Development of a landslide susceptibility assessment for a rail network

Engineering Geology 215 (2016) 1–9

Contents lists available at ScienceDirect

Engineering Geology journal homepage: www.elsevier.com/locate/enggeo

Development of a landslide susceptibility assessment for a rail network Karlo Martinović a,b,⁎, Kenneth Gavin a,c, Cormac Reale a,c a b c

Gavin and Doherty Geosolutions, A2 Nutgrove Office Park, Rathfarnham, Dublin 14, Ireland School of Civil Engineering, Newstead, University College Dublin, Ireland Faculty of Civil Engineering and Geosciences, TU Delft, Stevinweg 1, 2628 CN Delft, Netherlands

a r t i c l e

i n f o

Article history: Received 16 June 2016 Received in revised form 4 October 2016 Accepted 12 October 2016 Available online 21 October 2016 Keywords: Landslide susceptibility Engineered slopes Logistic regression Road Rail Shallow slides

a b s t r a c t This paper examines the applicability of a landslide susceptibility assessment approach to engineered slopes using data from the Irish Rail network. A logistical regression model was used to determine the susceptibility of landslide occurrence on an asset by asset basis using input factors derived specifically for man-made earthworks. Records of past failures were used to train the model to predict the probability of future failures occurring. The model was used to analyse a substantial section of the Irish Rail network comprising of 1184 slopes. The database of assets was split into training and validation datasets and similar levels of predictive performance were achieved with both datasets indicating the applicability and robustness of the approach. The results of the study show that simple asset databases, partially populated by visual survey data, can be used effectively to carry out a landslide susceptibility analysis. This enables proactive identification of critical assets as opposed to the current reactive industry standard, which represents an important step forward in creating objective risk rating systems for transport network earthworks. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Landslides are a serious geohazard across the world, resulting in financial losses measured in hundreds of billions euros in damage annually (Aleotti and Chowdhury, 1999), injuries and fatalities (Zêzere et al., 2008; Klose et al., 2015). One of the areas where consequences are high is along major transportation networks, where damage to infrastructure causes significant delays, high replacement/rehabilitation costs and impacts the reputation of the operator. Significant research effort over the last twenty years has been focussed on predicting the triggering mechanisms for landslides, their spatial and temporal distributions and their consequences. As a result, a number of techniques for mapping landslide susceptibility, hazard and risk have been developed and applied to different geographic areas (Guzzetti et al., 1999; Aleotti and Chowdhury, 1999; Dai et al., 2002; Lee and Jones, 2004; Fell et al., 2005; Corominas et al., 2014). Landslide susceptibility assessments (LSA) considers the likelihood of landslide occurrence in a given study area. It can be considered as an initial step in the landslide hazard and risk assessment process. These extend susceptibility assessment by incorporating temporal characteristics (return periods), landslide magnitude as well as their ⁎ Corresponding author at: School of Civil Engineering, Newstead, University College Dublin, Ireland. E-mail addresses: [email protected] (K. Martinović), [email protected] (K. Gavin), [email protected] (C. Reale).

http://dx.doi.org/10.1016/j.enggeo.2016.10.011 0013-7952/© 2016 Elsevier B.V. All rights reserved.

consequences on elements at risk (Varnes, 1984). Landslide susceptibility assessment methods can broadly be considered as either qualitative or quantitative approaches. Qualitative methods are subjective as they rely solely on expert opinion and engineering judgment. For example, geomorphological mapping uses available maps or terrain surveys to determine landslide susceptibility by identifying sites with similar geological and geomorphological features to those where landslides have previously occurred. These approaches usually include different ranking processes achieved by weighting the various input factors. Although these methods result in numerical values of susceptibility they are still qualitative as the weightings are attained through expert opinion. The most widely used methods include the analytic hierarchy process (Yalcin, 2008; Komac, 2006) and the weighted linear combination (Ayalew et al., 2004; Akgun et al., 2008; Ahmed, 2015). Quantitative methods are based on finding a numerical correlation between input factors and landslide occurrence. This correlation can be obtained by either a deterministic or a statistical approach. These inputs factors normally include a range of topographical, geological, geotechnical and environmental characteristics of the study area, typically presented in thematic GIS maps. The deterministic approach is based on geotechnical slope stability calculations, and requires either exhaustive knowledge of geotechnical input data or else the simplification of geotechnical and geometrical features (Van Westen et al., 2006; Godt et al., 2008). The statistical approach is based on determining the influence each input factor has on landslide occurrence within the study area by examining past failure data using a variety of statistical techniques.

