Considering Parameter Uncertainty in a GIS-Based
Sliding Surface Model for Large Areas
Martin MERGILI a,b , Ivan MARCHESINI c , Mauro ROSSI c , Massimiliano ALVIOLI c , Barbara SCHNEIDER-MUNTAU e , Mauro CARDINALI c , Francesca ARDIZZONE c , Federica FIORUCCI c , Daniela VALIGI d , Michele SANTANGELO c , Francesco BUCCI c and Fausto
GUZZETTI c a
Department of Geography and Regional Research, University of Vienna, Austria b
Institute of Applied Geology, BOKU University, Vienna, Austria c
CNR-IRPI, Perugia, Italy d
Department of Physics and Geology, University of Perugia, Italy e
Division of Geotechnical and Tunnel Engineering, University of Innsbruck, Austria
Abstract. The GIS-based open source software r.slope.stability computes broad-scale spatial overviews of shallow and deep-seated slope stability through physically-based modelling. We focus on the landslide-prone 90 km² Collazzone area, central Italy, exploiting a comprehensive set of lithological, geotechnical and landslide inventory data available for that area. Inevitably, the geotechnical and geometric parameters are uncertain, particularly for their three-dimensional variability. Considering the most unfavourable set of geotechnical parameters (worst case scenario, appropriate for engineering purposes) is less useful to obtain an overview of the spatial probability (susceptibility) of landslides over tens of square kilometres. Back-calculation of the pa-rameters based on topographic and geotechnical considerations would better suit for such a purpose, but obtaining one single parameter combination would require information on one of the parameters. Instead, we estimate the slope failure probability by testing multiple combinations of the model parameters sampled deterministically. Our tests indicate that (i) the geotechnical parameterization used allows to reproduce the observed landslide distribution partly (a challenge consists in the appropriate treatment of the variation of the geotechnical parameters with depth); (ii) the evaluation outcome depends strongly on the level of geographical aggregation; and (iii) when applied to large study areas, the approach is computing-intensive, and requires specific strategies of multi-core computing to keep computational times at an acceptable level.
Keywords. GIS, uncertainty, slope stability model
1. Introduction
GIS-based slope stability models assume an infinite slope with a planar, slope-parallel failure plane (Van Westen et al., 2006), and are best suited for analysing shallow slope instability. More complex models consider the three-dimensional geometry of possible slope failures, and are suitable for the analysis of deep-seated slope stability (e.g., Bishop, 1954; Janbu et al., 1956). The latter models rely on complex neigh-bourhood relationships, and their implementation in GIS environments is not trivial (attempts were made, e.g., by Xie et al., 2003, 2004a, b, 2006; Marchesini et al., 2009; and Jia et al., 2012). Mergili et al. (2014a,b) have introduced the model r.slope.stability in an attempt to bridge the gap between GIS and three-dimensional slope stability models.
In this study, we compare modelled shallow and deep-seated landslide susceptibility maps derived with r.slope.stability for the 90 km² Col-lazzone area in Umbria, central Italy. The aims of the study are the following:
1. To evaluate the effectiveness of ge-otechnical sampling and testing to cap-ture the spatial variability of the ge-otechnical parameters, and to highlight the major challenges of an appropriate geotechnical parameterization.
2. To highlight a method considering pa-rameter uncertainty in physically-based slope stability modelling by computing the slope failure probability from a large number of values of the factor of safety derived with different combinations of input parameters.
3. To demonstrate how the model per-forms for different types of landslides,
© 2015 The authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License. doi:10.3233/978-1-61499-580-7-952
and at different levels of spatial aggre-gation of the reference units.
4. To present a strategy to reduce the com-putational time.
2. Materials and Methods 2.1. The Collazzone area
The Collazzone area (~90 km² in Umbria, central Italy) has been the subject of numerous land-slide-related studies in the past 15 years (e.g., Fiorucci et al., 2011 and references therein, Mergili et al., 2014a, b). Much of the area con-sists of unconsolidated clastic sediments. Thir-teen sets of the geotechnical parameters effective cohesion (c’) and effective angle of internal friction (’) were obtained through direct shear tests (Figure 1). Strike and dip of bedding traces were obtained at several places (Marchesini et al., 2013, 2014). From this information the bedding planes of 67 layers – all > 2 m thick – were as-signed to one of four lithological classes. In addition, we used a 10 m × 10 m Digital Eleva-tion Model (DEM).
