# Are real-world shallow landslides reproducible by physically-based models? Four test cases in the Laternser valley, Vorarlberg (Austria)

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## Abstract

In contrast to the complex nature of slope failures, physically-based slope stability models rely on simplified representations of landslide geometry. Depending on the modelling approach, landslide geometry is reduced to a slope-parallel layer of infinite length and width (e.g., the infinite slope stability model), a concatenation of rigid bodies (e.g., Janbu’s model), or a 3D representation of the slope failure (e.g., Hovland’s model). In this paper, the applicability of four slope stability models is tested at four shallow landslide sites where information on soil material and landslide geometry is available. Soil samples were collected in the field for conducting respective laboratory tests. Landslide geometry was extracted from pre- and post-event digital terrain models derived from airborne laser scanning. Results for fully saturated conditions suggest that a more complex representation of landslide geometry leads to increasingly stable conditions as predicted by the respective models. Using the maximum landslide depth and the median slope angle of the sliding surfaces, the infinite slope stability model correctly predicts slope failures for all test sites. Applying a 2D model for the slope failures, only two test sites are predicted to fail while the two other remain stable. Based on 3D models, none of the slope failures are predicted correctly. The differing results may be explained by the stabilizing effects of cohesion in shallower parts of the landslides. These parts are better represented in models which include a more detailed landslide geometry. Hence, comparing the results of the applied models, the infinite slope stability model generally yields a lower factor of safety due to the overestimation of landslide depth and volume. This simple approach is considered feasible for computing a regional overview of slope stability. For the local scale, more detailed studies including comprehensive material sampling and testing as well as regolith depth measurements are necessary.

## Keywords

Slope failure Landslide geometry Infinite slope stability model Janbu’s model r.slope.stability Differential digital terrain model## Introduction

Landslides are a common geomorphological feature in mountain regions often putting lives and infrastructure at risk. The term “shallow landslides” typically refers to translational sliding movements of soil material (earth and/or debris), characterized by a pre-defined, planar sliding surface in a depth of up to 2.0 m (e.g., Cruden and Varnes 1996; Hungr et al. 2014). In the past decades, the Laternser valley (Vorarlberg, Austria) was repeatedly affected by rainfall-triggered shallow landslides (Andrecs et al. 2002; Markart et al. 2007). Since the 1950s, more than 800 shallow landslides have been documented in a comprehensive shallow landslide inventory (Zieher et al. 2016). To be aware of the associated risks, it is necessary to assess shallow landslide susceptibility, hazard, and risk area-wide. Various techniques have been proposed for landslide susceptibility modelling/mapping (i.e., heuristic, statistically-, and physically-based). Amongst them, physically-based landslide susceptibility models employ physical laws to assess slope stability. They typically rely on the limit equilibrium concept relating stabilizing to destabilizing forces. The proposed techniques differ in the complexity of the considered landslide geometry (shape of the potential sliding surface) in two (e.g., Bishop 1955; Fellenius 1927; Janbu 1954; Morgenstern and Price 1965) and three dimensions (e.g., Hovland 1977; Hungr 1987; Lam and Fredlund 1993; Mergili et al. 2014). While slope failures show complex geometrical shapes in nature, their representation in physically-based slope stability models is simplified. Shallow landslides are approximated by either a slope-parallel layer of infinite length and width (e.g., the infinite slope stability model, ISSM), a concatenation of rigid bodies of infinite width (e.g., Janbu’s model), or a representation of discrete, 3D units (columns on the basis of raster cells; e.g., the r.slope.stability model, RSS). Consequently, the considered sliding surfaces are either planar (ISSM), an irregular 2D polyline (2D models) or an irregular 3D surface (3D models). Furthermore, some of these approaches include inter-slice forces between the geometrical subunits (e.g., Janbu 1954) while others assume them to cancel each other out (e.g., Fellenius 1927). The result of physically-based slope stability models based on the limit equilibrium concept is a dimensionless factor of safety (FOS) which is a quantitative measure of slope stability. Slope failures are predicted, if the FOS falls below 1. In engineering, these models are usually applied at local scale to evaluate the stability of a single slope unit in the context of a specific engineering task. For the assessment of slope stability at catchment scale, the ISSM has proven feasible in combination with geographical information systems (GIS). Most spatially distributed physically-based shallow landslide susceptibility models include the infinite slope approach, often combined with an infiltration model (e.g., Baum et al. 2008; Dietrich et al. 1995). Recently, models including a more complex landslide geometry (e.g., ellipsoidal and truncated sliding surfaces) have been implemented in GIS (Mergili et al. 2014; Xie et al. 2006). For all these physically-based slope stability models, the result is a FOS map which is a spatially distributed quantitative measure of slope stability.

