Numerical modelling of landslide runout. A continuum mechanics approach

Increasing population density and development of mountainous terrains bring human settlements within reach of landslide hazards. Perhaps the most serious threat arises from small, high frequency landslides such as debris flows and debris avalanches. On the other hand, large and relatively rare rock avalanches also constitute a significant hazard, due to their prodigious capacity for destruction. Such landslides involve the spontaneous failure of entire mountain slopes, involving volumes measured in tens or hundreds million m3 and travel distances of several kilometres. Flow-like movements of rocks can be identified among the most dangerous and damaging of all landslide phenomena. Since it often proves impossible to mitigate their destructive potential by stabilising the area of origin, risk analyses, including predictions of runout, have to be performed. With these predictions losses can be reduced, as they provide means to define the hazardous areas, estimate the intensity of the hazard, and work out the parameters for the identification of appropriate protective measures. At the same time, reliable predictions of runout can help to avoid exceedingly conservative decisions regarding the development of hazardous areas. Risk evaluation of these events requires the comprehension of two fundamental problems: the initiation and the runout. Even though the specification of the initial conditions is also a primarily problem, which is not yet resolved, the runout, that is the flowing and stopping phases of the mass, is here analysed. Numerical simulation should provide a useful tool for investigating, within realistic geological contexts, the dynamics of these flows and of their arrest phase. In the 1970’s the most widely used and perhaps earliest model proposed for the analysis of rockslides and similar phenomena was that of a rigid block on an inclined plane. In recent years, new and more sophisticated models based on a continuum mechanics approach have emerged. Together with continuum mechanics models, a noteworthy type of modelling is that based on a discontinuum mechanics approach, in which the run out mass is modelled as an assembly of particles moving down along a surface. It is probably fair to state that Savage and Hutter in 1989 developed the first continuum mechanical theory capable of describing the evolving geometry of a finite mass of a granular material and the associated velocity distribution as an avalanche slides down inclined surfaces. Their model provided a more complete analysis of such flows than previous models had done, and its extension as well as comparison with laboratory experiments demonstrated it to be largely successful. A continuum mechanics approach assumes that during an avalanche, the characteristic length in the flowing direction is generally much larger than the vertical one, e.g. the avalanche thickness. Such a long-wave scaling argument has been widely used in derivation of continuum flow models. This leads to depth-averaged models governed by generalized Saint Venant equations. Nowadays, these models provide a fruitful tool for investigating the dynamics and extent of avalanches. Anyway, whatever the applied analytical model, results of a numerical simulation depend on the value assigned to the constitutive parameter of the assumed rheology. The aim of the dissertation is the development and validation of a three dimensional numerical model able to run analyses of propagation on a complex topography and the setting of a procedure direct to define some reference values for characteristic parameters of an assumed rheology. Case histories having a different runout path and material type are analysed and compared, the obtained values could be considered useful guidelines to study a potential landslide. The choice of a certain approach rather than another is the result of a careful analysis of advantages and disadvantages of each existing method. All choices are made never forgetting to remain focused on real problems and real behaviour of a mass. By consequence, each problem tackled and solved is directed to guarantee more realistic results. Whatever the chosen numerical approach, it is fundamental to know in detail the type of phenomenon that will be studied. In this sense, it is important to learn from past events and to always have on mind that each analysed problem is not abstract but it is linked to a real site. In the present work, a continuum mechanics approach has been followed. The original version (SHWCIN) of the implemented three dimensional code was developed at the Institut de Physique du Globe de Paris but before using it to run analysis of propagation on a complex topography many fundamental changes are necessary. Trying to reduce the uncertainty range of values to be assigned in prediction to rheological parameters, the numerical code DAN (Hungr, 1995) is applied to back analyse a set of case histories of landslides selected from literature. For prediction, the main limitation of DAN is due to the fact that it reduces a complex and heterogeneous 3D problem into an extremely simple formulation and the width of propagation is a part of the input data. But, when a back analysis is run, the geometry of propagation is already known. Therefore, the limits of DAN in some way disappear. Also, cases for which a DEM (Digital Elevation Model) is not available can be analysed. Moreover, advantages in using this code are mainly due to its simplicity, it makes possible an immediate and rapid numerical simulation of many real cases. The methodology here proposed consists in using DAN to run back analyses of as many case histories as possible and the new three dimensional code to predict propagation of a mass on a complex topography. It is important to underline that when values obtained from back analyses are used to simulate a potential landslide, only cases having similar characteristics (e.g. run out area shape, material type) can be compared. To guarantee correctness of this approach it is necessary to verify that DAN results, if used as input data in a three dimensional numerical code, give approximately the same solution. Cases for which a DEM pre-collapse is available are analysed with both DAN and the new code. After a critic overview of landslide classifications and a detailed description of those phenomena known as rock avalanches (Ch. 2), a description of existing propagation methods has been done, underlining advantages and disadvantages of each considered approach (Ch. 3). On the basis of possibility of application on analysis of real cases a continuum mechanics approach has then been followed, two numerical codes have been analysed: SHWCIN and DAN (Ch. 4). The SHWCIN code was originally used to carry out simple numerical simulations of a mass released from a gate or from a hemi-spherical cap on an inclined plane and results were analysed considering the centre line section. To simulate the movement on a complex three dimensional topography, the code has been numerically implemented allowing to: reduce mesh-dependency effects on results of propagation by using an irregular mesh, change gravity components as a function of the considered topography, change earth pressure coefficients in a condition of anisotropy of normal stresses, take into account both different constitutive laws and pore water effects. Each of these changes has been carefully validated. Once the final version of the code was obtained it has been tested through numerical analysis of laboratory tests and back analysis of case histories obtained from literature (Ch. 5). In order to create a database of well described phenomena and rheological parameters, that can be useful guidelines when prediction is the aim of an analysis, case histories have been analysed with DAN following a procedure that gives the possibility of calibrating the model in order to obtain the best value for each of the parameters required by the assumed rheology (Ch. 6).