2.2. The model r.slope.stability
r.slope.stability (Mergili et al., 2014a, b) is a GIS-based, three-dimensional model application for computing shallow and deep-seated slope stability. The tool was developed as a C-based raster module within the GRASS GIS software (GRASS Development Team, 2015). The numer-ical model implements a modification of the three-dimensional sliding surface model pro-posed by Hovland (1977), and revised and ex-tended by Xie et al. (2003, 2004a, b, 2006). Compared to the latter model, r.slope.stability introduces a more advanced approach to compute the seepage forces (Mergili et al., 2014a). Given a DEM and a set of thematic layers, the model evaluates the slope stability for a large number of randomly selected potential slip surfaces,
ellip-soidal in shape. Randomization of the ellipsoid parameters is constrained by user-defined mini-ma and mini-maximini-ma of the ellipsoid dimensions and position. Truncated ellipsoids can be used to model the presence of weak layers, or layer inter-faces at defined depths – or defined regular or irregular surfaces – within the soil or the bedrock. Any single GIS raster cell may be intersected by multiple sliding surfaces, each associated with a computed Factor of Safety (FoS). For each pixel, the lowest value of the computed FoS is taken as the relevant one. This information is used to obtain a spatial overview of potentially unstable regions over areas up to several square kilome-tres.
The geotechnical parameters required as in-put may be discretized in two different ways:
1. Based on the lithological classes, dis-crete data units are defined on a horizon-tal basis, containing information on (i) c’, (ii) ’, (iii) dry specific weight, and (iv) saturated water content. A few layers, including the base of the soil, may be specified to truncate the ellipsoids. We use this way of discretization for compu-ting the shallow slope stability.
2. r.slope.stability further allows to assign the parameters (i) – (iv) based on specif-ic layers. Relying on raster datasets rep-resenting the base of each geological layer, r.slope.stability can handle sets of up to 100 layers. Each layer is associat-ed to a lithological class, determining the relevant parameters. Each ellipsoid is truncated at the base of each inter-sected layer, and values of the FoS are computed for the entire ellipsoid and for the truncated shapes. We use this way of discretization for computing the deep-seated slope stability.
r.slope.stability includes the option to split the study area into a number of non-overlapping tiles, and to process the tiles in parallel, allowing to exploit the total number of available cores, reducing the computational time.
Figure 1. Range of the geotechnical parameters c’ and ’ derived from a set of 13 direct shear tests in the Collazzone area. The range suggested by Prinz and Strauss (2011) for the relevant lithological classes is indicated as well as the range of combinations supported by a ’ – c’ regression.
2.3. Geotechnical and geometric parameterization
The values of c’ and ’ derived from the direct shear tests are highly variable in space. These variations are not necessarily related to clearly defined lithological or soil classes (Figure 1), leading to considerable uncertainties propagating to the results of GIS-based deterministic slope stability models. Well-designed strategies to select appropriate sets of parameters are required. Such strategies may consist in:
1. Back-calculating the parameters. For ar-eas with rainfall-triggered landslides where the topography of the slopes is mainly controlled by landslides, it may be considered a valid approximation to set the value of FoS for the steepest por-tions of the study area (or of a certain lithological class) to 1.0 under dry condi-tions, to back-calculate the associated geotechnical parameters, and to compute FoS for fully saturated conditions (most unfavourable assumption; Mergili et al., 2014a). This requires information on one
of the parameters, either c’ or ’, other-wise there will be no unique result. 2. Using the combination of measured
pa-rameters leading to the most unstable conditions, and the most conservative results (e.g., Mergili et al., 2012). It shall be emphasized that here, only val-ues of c’ or ’ derived from a single la-boratory test should be used together as c’ and ’ are interdependent.
3. The most advanced method consists in considering a combination of multiple sets of parameters to compute the slope failure probability Pf by testing multiple combinations of the parameters sampled deterministically or stochastically, and evaluating the ratio between the number of parameter combinations yielding a value of FoS below 1 and the total number of tested combinations. This approach allows considering the full range of measured values of c’ and ’ and, for shallow landslides, soil depth (Mergili et al., 2014b).
Whilst the back-calculation (1.) , if aiming at obtaining one single pair of c’and ’, requires
information on one of the two parameters, appli-cation of the parameters yielding the most con-servative results (2.) is useful in geotechnical engineering, where a conservative prediction of stability or instability is needed. Here, we test multiple parameter combinations (3.) to gain an idea on the spatial probability of landslides. 2.4. Evaluation
We evaluate the values of Pf yielded with r.slope.stability with the inventories of shallow and deep-seated landslides available for the Col-lazzone area. The quality of the predictions is quantified by the area under the ROC (Receiver Operating Characteristics) Curve (AROC). We compare the outcomes obtained at two different levels of spatial aggregation:
1. Using single pixels, and 2. Using slope units
For slope units, all slope units with observed landslides are considered as observed positives, all slope units without landslides as observed negatives, whilst the values of Pf represent the averages of the pixel values of the slope unit.
