Slope stability analysis and modelling

Various methods with different levels of sophistication and detail can be used for the analysis and modelling of the stability of steep periglacial rock walls. The choice of an appropriate method depends primarily on the aim of the investigation, but is also strongly influenced by the size and conditions of the investigation zone and the availability of data.

Three types of approaches can be distinguished (e.g., Soeters and Westen, 1996; Guzzetti et al., 1999; Baillifard et al., 2003). These approaches are particularly popular in landslide research, but are also used for slope stability investigations in bedrock:

1. GIS-based heuristic/statistical methods comparing the distribution of observed rock avalanches (by means of an inventory) with the distribution of environmental factors thought to cause landslides either directly or indirectly (Carrara et al., 1995; Baillifard, 2003; Carrara and Pike, 2008).

2. Kinematic stability analyses using stereographic interpretations to assess possible failure mechanisms (e.g., Norrish and Wyllie, 1996; Jaboyedoff et al., 2004b).

3. Physically-based approaches that evaluate stability using physical laws (e.g. Stead et al., 2006).

2.2.3.1 GIS-based heuristic/statistical methods

Geographic Information Systems (GIS) can be used to store, display and analyse data, thereby enabling the selection of specific combinations of mass movement parameters to better under- stand spatial distribution of various slope failure types. GIS-based slope stability investigations include qualitative heuristic or quantitative statistical modelling techniques. For the most parts, different parameter maps are used and combined to define the spatial variability of geological, geomorphological, terrain and landslide inventory parameters (e.g., Carrara et al., 1995; Van Westen et al., 2003; Günther et al., 2004; Carrara and Pike, 2008). This approach is often used

Chapter 2 

for landslide susceptibility analyses in sedimentary material; applications for steep bedrock slopes are still rare.

In heuristic methods the expert opinion making the survey is drawn upon to classify the groups. This approach is based on a combination of different parameter maps with assigned qualitative weighting values (Soeters and van Westen, 1996). Statistical approaches involve the overlaying of parameter maps with statistical calculations, and quantitative predictions can be done for areas currently free of slope failures but where similar conditions exist (Soeters and van Westen, 1996). The importance of contributing factor combinations is calculated and weighting schemes can be introduced. The type and accuracy of the available data, however, is decisive for the use of a quantitative (statistic) method (Ruff and Rohn, 2008; Ruff and Czurda, 2008).

GIS-based factor and susceptibility analyses are widely used for landslide processes. How- ever, for slope failures from bedrock, very few GIS-based factor studies exist. Giardino et al. (2004) performed qualitative classification of large slope instabilities in the Susa and Aosta Val- leys (Italy). Marquínez et al. (2003) analysed the rockfall susceptibility over a 500 km2 _{large area}

in the Cantabrian Range (North Spain). They found in a combined GIS-based analysis of talus scree, several topographic factors and lithology that the parameter topographic roughness was the most significant variable. Baillifard et al. (2003) used a GIS-based parameter rating approach for rockfall hazard mapping along a mountainous road in the Valais (Switzerland) over a length of 4 km. They performed an automatic assessment of susceptibility using the five criteria prox- imity to fault, scree slope, presence of a rock cliff, steep slope, and road for a limited area along an alpine road where a slope failure had already occurred.

Abdallah et al. (2004) used GIS-based analyses for establishing the relationships between mass movement occurrence and a comprehensive array of terrain parameters over a 2670 km2 large region of Lebanon. They demonstrate that remote sensing and GIS-based statistical corre- lations permit dual relations between the inherent parameters to mass movements to be de- fined, and the most significant ones relating to them to be detected. Their study includes all types of mass movement and not only rock slope failures. Eight parameters, i.e., lithology, prox- imity to fault zone, soil type, distance to drainage line, rainfall quantity, land cover/use, slope gradient and slope aspect were considered and the factor lithology was found to be the most in- fluencing factor on mass movement occurrence.

Ruff and Rohn (2008) and Ruff and Czurda (2008) applied an index method for landslide hazard assessment in a 114 km2 _{large area in the Eastern Alps on a working scale of 1:25,000}

(Vorarlberg, Austria). Their work is based on 107 rock and soil slides. The factor layers geo- technical class, tectonic faults, bedding conditions, slope angle, slope aspect, vegetation and ero- sion were used in the assessment and each factor was weighted with an index ranging from 0 to 1 according to its importance and iteratively combined into a landslide susceptibility map. The geotechnical class and slope angle were found to have the strongest influence on slides. These studies reveal that the choice of factors has a strong influence on the results. Therefore, a pref- erably broad and complete range of factors should be considered to avoid unbalanced or even biased analyses. The investigated factors and level of detail is also related to the size of the in- vestigation area and the investigation scale. The presented studies show that GIS-based analyses are applicable on different scales. However, the level of detail often decreases in studies over larger areas.

Scientific Background 

2.2.3.2 Kinematic stability analyses

Kinematic slope stability analysis can be used to evaluate the potential for failure and assess the failure mechanism (e.g., Goodman, 1989; Giani, 1992; Stead et al., 2001). The geometric rela- tionship between the orientation of the discontinuity planes and the orientation of the topogra- phy determine the kinematic stability of a slope. The first step in assessing a kinematic failure potential is detailed evaluation of the rock mass structure. Interpretation of the geologic struc- tural data requires the use of stereographic projections that allow the three-dimensional orienta- tion data to be represented and analyzed in two dimensions. The most commonly used projec- tions are the equal-area net and the polar net (e.g., Hoek and Brown, 1980; Hoek and Bray, 1981; Norrish and Wyllie, 1996; Figure 2.7.1). For such kinematic analyses the orientations of a large number of geological discontinuities have to be measured in situ.