Besides geotechnical input parameters characterizing the involved material, physically-based models require data on topography (e.g., slope angle) and depth of the pre-defined sliding surface. Topographic data are usually derived from digital terrain models (DTMs), which have become readily available. The depth of the pre-defined sliding surface is more difficult to obtain. It can be assessed by (i) direct measurements (Andrecs et al. 2002; Wiegand et al. 2013), (ii) means of geophysics (Davis and Annan 1989; Sass 2007), or modelling (Dietrich et al. 1995; Catani et al. 2010). Moreover, depth and volume of past landslides can be assessed efficiently with the help of multi-temporal remotely sensed elevation data (Zieher et al. 2016).

Numerous studies have focussed on the area-wide assessment of slope stability at catchment scale by applying physically-based slope stability models which include the infinite slope approach (e.g., Baum et al. 2005; Gioia et al. 2016; Montrasio et al. 2011). In such studies, little attention has been paid to the effect of the simplified landslide geometry considered by the ISSM. However, this issue must be regarded for the interpretation of the resulting FOS maps. In this paper, four slope stability models including different representations of landslide geometry are tested at four sites affected by shallow landslides, where information on soil material properties and geometries of slope failures are available. Simplifications of the models with regard to landslide geometry are tested against real-world geometries of the selected cases. The applicability of the widely used infinite slope stability model is investigated in detail. The ISSM’s predictions are compared to the results of models with 2D (Janbu’s model) and 3D (r.slope.stability, 3DVA) approximations of the slope failures. For the comparison of the methods, models with comparable physical basis but different geometrical representations of the slope failures were chosen. Further influencing factors such as effects of high vegetation (root cohesion) or variable soil saturation were neglected. Omitting the root cohesion together with the assumption of completely saturated conditions is considered as worst-case scenarios. Under equal conditions for the applied models, the results are better comparable.

- 1.
To conclude on the ability of the tested models to reproduce the observed landslides with the given parameterization;

- 2.
To learn about the effects of different representations of landslide geometry on the respective model results;

- 3.
On this basis, to identify potential pitfalls in slope stability modelling.

The present article is divided into four main sections. First, the study area including the landslide-triggering rainfall event in August 2005 is described in the “Study area” section. The conducted laboratory experiments, the landslide geometry data, and the modelling approaches are introduced in the “Materials and methods” section. Model results and comparisons are presented and discussed in the “Results and discussion” section. Finally, concluding remarks summarizing the key findings are provided in the “Conclusions” section.

## Study area

Metadata for the four sampled landslide sites and results of the conducted laboratory tests

Parameters | BIN | BON | MAZ | ROH |
---|---|---|---|---|

Latitude (degree) | 47.2722 | 47.2673 | 47.2679 | 47.2699 |

Longitude (degree) | 9.7040 | 9.7256 | 9.7352 | 9.7001 |

Scar area (m | 437 | 363 | 1036 | 487 |

Sample depth 1 (cm) | 45 | 30 | 37 | – |

Sample depth 2 (cm) | 92 | 80 | 67 | 108 |

Depth of landslide crown (m) | 1.1 | 1.2 | 0.9 | 1.7 |

Angle of internal friction (degree) | 25.9 | 30.3 | 29.3 | 37.2 |

Cohesion (kPa) | 5.6 | 6.2 | 4.6 | 17.6 |

Plastic limit (mass %) | 23.5 | 26.8 | 26.6 | 18.9 |

Liquid limit (mass %) | 40.0 | 46.2 | 41.8 | 23.1 |

Dry density (g/cm | 1.36 | 1.37 | 1.45 | 1.99 |

Porosity (%) | 46.3 | 48.9 | 45.1 | 25.5 |

Soil type | Clay; medium plastic | Clay; medium plastic | Silt; medium plastic | Clay/silt; slightly plastic |