3. Results and Discussion
3.1. Geotechnical sampling and testing
Looking at the range of values of c’ and ’ illus-trated in Figure 1, derived from 13 frame shear tests on samples taken in the study area, the min-ima and maxmin-ima correspond remarkably well to the minima and maxima given by Prinz and Strauss (2011) for the relevant grain size classes. On the first glance, this observation indicates a low cost efficiency of geotechnical tests in gen-eral. Testing only the granulometry would be much faster, and easier. However, geotechnical tests, are important as, regarding peak strength, c’ and ’ are interdependent (Muir Wood, 1990; Atkinson, 1993; see Figure 1) for one soil type (depending on density and water content) and quantifying this interdependence may help to better constrain the range of parameter combina-tions expected for specific lithologic units or for an area in general. However, our data set is too small to derive meaningful correlations for each
class. It has further turned out that, for our study area, with an increasing number of samples, R² decreases significantly.
3.2. Slope failure probabilities
Figure 2 shows the distribution of (a) shallow and (b) deep-seated slope failure probabilities Pf for the Collazzone area modelled by r.slope.stability. All results build on the assump-tion of fully saturated material and slope-parallel seepage, which is considered as the most unfa-vourable (conservative) assumption.
Regarding the values of Pf for shallow slope stability, the results shown correspond to 729 combinations of c’, ’ (constrained by the large rectangle in Figure 1) and soil depth. 16.3% of the Collazzone area display values of Pf 0.1, 6.3% of the area display values of Pf 0.2, and 1.7% of the area display values of Pf 0.3.
For deep-seated slope stability, the model indicates a higher level of slope failure probabil-ity (derived from 100 combinations of c’ and ’): 48.8%, 35.7% and 26.5% of the areas display values of Pf 0.1, 0.2 and 0.3. The result be-comes less conservative when constraining c’ according to the regression shown in Figure 1 (38.2%, 30.6%, and 25.1%, respectively), which we consider a more realistic assumption. The values of Pf decrease when additionally assum-ing layer- instead of slope-parallel seepage.
Whilst 7.7% and 9.3% of the Collazzone ar-ea are affected by shallow and deep-sar-eated land-slides, respectively, the average values of Pf over the entire area are 4.4% (shallow slope stability) and 21.1% (deep-seated slope stability; 20.4% with regression; 12.4% with regression and lay-er-parallel seepage).
This comparison reveals a mismatch in terms of a less conservative prediction for deep-seated landslides. Even though the geotechnical data are spatially discretized in different ways, the results build on the same geotechnical data-base, this observation indicates a limited under-standing of the spatial variation of the geotech-nical parameters. In particular, there is a lack of knowledge on the increase of c’ and ’ with depth, which is not considered at all.
Figure 2. Slope failure probabilities Pf in the Collazzone area for (a) shallow and (b) deep-seated slope stability.
3.3. Evaluation outcomes
Apparently, r.slope.stability performs better for shallow than for deep-seated slope failure proba-bility, most probably due to the uncertainties connected to the lithological layering. Evaluating the results obtained using pixels, AROC = 0.694 for shallow and AROC = 0.654 for deep-seated slope failure probability with slope-parallel seep-age (0.640 with layer-parallel seepseep-age). AROC is relatively insensitive to changes in the geotech-nical parameterization.
Whilst the results of GIS-based slope stabil-ity models are most commonly discretized and validated using pixels, slope units would be another acceptable level of discretization (Jia et al., 2012). As a drawback, slope units require appropriate strategies to (i) define meaningful
units and (ii) discretize the landslide inventory and the model results to the slope units.
When discretizing the results for a 79 km² subsection to slope units instead of pixels, the values of the AROC for shallow and deep-seated slope failure probabilities increase to 0.77 and 0.72. We observe that this range is similar to the range of AROC yielded with statistical models applied to the same subsection and discretized to the same slope units (0.71–0.75, depending on the method, Rossi et al., 2010). This comparison indicates that the variability of the input parame-ters has to be better understood to make physical-ly-based model results significantly better than statistical ones.
3.4. Computational time
Employing parallel processing has decreased the computational time by a factor of up to >20,
using a machine with 42 processing units and dividing the study area into 182 tiles. This way, processing of the entire Collazzone area was completed in less than 24 hours.
4. Conclusions
We have shown that 3D slope stability modelling is feasible for study areas larger than single slopes, using GIS techniques in combination with appropriate strategies to reduce computing time e.g., exploiting parallel processing. Howev-er, the large and obviously unpredictable spatial variability of input parameters – particularly subsurface data such as c’ and ’, but also slope hydraulics – imposes a high level of uncertainty. We have tested an approach to deal with this uncertainty. However, the ability to predict the observed distribution of landslides remains mod-erate. A challenge consists in the parameteriza-tion of changes with depth in the geotechnical parameters. Evaluation of the results at a higher level of aggregation (slope units) instead of the pixels lead to better results, and the results are better for shallow slope stability than for deep-seated slope stability. We further conclude that – in contrast to studies at a very detailed scale – geotechnical sampling and testing plays a less dominant, but still important role: the large vari-ability of the values obtained covers the same range as the range suggested by a textbook which, however, gives no information on the range of parameter combinations.
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