2

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

Once the influencing factors have been determined, they can then be used to determine the probability of landslide occurrence in other parts of the study area (Carrara et al., 1991). As statistical methods rely heavily on large datasets for accuracy, having a detailed landslide inventory is an important requirement in order to obtain meaningful results. Multivariate statistical methods simultaneously evaluate the influence that multiple factors have on landslide occurrence, and are widely used in research. Methods including discriminant analysis (Baeza and Corominas, 2001; Süzen and Doyuran, 2004), logistic regression (Dai et al., 2001; Ohlmacher and Davis, 2003; Ayalew and Yamagishi, 2005; Bui et al., 2015) and artificial neural networks have also been developed and widely applied (Ermini et al., 2005; Yesilnacar and Topal, 2005). Comparisons of the performance of these methods can be found in the literature (Nefeslioglu et al., 2008, Yilmaz, 2010, Park et al., 2013, Kavzoglu et al., 2014). As each of the methods has different input requirements, their applicability varies depending on the size of the study area and the scale/availability of input data (Van Westen et al., 2008; Cascini, 2008; Corominas et al., 2014). Although numerous examples of the development and application of LSA techniques for natural slopes can be found in the literature, there is a dearth of information related to man-made or engineered slopes on transport networks. Given that relatively small landslides are sufficient to cause serious accidents such as train derailments (Fig. 1), the consequences of these slips can be high. Anthropogenic

factors related to construction means that in general cut slopes and man-made embankments are at a higher risk of failure than natural slopes with similar geometry (Jaiswal et al., 2010a, 2010b). While landslide susceptibility, hazard and risk assessments for transportation networks are considered in Budetta (2004), Remondo et al. (2008), Bednarik et al. (2010), Jaiswal et al. (2010a, 2010b, 2011), Quinn et al. (2010), Das et al. (2010), Michoud et al. (2012) and Devkota et al. (2013), they usually refer to natural terrain landslides in the buffer zone around relatively short segments of a transport network, and do not deal specifically with the stability of engineered slopes across the entire network. Landslides on cut slopes and fill slopes are briefly discussed in recent risk zoning guidelines by Fell et al. (2008). One possible explanation for the lack of treatment of network wide LSA's is the difficulty in obtaining records of past landslides. Both the earthworks themselves and the landslides triggered on them are of much smaller magnitude than those commonly reported on natural slopes and the debris is usually quickly removed. This makes the preparation of a landslide inventory using conventional methods (i.e. multi-temporal aerial imagery) difficult. The problem is further exacerbated by the long-linear nature of transport networks, which makes the collation of factor maps over such a vast area on a scale detailed enough to adequately describe the assets a significant problem. Most asset managers compile databases containing a wide range of data related to the condition of their earthworks. Data is typically gathered through walkover visual surveys and with the help of remote sensing (e.g. LiDAR surveys to measure geometrical characteristics). The data, while comparable to that typically used in landslide susceptibility assessments, has some additional fields for asset specific information (e.g. age, drainage type and condition etc.). Each asset in the database can be used as a mapping unit for a landslide susceptibility assessment. This study aims to examine the possibility of using a slope database compiled by Irish Rail to develop a landslide susceptibility assessment (LSA) approach. The susceptibility assessment was carried out using a logistical regression technique that is commonly used in LSAs in natural terrain (Budimir et al., 2015). Appropriate input parameters are proposed and their influence on slope stability is examined.

2. Case study on the Irish Rail network

Fig. 1. Typical rainfall induced shallow slides on railway assets in Ireland (a) an embankment on the Dublin – Sligo line, (b) a cutting on the Tralee – Mallow line.