### Tectonics and geology

The tectonic structure of the valley is dominated by various nappes. Helvetic nappes in the western and northern part of the valley are characterized by competent limestones (e.g., *Schrattenkalk*, *Seewerkalk*) and marls with calcareous layers (e.g., *Drusbergschichten*). Superimposed to the south-east, ultrahelvetic nappes are mostly built up of clayey marls and shales (e.g., *Leimernmergel*). On top extending to the south-east, penninic nappes underlie more than half of the valley. These are characterized by sandstones (e.g., *Reiselsberger Sandstein*, *Planknerbrückenserie*) and thinly layered marls (e.g., *Piesenkopfschichten*) (Friebe 2007; Heissel et al. 1967; Oberhauser 1982; Oberhauser 1998). Above all, the widespread moraine deposits as well as hillside debris are overly susceptible to shallow landsliding. In many cases, subglacial till is reported to form an impermeable layer acting as a sliding surface for the unconsolidated material on top. Only in rare cases also subglacial till was mobilized. Additionally, marls of the Ultrahelveticum, often forming dip slopes, and less competent sandstones of the Penninicum are overly affected by shallow landslides (Zieher et al. 2016).

### Climate

### Landslide-triggering rainfall event on 22/23 August 2005

Antecedent rainfall conditions from November 2004 on to the 22/23 August 2005 event generally fell below the long-term mean. Therefore, it can be expected that the antecedent soil moisture preceding the rainfall event was below average. Effects of snow can be excluded during the summer months. After days with minor rainfalls in mid-August, a phase of intense precipitation started on August 22. At Innerlaterns station, the cumulative precipitation sum of the rainfall event amounted to 256 mm (Fig. 2a). The highest rainfall intensity was recorded in the late evening on August 22 and during the night hours (21 to 22 p.m. 19.4 mm/h). With the help of multiple orthophoto series and two DTMs based on airborne laser scanning (ALS), a detailed shallow landslide inventory was prepared (Zieher et al. 2016; Fig. 2b). In total, 478 shallow landslides associated with the rainfall event in August 2005 were mapped.

## Materials and methods

### Test sites and field work

Geotechnical samples were collected at four sites where shallow landslides had been triggered in the course of the rainfall event in August 2005. The slope failures occurred during the night hours from 22/23 August. Therefore, hardly any eyewitness reports on the exact time of failure are available throughout the valley. In the geological map (Fig. 1b), the sampled shallow landslide locations are mapped as hillslope debris (BIN), till deposits (BON, MAZ), and *Drusbergschichten* (marls with calcareous layers; ROH). These geological units have been identified as overly susceptible to shallow landsliding in the Laternser valley (Zieher et al. 2016). Particularly, the slope-parallel dipping marls of the *Amdener Mergel* (BIN), *Leimernmergel* (BON, MAZ), and *Drusbergschichten* (ROH) provide potential sliding surfaces at the bedrock-regolith interface. Stabilizing effects of high vegetation can be excluded at the test sites BON and MAZ as these landslides occurred on extensively used grass land. In case of the slope failures at the test sites BIN and ROH, single trees above the scarp may have contributed to the stability of the slopes. The four landslides turned into debris avalanches (BIN, BON, MAZ) and a debris flow (ROH) with runout distances of up to 150 m. Accumulated material on roads and within agricultural areas was removed subsequently.

### Landslide geometry derived from multi-temporal airborne laser scanning

^{−2}while it is distinctively higher for 2011 with 15.4–19.5 pts m

^{−2}. Also the error margins, including systematic errors, positional uncertainty due to the size of the laser beams’ footprints, and the registration error, must be provided area-wide and are hence conservative. In addition, none of the scar areas at the test sites re-vegetated. Particularly, low vegetation would have an adverse impact on the positional accuracy. It has been therefore generally assumed that (i) the accuracies of the ALS point clouds are sufficient for accurately detecting landslide depths for the purpose of the present study and (ii) the morphology of the landslide scars is sufficiently represented by the derived raster datasets. In addition, it is presumed that the surface mainly changed due to shallow landsliding and further processes play a minor role.

