Elsevier

Geomorphology

Volume 103, Issue 1, 1 January 2009, Pages 136-142
Geomorphology

Finite Element simulation of a slow moving natural slope in the Upper-Austrian Alps using a visco-hypoplastic constitutive model

https://doi.org/10.1016/j.geomorph.2007.10.019Get rights and content

Abstract

A large-size creeping natural slope was simulated with the Finite Element (FE) method, using a visco-hypoplastic material model, which describes the mechanical behaviour of cohesive soils, allowing for viscous effects (i.e. creep, relaxation and rate-dependence of stiffness). First, the required material parameters were determined by means of standard geotechnical laboratory tests using representative soil samples taken from the slope. Then a FE mesh of a slope section was constructed and boundary conditions were established. The slope movements were simulated and compared with inclinometer measurements, which were available for a period of 16 years. The calculation results are in good agreement with the observed velocities. A parameter study was carried out in order to assess the influence of slope angle, initial void ratio, material parameters as well as their spatial distribution.

Introduction

Many slopes in cohesive soils exhibit gravity-driven creep movements as a result of the viscous behaviour of the soil material. Not only do these movements pose a threat to infrastructure and buildings on or below the slope, they may also represent an initial stage of active landslides or earth flows with even more detrimental impact. Hence, it is important to be able to predict the behaviour of creep movements in slopes, i.e. to predict displacements and velocities as well as their evolution over time. For this reason conventional limit equilibrium analysis is meaningless, as this method only calculates a static state of the slope. Numerical models, on the other hand, can be a useful tool, provided that an appropriate constitutive law is used that describes the material behaviour in an accurate way. This study focuses on creep movements in slopes consisting of cohesive soil materials that exhibit viscous behaviour, i.e. creep (strain rate  0 and stress rate = 0), relaxation (strain rate = 0 and stress rate  0) and strain-rate dependent stiffness and shear strength. Therefore, a constitutive equation should be used that takes these phenomena into account. In literature many studies involving numerical simulations of creeping slopes using elastoplastic and elasto-viscoplastic equations can be found (e.g. Cristescu et al., 2002, Desai et al., 1995, Samtami et al., 1996, Vulliet and Hutter, 1988). For the viscous part of deformation most of these studies use Bingham, Newton or Norton creep laws. However, many of these material models are very complicated with respect to the determination of the required material parameters. Their calibration cannot always be easily performed with standard soil mechanical laboratory tests, as is the case with visco-hypoplasticity. Furthermore, in contrary to many of the above mentioned elasto-viscoplastic equations, in the visco-hypoplastic model used in this study there is a strict separation between material constants and state dependent variables (i.e. stress, density and the most recent deformation history).

The visco-hypoplastic equation has already been validated for numerous geotechnical problems, including simulation of slope deformation due to open pit mining, in which quantitative accurate results could be achieved (e.g. Karcher, 2003).

In a previous study the model was applied on a large-size natural creeping slope ‘Stambach’ in the province of Upper-Austria by means of a numerical element test programme, in which small soil segments were simulated (Van den Ham et al., 2006). Despite the strongly simplified initial and boundary conditions, which were a consequence of the simplicity of the programme used (a programme that was originally developed for simulating laboratory element tests), results fitted fairly well with measured slope movements. However, inherent to the programme, no spatial influences such as material heterogeneities could be taken into account. Also spatial patterns of displacement and velocities could not be analysed. Therefore in this study the Stambach slope movements were simulated with the Finite Element (FE) method, making simulation of larger slope sections and incorporation of the above mentioned spatial factors possible.

The main objective of this paper is to show the applicability of the visco-hypoplastic equation using the FE method for predicting creep movements. Furthermore, it is attempted to quantify the influence of simplifications and assumptions concerning initial state variables, boundary conditions, material distribution and slope geometry due to the limited availability of subsurface information at the one hand and the limited possibility to incorporate the available information in the model at the other hand. By means of a parameter study it was tested how the model responds on different slope angles, initial void ratios, material parameters and their spatial distribution.

Section snippets

Visco-hypoplastic constitutive model

The visco-hypoplastic equation represents a tensorial, incremental non-linear function, describing the stress–strain–time behaviour of soils with viscous properties. The incremental stiffness, by which strain rate is related to stress rate, depends on density, effective mean pressure and most recent deformation history. The material law was developed as an extension of hypoplasticity, which describes the behaviour of cohesionless granular soils and which distinguishes itself from

Characterisation of the slope movements

The Stambach slide is a dormant earth flow located in the province Upper-Austria, above the village of Bad Goisern in the Traun Valley. The area belongs to the ‘Hallstatt zone of Bad Ischl-Bad Aussee’, a tectonic subunit of the Northern Calcareous Alps, and is formed mainly of Permian to Jurassic sedimentary rocks. The geological setting has strongly determined the present geomorphology of the region as well as the history of the slope studied. The landscape is characterised by gentle slopes,

Methods

In order to develop a FE model that is able to simulate the observed fields of displacement and velocities and with which the parameter study can be performed, the following steps were passed through: (1) determination of material parameters and testing whether the visco-hypoplastic law is able to describe the soil behaviour of the soils studied by back-predicting the element tests with an element test programme in which the material law was implemented, (2) construction of a FE mesh and

Results and discussion

Table 2 shows the visco-hypoplastic material parameters of Haselgebirge and Fleckenmergel. The values of Iv are in agreement with the classification of both materials to be clays of low to medium plasticity.

Fig. 7 shows the observed and simulated decrease of void ratio (e) over depth as well as the influence using initial OCR's varying between 1.5 and 5. Increasing the initial OCR from 1.5 to 5 leads to a reduction of void ratio of less then 0.1 for all depths. It has to be mentioned that the

Conclusions and outlook

This paper deals with the simulation of a creeping natural slope by means of the visco-hypoplastic law and the FE method. The model was designed in such a way that the influence of spatial and temporal discretisation was excluded and the available field information concerning material distribution, initial state variables and slope hydrological regime could be incorporated. The results show that, following the applied methodology, the observed slope movements can be simulated in a quite

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