New methods for the detection and measurement of geological discontinuities were devel- oped based on high-resolution DTMs (Figure 2.7.2). The increasing availability and precision of DTMs aids in the assessment of landslide prone areas where is very limited availability of on- site data (e.g. Derron et al., 2005). From such DTMs with resolution in cm-dm range, topog- raphic parameters, morpho-tectonic features and geological structures can be extracted. The main discontinuity sets can be distinguished and their geometrical pattern determined. There- fore, a preliminary assessment of potentially unstable areas may be performed with kinematic analyses using only a DTM (e.g., Jaboyedoff et al, 1999; Broccolato et al., 2006).

Further structural and stability analysis with a DTM is made possible by the recent devel- opment of geologically oriented GIS tools (e.g, Günther, 2003; Jaboyedoff et al., 2004c; Mote, 2005; Broccolato et al., 2006). Such tools have been applied, for example, for preliminary rock- fall hazard assessment in Norway (Derron et al., 2005) and kinematic analyses of the Eiger rockslide in Switzerland (Oppikofer et al., 2008). Aksoy and Ercanoglu (2007) developed a dif- ferent approach for kinematic analyses of discontinuity-controlled rock slope instabilities, where kinematic analyses of DTMs are combined with fuzzy set theory.

Figure 2.7: 2.7.1 shows a comparison of the measurements of poles and planes made on a DTM (A) and in the field (B) in the lower hemi- sphere stereographic projection. 2.7.2 shows a colour shaded DTM based on the COLTOP-3-D method by Jaboyedoff et al. (2007), where each position in the lower hemisphere stereographic projection has a corresponding colour value. (Source: Derron et al., 2005)

Chapter 2 

2.2.3.3 Numerical slope stability modelling

Numerical slope stability modelling methods provide a powerful tool for the assessment of fail- ure mechanisms by giving approximate solutions with respect to physical processes, which would not be solvable using conventional techniques (e.g. kinematic analysis). Many rock slope stability problems involve complex geometry, lithology, in situ stresses, and hydraulic conditions, and are further complicated by coupling between these various parameters. For such complex slope stability analyses numerical methods are often required. Numerical methods used for rock slope stability analysis in 2-D and 3-D may be divided into three approaches: continuum, dis- continuum and hybrid modelling. The different approaches are described in detail in Stead et al. (2001, 2006) and Eberhardt et al. (2004).

Detailed topographic, geomechanical and geotechnical characteristics of the rock mass are the basic input data necessary for numerical slope stability modelling. The quality of the input data made available for the analysis may vary such that the objective of the numerical analysis focuses on prediction of a slope failure when high quality in situ instrumentation data is present, or in cases where the data is limited, as providing a means to establish and understand the dominant mechanisms that may affect the behaviour of a slope (Eberhardt, 2006).

Bhasin et al. (2004) performed dynamic analysis and parametric studies for the rock slope stability problem at Oppstadhornet and Kveldsvik et al. (2009) for the Aknes rock slope (both western Norway) using the distinct element method UDEC. The purpose of analysis was to gain insight into the deformation mechanism of the rock slope and to estimate the volume of rock mass that could potentially slide when subject to dynamic forces such as earthquakes. This estimation was required in order to assess the runup heights of waves (tsunami) in a fjord that could potentially be caused by the rock slide. Similar analyses were performed in the area of the Tafjord slide (Norway, 1934), to assess whether subsequent slides were to be expected. For the Randa rock avalanche (Switzerland, Eberhardt et al., 2004; Willenberg, 2004), Brenva rock ava- lanche (Barla and Barla, 2001) and the Tschierva rock avalanche (Paper V), back-calculations of the slope failure were performed to evaluate failure mechanism and contributing factors. Cou- pled hydromechanical modelling was performed by Gugliemi et al. (2008), Bonzanigo et al. (2001) and Paper V to assess the influence of water pressure on slope instability.

Günther et al. (2006) developed a GIS-based specification tool for interactive setup and parameterisation of numerical models with GIS data to be processed with UDEC. They repre- sent a first approach to interlinking a GIS (Geographical Information System) with a 2-D nu- merical simulation scheme (UDEC) for the modelling of rock slope instability phenomena on vertical 2-D cross sections through a GIS-based specification tool.

These selected studies have shown that numerical slope stability modelling is possible based on a range of elementary topographic, geological and geotechnical information. However, for sophisticated investigations and forecasting issues, extensive instrumentation of the slopes is re- quired in order to obtain reference values of displacements, water pressure etc. Such permanent geophysical installations are very rare in high-alpine rock walls (c.f. chapter 2.2.2.2). Studies of alpine rock slope instabilities have shown that numerical models are a powerful tool for the as- sessment of failure mechanisms (e.g., Barla and Barla 2001; Eberhardt et al., 2004), but the nec- essary level of topographic and geotechnical detail limits their application for prediction issues.

3 Conceptual Framework