Metadata of the two ALS campaigns covering the state of Vorarlberg

ALS campaign | Point density demanded | Reported accuracy | Spatial resolution | |
---|---|---|---|---|

Horizontal | Vertical | |||

2004 | 1 pt per m | – | ±20 cm | 1.0 m |

2011 | 4 pts per m | ±10 cm | ±7.5 cm | 0.5 m |

Statistics of landslide length and vertical depth distributions derived from dDTM evaluation within the scar areas

Vertical depth (m) | BIN | BON | MAZ | ROH |
---|---|---|---|---|

Minimum | 0.07 | 0.04 | 0.04 | 0.03 |

First decile | 0.51 | 0.29 | 0.69 | 0.79 |

First quartile | 0.69 | 0.49 | 1.12 | 1.09 |

Median | 0.94 | 0.69 | 1.77 | 1.63 |

Mean | 0.90 | 0.73 | 1.74 | 1.92 |

Third quartile | 1.09 | 0.94 | 2.36 | 2.69 |

Ninth decile | 1.27 | 1.23 | 2.73 | 3.53 |

Maximum | 1.65 | 1.65 | 3.36 | 4.55 |

Length (m) | 31.1 | 29.5 | 68.0 | 47.2 |

D/L ratio | 0.047 | 0.050 | 0.046 | 0.075 |

Statistics of the slope angle distributions evaluated within the scar areas of the four shallow landslides for the two DTMs

Slope angle (degree) | BIN | BON | MAZ | ROH | ||||
---|---|---|---|---|---|---|---|---|

DTM 2004 | DTM 2011 | DTM 2004 | DTM 2011 | DTM 2004 | DTM 2011 | DTM 2004 | DTM 2011 | |

Minimum | 11.3 | 3.2 | 3.7 | 4.8 | 8.9 | 4.8 | 9.9 | 22.0 |

First decile | 18.5 | 14.9 | 10.1 | 9.5 | 17.4 | 17.4 | 31.9 | 32.5 |

First quartile | 23.1 | 21.0 | 21.3 | 17.5 | 19.0 | 20.0 | 35.4 | 35.6 |

Median | 27.4 | 27.7 | 27.3 | 28.2 | 21.1 | 24.4 | 40.7 | 38.8 |

Mean | 26.7 | 27.9 | 26.7 | 27.5 | 22.0 | 24.4 | 39.7 | 41.5 |

Third quartile | 30.2 | 33.3 | 32.2 | 35.0 | 24.0 | 27.7 | 43.2 | 44.9 |

Ninth decile | 32.8 | 38.8 | 37.0 | 39.3 | 27.7 | 29.6 | 46.3 | 50.9 |

Maximum | 39.9 | 48.5 | 46.3 | 51.0 | 38.5 | 44.0 | 52.0 | 64.7 |

### Infinite slope stability model

where *c'* is the effective cohesion, *l* is the unit length, *N'* is the effective normal force, *φ'* is the effective angle of internal friction of the soil material, *W'* is the effective weight of saturated soil, *β* is the slope angle, and *F* _{ s } is the seepage force. All forces are calculated as unit forces where the width corresponds to 1 unit length (e.g., Mergili et al. 2014; Fellin 2014; Ghiassian and Ghareh 2008). The model’s formulae and the workflow for parameter testing were implemented in the R open source software environment for statistical computing (R Core Team 2016).

The results of the ISSM are highly sensitive to the parameters representing landslide geometry assumed by the model (i.e., slope angle and landslide depth). The model was applied for the four sampled landslide locations assuming the results of the laboratory tests to be representative for the local material characteristics. Based on the respective parameter values (i.e., specific weight, effective cohesion, and effective angle of internal friction; Table 1), the impact of landslide depth and slope angle is assessed in detail.

### Janbu’s model

where the sum of resisting forces *T* _{ i } and stabilizing forces from adjacent slices *E* _{ i } are related to the sum of driving forces *S* _{ i } and destabilizing forces from adjacent slices *E* _{ i + 1} for each slice *i*. All forces are calculated as unit forces where the width corresponds to 1 unit length. *c'* is the effective cohesion, *l* _{ i } is the length of slice *i*, *N* _{ i } *'* is the effective normal force, *φ'* is the effective angle of internal friction, *E* _{ i } is a stabilizing force resulting from the passive earth pressure exerted by the slice below, *W* _{ i } *'* is the slice’s weight of saturated soil, \( {F}_{s_i} \) is the seepage force, and *E* _{ i + 1} is a destabilizing force resulting from the active earth pressure exerted by the slice above.