The area chosen for this study is the Athlone division of the Irish Rail network in the western region of the Republic of Ireland (Fig. 2). The division contains approximately one-third of all Irish Rail's earthwork assets. Specifically, there is 550 km of active track containing 709 embankments and 449 cuttings, 74 of which are rock cuttings. The bedrock underlying the region is primarily composed of limestone and calcareous shales. Surface deposits in the area are largely derived from glacial drift. The most widespread deposit is glacial till, commonly known as boulder clay, an unsorted material characterised by the presence of clasts of differing sizes embedded within a matrix of clay sized particles. It accounts for almost 50% of Ireland's total surface area (Fealy and Green, 2009). Other significant soil types, include glaciofluvial sands and gravels; alluvium found in floodplains; and peat - a soft postglacial deposit with a high proportion of organic materials. The rail track in the study area is generally flat with an elevation ranging from sea-level to a maximum elevation of 115 m above sea-level. The land surrounding the rail network is primarily used for agricultural purposes (pastures and crops) with deep-rooted vegetation being scarce. The earthworks themselves have more significant tree coverage in places. The climate is temperate oceanic, with average annual precipitation ranging from 1400 mm on the west Atlantic coast to just over 800 mm in the Midlands at the eastern perimeter of the study area (Fitzgerald and Forrestal, 1996). The soil type encountered in cuttings can be reliably inferred from regional soil maps. The embankments were constructed in the 19th century by end-tipping of locally won material (Nelder et al., 2006) and

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

3

with 2011 and 2014 having between 5 and 10% more rainfall than the 30-year average, while rainfall for the remaining study period was average or below. This may indicate that single rainfall events are more instrumental in triggering failures than antecedent or cumulative rainfall, which is in concordance with existing research on shallow landslides (Aleotti, 2004).

As different triggering mechanisms are responsible for initiating different landslides it is common practice to carry out a LSA for each landslide type separately (Corominas et al., 2014). The LSA in this study was performed for shallow translational slides, the most common failure type encountered across the Irish rail network (111 events from this database selected for further analysis) and generally across transport networks (Jaiswal and van Westen, 2009, Oh and Pradhan, 2011). The location of these events is shown in the Fig. 3 which includes information on average rainfall in the study area.

3. A review of factors affecting LSA for engineered slopes Budimir et al. (2015) performed an extensive literature review, compiling ninety one papers, on the application of logistic regression analyses to landslides on natural terrain with the aim of determining the frequency and significance of input factors used in the susceptibility analyses. Because such a range of input parameters was used across the studies, there are no established universal criteria for selecting input factors.

Fig. 2. Athlone division rail lines (thick red line) in the Irish rail network (thin red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

given the form of construction it is likely that the material is from nearby cuttings. In recent years Irish Rail has kept an earthwork failure register with records of landslides on cuttings and embankments. During the period 2010 to 2014, a total of 194 slope failures were registered in the Athlone division. Some interesting trends can determined from the data: • The majority of failures (67%) were shallow translational landslides (Cruden and Varnes, 1996), triggered by rainfall or as a consequence of faulty drainage. While detailed measurements were not recorded for every event, landslides were typically 3 m to 10 m wide, with a failure depth between 0.5 m and 1.0 m. Failure surfaces were generally planar and parallel to the original slope surface • Debris material resulting from the shallow slides was occasionally very mobile, due to the material being saturated with water, thereby allowing the debris to reach the tracks. While the tracks were usually not damaged due to the small volume of debris, on occasions it led to serious consequences such as long traffic disruptions or even derailments of oncoming trains (RSC, 2014). • 81% of failures occurred on cuttings even though they account for only a third of the assets. • Landslide failure mechanisms other than shallow translational failures occurred infrequently. Failures on rock cuttings were mostly found to be a result of weathering and erosion with very few true wedge failures (falls, topples and slides). A small number of rotational landslides were recorded. These were mostly attributed to human intervention (mainly undercutting of the slope toe) or inadequate soil resistance, and typically occurred on embankments. • Rainfall conditions in the Athlone division area during the failure recording period were analysed using data from four synoptic stations. Analysis showed that none of the years had exceptional precipitation,

Fig. 3. Location of landslide events in the Athlone division, including data on mean annual rainfall bands.

