribution).

Discretisation in space and time

Sliding and flowing rock and soil masses show very large displacements and deformations. If a traditional Lagrangian Finite Element would be used for the calculations, also the finite element mesh would be subjected to these large displacements and deformations. This would lead quite rapidly  to a highly distorted mesh and, as a consequence, the calculated results become inaccurate. For this reason we decided to use a particular type of combined Eulerian-Lagrangian method. For such method, material displacements do not distort the FE mesh, such that accurate calculation results can be retained.
The discretization in space is done through  isoparametric finite elements. Several types of elements can be used in the Tochnog FE code. We often use triangular three-node elements in 2D, and hexahedral eight-node elements in 3D.
For discretization in time, Euler backward time stepping is applied, because of its high numerical stability. On top of this Euler scheme, we apply automatic time stepping and control of the number of equilibrium equations, such that a guaranteed bound is obtained of the unbalance error at the end of each time step.
Since we disconnect material displacements from the finite element mesh, state variables need to be transported through the mesh. This is done by a Streamline Upwind Petrov Galerkin method (SUPG).

Material law

For the calculations we applied classical elasto-plasticity to model the non linear path-dependent behavior of soils.
The parameters adopted for the linear elastic part are the traditional Young modulus and Poisson ratio. As yield rule, the Mohr-Coulomb rule has been used. Since we cope with granular materials, a non-associated flow rule has been applied.

Large deformation material description

As mentioned before, the displacements and strains in slides of rock and soil masses can be very large, especially for flow-like movements. For sliding and flowing masses, as in the case of large rock and debris avalanches, an updated Lagrange model is the suitable. We apply an incrementally objective Lagrangian model, based on a polar decomposition of the incremental deformation tensor.

Start of calculation

To start the numerical calculations, we must reach the initial equilibrium stress state. This section of the computation is performed through quasi-static time stepping, during which all inertial effects were left out. The assumption is that this part of the computation models the very long time nature did take to establish the initial gravity state.

Actual landslide calculation

A pre-defined slip or failure surface has been used during the performed simulations. Such pre-defined failure surface can either be determined from preliminary finite elements stability calculations, from in-situ evidences like major tension or shear cracks, or from post-event descriptions of the main failure surface.
The initial movement or occurrence of the landslide can be triggered by either lowering cohesion in time (for example, to simulate heavy rainfall effects), or imposition of a base acceleration diagram (to simulate seismic triggering).

References

G.B. Crosta, S.Imposimato and D.G. Roddeman (2003) "Numerical modeling of large landslide stability and runout". Natural Hazards and Earth System Sciences 3, 523-538.

G.B. Crosta, S. Imposimato and D.G. Roddeman (2006) "Continuum numerical modelling of flow-like landslides". NATO ARW, Landslides from massive rock slope failure, Evans, S.G., Scarascia Mugnozza, G., Strom, A., Hermanns, R., (eds) NATO Science Series, Earth and Environmental Sciences, 49,  211-232.

G.B. Crosta is from the University of Milano-Bicocca, Dipartimento di Scienze Geologiche e Geotecnologie, http://www.unimib.it

S. Imposimato and D.G. Roddeman are from FEAT.

... FEAT