### 3D approaches

*a*

_{ i }is the basal area of each soil column derived from

where *s* _{ c } is the cell size for squared raster cells, \( {\beta}_{x{ z}_i} \) is the slope angle component in east-west direction, and \( {\beta}_{y{ z}_i} \) is the slope angle component in north-south direction (Xie et al. 2003). In Eq. 3, resisting forces *T* and driving forces *S* are summed over all columns *i* within the scar area. *c'* is the effective cohesion per unit area, \( {W}_i^{\prime } \) is the effective weight of saturated soil, *β* _{ i } is the inclination of the sliding surface at the considered column, *φ'* is the effective angle of internal friction, and \( {\beta}_{m_i} \) is the apparent dip of the sliding surface at the considered column in down-slope direction (alignment of the ellipsoid). *N* _{ s } and *F* _{ s } are the contributions of the seepage force to the normal force and the shear force. No inter-column forces are considered. The principles of the FOS calculation are discussed in detail by (Mergili et al. 2014). r.slope.stability further includes several functionalities to combine the FOS values computed for various sliding surfaces to landslide susceptibility maps (Mergili et al. 2014). In the present work, however, single truncated sliding surfaces are used, corresponding to the sliding surfaces of the considered shallow landslides.

*T*

_{ i }and driving forces

*S*

_{ i }for all columns

*i*within the scar area:

where *c'* is the effective cohesion per unit area and *a* _{ i } is the basal area of each soil column derived from Eq. 4. The slope angle components \( {\beta}_{x{ z}_i} \) and \( {\beta}_{y{ z}_i} \) were computed after (Horn 1981). The effective weight of saturated soil *W* _{ i } *'* and the effective normal force are calculated based on each column’s volume. *φ'* is the effective angle of internal friction, *β* _{ i } is the inclination of the sliding surface at the considered column, and \( {F}_{s_i} \) is the seepage force. Effects of active and passive earth pressure are neglected.

## Results and discussion

FOS for the four test sites based on the ISSM, the Janbu’s approach, and the tested 3D approaches for fully saturated and dry conditions (values below 1.0, indicating predicted slope failures, are highlighted)

Site | FOS (dry) | FOS (saturated) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ISSM | Janbu | 3DVA | RSS | ISSM | Janbu | 3DVA | RSS | |||

Median depth | Maximum depth | Median depth | Maximum depth | |||||||

BIN | 2.01 | 1.54 | 1.81 | 2.30 | 2.68 | 1.23 | | 1.09 | 1.44 | 1.63 |

BON | 2.70 | 1.76 | 2.28 | 3.08 | 3.48 | 1.69 | | 1.38 | 1.95 | 2.15 |

MAZ | 1.72 | 1.49 | 1.90 | 1.85 | 3.06 | | | | 1.04 | 1.71 |

ROH | 2.07 | 1.35 | 1.55 | 2.22 | 2.15 | 1.52 | | | 1.67 | 1.60 |

### Modelling results using the ISSM

Simulations based on median landslide depths result in more stable conditions predicted by the ISSM than for maximum landslide depths. The FOS for dry conditions using the ISSM based on median landslide depths in decreasing order is 2.70 (BON), 2.07 (ROH), 2.01 (BIN), and 1.72 (MAZ), compared to 1.76 (BON), 1.54 (BIN), 1.49 (MAZ), and 1.35 (ROH) for simulations with maximum landslide depths. Assuming fully saturated conditions, all test sites are predicted to fail by the ISSM using maximum landslide depths. Based on median depths, all test sites except MAZ remain stable. The FOS for fully saturated conditions using the ISSM based on medium landslide depths in decreasing order is 1.69 (BON), 1.52 (ROH), 1.23 (BIN), and 0.96 (MAZ), compared to 0.99 (BON), 0.88 (ROH), 0.88 (BIN), and 0.78 (MAZ) for simulations with maximum landslide depths. The ratios between FOS values based on median depths for dry and fully saturated conditions are 1.63 (BIN), 1.60 (BON), 1.79 (MAZ), and 1.36 (ROH). The respective ratios using the maximum landslide depths are 1.75 (BIN), 1.78 (BON), 1.91 (MAZ), and 1.54 (ROH). The latter are higher due to the effects of cohesion. At shallower depths, the stabilizing effect of cohesion is markedly higher than further below (see the “Conclusions” section).

