This paper presents recommended methodologies for the quantitative analysis of landslide hazard, vulnerability and risk at different spatial scales (site-specific, local, regional and national), as well as for the verification and validation of the results. The methodologies described focus on the evaluation of the probabilities of occurrence of different landslide types with certain characteristics. Methods used to determine the spatial distribution of landslide intensity, the characterisation of the elements at risk, the assessment of the potential degree of damage and the quantification of the vulnerability of the elements at risk, and those used to perform the quantitative risk analysis are also described. The paper is intended for use by scientists and practising engineers, geologists and other landslide experts.

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Recommendations for the quantitative analysis of landslide risk

Dilatancy is often considered a unique function of the stress ratio η = q/p′, in terms of the triaxial stress variables q and p′. With this assumption, the direction of plastic flow is uniquely related to η, irrespective of the material internal state. This obviously contradicts the facts. Consider two specimens of the same sand, one is in a loose state and the other in a dense state. Subjected to a loading from the same η, the loose specimen contracts and the dense one dilates. These two distinctly different responses are associated with a single η but two different values of dilatancy, one positive and the other negative. Treating the dilatancy as a unique function of η has developed into a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing). A theory is presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics. Micromechanical analysis is u...

Dilatancy for cohesionless soils

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Semi-implicit finite difference methods for three-dimensional shallow water flow

The paper outlines the theory of generalized plasticity in which yield and plastic potential surfaces need not be explicitly defined, and shows how a very effective general model describing the behaviour of sands and of clays under monotonic or transient loading can be developed. The model is currently one of the simplest and yet one of the most effective ones for describing the full range of behaviour.

The hierarchical structure of the model limits the number of parameters which have to be experimentally determined for a given material to those strictly necessary for the problem at hand.

A discussion of currently used models is included.

Generalized plasticity and the modelling of soil behaviour

This paper describes recent advances in stability analysis that combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load. These methods, known as finite-element limit analysis, do not require assumptions to be made about the mode of failure, and use only simple strength parameters that are familiar to geotechnical engineers. The bounding properties of the solutions are invaluable in practice, and enable accurate limit loads to be obtained through the use of an exact error estimate and automatic adaptive meshing procedures. The methods are very general, and can deal with heterogeneous soil profiles, anisotropic strength characteristics, fissured soils, discontinuities, complicated boundary conditions, and complex loading in both two and three dimensions. A new development, which incorporates pore water pressures in finite-element limit analysis, is also described. Following a brief outline of the new techniques, stability solutions ...

Geotechnical stability analysis

This paper extends the bounding surface, generalized plasticity, model of part I to reproduce the behaviour of sands under both static and transient loading. The essential features of the first model are preserved but the following changes are introduced: (I) the shape of the yield surface is modified; (II) a non-associative flow rule is introduced; (III) the hardening parameter of the bounding surface includes not only volumetric but also deviatoric plastic strain; (IV) plastic volumetric and deviatoric strains are introduced during unloading. Each of these modifications can be introduced separately in a hierarchical manner to model in an improved way the behaviour of sands. Good comparison with experimental observations is recorded. The simplicity of the original model is preserved with modifications being introduced progressively to model rising complexity of the phenomena. See also IRRD 288366. (Author/TRRL)

Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands

Explicit dynamic codes which are used currently for the study of plastic deformations in impact, or with some modification for metal forming, suffer two serious limitations.



First, only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing.



Second, even with the use of such elements, special devices such as reduced integration must be introduced to avoid locking and reduce costs. These necessitate complex hour glass control, mending-type procedures.



The main difficulties are those due to the need of treatment of (almost) incompressible deformation modes. Recently, similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem, thus allowing an almost unrestricted choice of element interpolations. © 1998 John Wiley & Sons, Ltd.

Triangles and tetrahedra in explicit dynamic codes for solids

This paper presents a depth-integrated model that can be used to simulate the flowslides, mudflows and debris flows that are caused by the failure of tailing dams, mining waste dumps and other similar structures. The sliding mass is first determined using a coupled elastoplastic finite element code and a suitable constitutive equation. Once failure has been triggered, propagation of the mobilised material is analysed considering flow properties averaged over depth. A simple law of pore pressure dissipation is postulated for cases in which the consolidation and propagation times are of the same order of magnitude.

Modelling tailings dams and mine waste dumps failures

Several models describing soil response under cyclic loading and the 'liquefaction' potential have been introduced in recent years with limited success. Most of these are over-complex for realistic parameter identification and have not been widely adopted for practical use. This paper introduces a relatively simple modification of the well-known critical state model which accounts reasonably well for the phenomena observed under cyclic tests and indeed improves the performance of critical state models in monotonic loading. This model is compared with experimental results and with the 'densification model' introduced earlier by the authors and shows good predictive capacity. The model is of a generalized plasticity-bounding surface type. In its simplest form, suitable for clay-like materials, it requires the identifications of a single parameter additional to those required for a standard, critical state model. See also IRRD 288367. (Author/TRRL)

M. Pastor

Papers

Generalized plasticity and the modelling of soil behaviour

Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands

Triangles and tetrahedra in explicit dynamic codes for solids

Modelling tailings dams and mine waste dumps failures

Simple model for transient soil loading in earthquake analysis. I. Basic model and its application