4

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

The authors identified the following reasons in which natural slopes and engineered slopes may differ; and the effect that has on the selection of input factors for engineered slopes: 1. The controlled manner of constructing engineered slopes means some features affecting natural slopes are not applicable to engineered slopes: detrimental effects of road networks and stream networks in the area are mitigated using engineered solutions such as culverts, bridges etc. 2. The average height of slopes on a transport network is typically much smaller than natural slopes. This affects the maximum size and type of landslides that can occur. Major transport networks are typically also set in a much more limited elevation range as opposed to mountainous areas normally used as study areas in natural terrain LSAs. 3. For LSAs on natural slopes, pixels on a GIS map are commonly used as mapping units. For transport networks positioned along linear transport networks, any feature present on one asset has no effect on a neighbouring one. It is therefore not possible to include any factor that is defined by its interaction with neighbouring mapping units, such as TWI (topographic wetness index), SPI (stream power index) or flow accumulation, normally applied to natural terrain LSAs. Suitable proxies that can describe the precipitation run-off influence from the natural terrain adjacent to the assets need to be developed in a way to be able to be collated by visual surveys over large areas. 4. Detailed-scale features such as engineered drainage and erosion can easily be observed from close-up walkover surveys regularly conducted on transport networks. 5. Engineered stabilisation works are a collective term for geotechnical and structural interventions carried out to increase slope stability such as retaining walls and soil reinforcement techniques. While these are sometimes also carried out on natural slopes in the vicinity of urban areas or transportation lines, they are rare and no research study on natural slope LSAs incorporate them. Based on the work of Budimir et al. (2015), van Westen et al. (2008), Corominas et al. (2014) and forensic analysis of landslides on the Irish rail network (Donohue et al., 2011; Gavin et al., 2014), a selection of the factors most applicable to natural and engineered slopes are presented in Table 1. In reality the selection will inevitably be governed by the type and quality of data recorded in the asset managers databases. In this study, nine factors were selected based on the guidelines in Table 1 and the availability of data. A short description of each factor is included below: Table 1 The list of factors for susceptibility analysis and their applicability for engineered and natural slopes. Both

Slope angle Soil type (soil cover) Lithology Engineered stabilisation works Drainage (engineered) Erosion Distance to roads/rails Distance to water flows/drainage Slope height Elevation Rainfall/climate zones Aspect Vegetation type TWI, SPI Adjacent slope Curvature Object type Distance to faults Depth to bedrock

X X X

Natural slope

Engineered slope

14 12

X X X X X X X X X X

Slopeheight [m]

Input factor

• Asset type: Whether the slope is a cutting or embankment. Cuttings are defined as excavations where the toe is at least 3 m below the surrounding natural ground level, while embankments are defined as man-made soil deposits where the crest is at least 3 m above the surrounding natural ground level. As a result of these definitions, assets naturally have varying length, with the average length of assets in Athlone division being 345 m. • Slope height and slope angle: These geometrical characteristics were obtained for the most critical section of each asset through processing LiDAR data flown along the Irish rail network (Fig. 4). While these parameters are routinely recorded through visual assessments, the visual method of data gathering is subjective and prone to significant errors (Martinovic et al., 2016). • Aspect is included as a proxy for a number of environmental factors such as, wind exposure, rain shadow, insolation, evapotranspiration etc. Hughes et al. (2009) show that the influence of aspect on slope stability is significant even for small-scale engineered slopes. • Vegetation type – this refers to the dominant vegetation cover on the slope face, classified as bare ground, grass, shrubs, and trees (Fig. 5). Data sources include visual walkover and aerial imagery surveys. • Adjacent slope is defined as the slope of the adjacent ground. In this study the following classification system was used: flat terrain (0); adjacent slope draining water away from the earthwork asset (−1); adjacent slope draining towards the earthwork asset (1) and category (2) for very steep adjacent natural slopes supplying large volumes of run-off precipitation. • Soil type – the authors reclassified the 1:100,000 quaternary deposit map of Ireland into six general soil categories: glacial till, granular material, soft clays, peat, non-engineered fill (made ground) and rock at surface. For each cutting a category was assigned using GIS software and further adjusted through visual observations where applicable. Due to a lack of detailed records, glacial till was assumed to be the construction material for all embankments. • Rainfall: the Athlone division area was divided into areas with mean annual rainfall values of 800–1000 mm, 1000–1200 mm and 1200– 1400 mm as per Fitzgerald and Forrestal (1996) and Walsh (2012). Mean annual rainfall values are taken from the latest 30-year observation period (1981–2010). A value was then assigned to each asset using GIS software. • Slope condition: one of the data types recorded through close-up visual surveys is slope condition, which represents a subjective description of surficial features observable on slopes. During a visual inspection, each asset is assigned a condition score ranging from 1 (“good condition”) to 4 (“very poor condition”) according to an internal Irish Rail guideline document. The document includes guidelines on scoring based on site observations, such as the presence and condition of various features such as drainage, erosion, water seepage and ponding, tension cracks and other instability signs, etc. In this study, slope