### Modelling results using Janbu’s model

For dry conditions, none of the test sites are predicted to fail using Janbu’s model. The resulting FOS values for Janbu’s model in decreasing order are 2.28 (BON), 1.90 (MAZ), 1.81 (BIN), and 1.55 (ROH). Compared to the results based on the ISSM using the maximum depths, the FOS for Janbu’s model is higher by ratios of 1.18 (BIN), 1.30 (BON), 1.28 (MAZ), and 1.15 (ROH). Assuming fully saturated conditions, the slopes at the test sites MAZ and ROH are predicted to fail while test sites BIN and BON remain stable. The resulting FOS values in decreasing order are 1.38 (BON), 1.09 (BIN), 0.98 (MAZ), and 0.84 (ROH). In case of test site ROH, the FOS based on Janbu’s model (0.84) is lower than that of the ISSM using the maximum landslide depth (0.88). Considering fully saturated conditions, the ratios of the resulting FOS based on Janbu’s model and the ISSM using maximum landslide depths are 1.24 (BIN), 1.39 (BON), 1.26 (MAZ), and 0.95 (ROH).

### Modelling results using 3D approaches

Both 3D models predict stable slopes at all four test sites for dry and fully saturated conditions. For dry conditions, the FOS values based on the 3DVA in decreasing order are 3.08 (BON), 2.30 (BIN), 2.22 (ROH), and 1.85 (MAZ). Resulting FOS values for RSS are well above 2.0 with 3.48 (BON), 3.06 (MAZ), 2.68 (BIN), and 2.15 (ROH). Only in case of test site ROH the FOS is slightly lower based on RSS (2.15) compared to the 3DVA (2.22). The maximum ratios of the FOS assuming dry conditions for each test site between the results of the ISSM for maximum depth and the respective 3D approach are 1.74 (BIN; FOS_{ RSS }/FOS_{ ISSM }), 1.98 (BON; FOS_{ RSS }/FOS_{ ISSM }), 2.05 (MAZ; FOS_{ RSS }/FOS_{ ISSM }) and 1.64 (ROH; FOS_{3DVA }/FOS_{ ISSM }). Assuming fully saturated conditions, respective FOS values for the 3DVA in decreasing order are 1.95 (BON), 1.67 (ROH), 1.44 (BIN), and 1.04 (MAZ). Except for location ROH (1.60), the FOS based on RSS is higher with 2.15 (BON), 1.63 (BIN), and 1.71 (MAZ) compared to that of the 3DVA. The maximum ratios of the FOS assuming fully saturated conditions for each test site between the results of the ISSM for maximum depth and the respective 3D approach are 1.85 (BIN; FOS_{ RSS }/FOS_{ ISSM }), 2.17 (BON; FOS_{ RSS }/FOS_{ ISSM }), 2.19 (MAZ; FOS_{ RSS }/FOS_{ ISSM }), and 1.90 (ROH; FOS_{3DVA }/FOS_{ ISSM }). Hence, compared to the ISSM, slope stability (the FOS) is overestimated by the 3D models by a factor of around 2.

### Comparison of the results obtained with the various models

Considering maximum landslide depth, the ISSM yields generally lower FOS compared to the 2D and 3D approaches for either dry or fully saturated conditions. Still, all four test sites were predicted correctly only by the ISSM. Calculations based on the maximum landslide depth indicate stable slopes under dry conditions and slope failures under fully saturated conditions. However, using the maximum landslide depth, the ISSM’s simplified landslide geometry leads to a general overestimation of landslide depth. Hence, also, landslide volumes are overestimated.

Using Janbu’s model, two of four test sites are predicted correctly. At test sites MAZ and ROH, slope failures are predicted assuming fully saturated while slopes at test sites BIN and BON are predicted to remain stable. Compared to the results of the ISSM, the FOS is generally higher. Only in case of test site ROH, the resulting FOS for fully saturated conditions based on Janbu’s model is slightly lower than the corresponding FOS calculated with the ISSM.

In addition, geotechnical parameter values may have been overestimated. For an appropriate determination of the shear parameters, it is important to conduct the shear tests at in situ stress levels. The shear tests have been conducted at the lowest stress levels technically possible (50 kPa). Nevertheless, the in situ stress level of shallow landslides might lie beyond this level (0–40 kPa). This may lead to an overestimation of the cohesion and a slight underestimation of the angle of internal friction for very shallow landslides. Furthermore, single parameter values cannot reflect the local variability of involved material properties.

### Effects of landslide geometry parameters in the ISSM

*Leimernmergel*had been reached, regolith depth ranges from 1.5 to 2.7 m in the vicinity of the landslide. Below 1.5 m, the penetration resistance increases markedly. This could indicate an overconsolidated layer or a blocky matrix. The maximum landslide depth of 1.65 m derived from the dDTM within the scar area coincides with the depth below which penetration resistance increases. Hence, the sliding surface may be located on top of this overconsolidated layer. However, it cannot be completely ruled out that the landslide was originally deeper and hence would yield a lower FOS using the ISSM.

## Conclusions

In the present study, four physically-based models including different representations of landslide geometry were tested to back calculate real-world slope failures. For the ISSM, the determining parameters for landslide geometry (i.e., slope angle and vertical landslide depth) were tested over ranges derived from DTMs within the scar areas. Material parameters were derived from laboratory tests conducted with material samples collected at the four test sites. The model results for the test sites using four approaches were compared. Landslide depths based on the dDTM were validated at one test site with the help of DCPTs.

It is possible to predict the four slope failures using the ISSM. For dry conditions, all test sites remain stable. Assuming fully saturated conditions and representativeness of the geotechnical parameters, the slope failures are predicted (FOS < 1) using the median slope angle derived from the post-event DTM and the maximum vertical landslide depth derived from a dDTM. Using Janbu’s model including a 2D representation of landslide geometry, two out of four failures were predicted for fully saturated conditions. No slope failures were predicted using 3D models. The differing results may be explained by the influence of cohesion.

It is shown that with increasing depth, the influence of cohesion on the FOS decreases non-linearly. Therefore, a more detailed representation of landslide geometry including shallower areas may lead to a higher FOS due to the influence of cohesion. There, the increased stabilizing effect of cohesion enhances the overall FOS. This may explain the higher FOS resulting from the 2D approach (where the shallower parts along the down-slope profile are considered) and the even higher FOS resulting from the 3D approaches (where also the shallower lateral portions of the landslides are considered). The resulting FOS based on the ISSM using the median landslide depth better corresponds to the results of the 2D and 3D approaches.

Field measurements theoretically yield the maximum regolith depth. If the bedrock acts as the sliding surface, the maximum regolith depth corresponds to the maximum landslide depth. Using such measurements as input data for the ISSM, conservative predictions of slope stability are obtained. The assessment of slope stability involving the ISSM at catchment scale should therefore be considered a regional overview showing potential areas for more detailed investigations. This is particularly important if landslide volumes are of interest, which are generally overestimated by the ISSM when using the maximum regolith depth.

The failure of the 3D models to correctly predict the observed slope failures may be related to the variability of the geotechnical parameters. Sliding surfaces most likely coincide spatially with geotechnically susceptible areas, layers or interfaces, spaced in a more or less irregular way. Even though much effort was put in sampling and testing, it appears hardly feasible to parameterize such patterns of localized patches of low soil strength, increased water input or increased hydraulic conductivity, or the effects of the vegetation (de Lima Neves Seefelder et al. 2016). This means that either even more detailed studies including comprehensive material sampling and testing as well as regolith depth measurements, or appropriate techniques for a stochastic representation of the variability of the key parameters, are necessary for studies of single landslides or slopes.

## Notes

### Acknowledgements

Open access funding provided by University of Innsbruck and Medical University of Innsbruck. We thank the federal state of Vorarlberg for kindly providing data for this study. This work has been conducted within the project C3S-ISLS, which is funded by the Austrian Climate and Energy Fund, 5th ACRP Programme.

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