10 8 6 4 2

X X X X X

0 0

X

10

20

30

40

50

60

70

80

Slope angle [°] Fig. 4. A scatter plot of asset height and angles in the Athlone division.

90

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

No landslides recorded 450

39

400

Number of assets

Landslides recorded

350

353

300 250

20

25

282

284

shrubs

trees

200 150 100

27

50 0

53 bare

grass

Vegetation type Fig. 5. Distribution of vegetation types across the Athlone divisions assets.

condition serves as a proxy for drainage and erosion. Only the scores of 1, 2 and 3 are included in this study as there was no asset with a condition score of 4 in the study area. As this LSA was carried out for shallow translational slides in soil, rock cuttings were excluded from the database. Lithology (bedrock geology) was omitted as the landslides were fully contained within the surficial soils which were described by the soil type parameter. 4. Logistic regression model An objective, data-driven method was selected as the LSA method used in this study as a contrast to the subjective hazard and risk ratings approaches typically employed by asset managers. Logistic regression (LR) was selected as it has been extensively used and validated in studies on slopes in natural terrain. Furthermore, in a review of LS methods by Brenning (2005) it was shown to be the technique which resulted in the lowest rate of error. Logistic regression is a suitable model for quantifying the relationship between a number of independent variables and a dichotomous dependent variable. A dichotomous variable can take one of two possible values: 0 or 1; true or false; in the case of the LSA, representing the presence or absence of a landslide for a slope unit. The goal of LR in LSA is to find the best-fit model to describe the relationship between physical and environmental factors on a mapping unit (independent variables) and the presence or absence of landslides (dependent variable) on that unit. The final result of this model is the landslide susceptibility value (p) for each mapping unit, ranging from 0 to 1, see Eq. (1) p¼

1 1 þ e−Z

ð1Þ

where: Z is the linear combination generated by the coefficients depending on the input data, obtained by Eq. (2) Z ¼ β0 þ β1 X1 þ β2 X2 þ … þ βn Xn

ð2Þ

where β1, β2, …, βn are the regression coefficients that determine the contribution of the different input factors (independent variables X1, X2, …, Xn), obtained iteratively using maximum likelihood estimation. β0 is the intercept value of the model. A different regression coefficient is assigned for each class of each factor, where a class is a subdivision of a factor. The influence of each class relative to another class of the same factor can be assessed by comparing the natural exponent of the coefficients (eβi), also known as the odds-ratio. A positive coefficient gives an odds-ratio greater than one,

5

suggesting that the landslide is more likely to happen. For a given odds ratio, the higher the value, the larger the influence that class has in increasing the susceptibility to landslide. Using this approach a comparison between two classes of the same factor can be undertaken while the other inputs remain unchanged. One of the advantages of the model is that different input data types can be accommodated, such as scalar or nominal data. In order to normalise data inputs, it is common practice to substitute nominal classes with ‘dummy’ binary variables which take the value of 1 if that condition is true and 0 otherwise. The number of dummy variables for each factor is one less than the number of classes, since one class takes the role of the default reference category, and a coefficient β of 0 is assigned to that class (Dai et al., 2001). For each nominal factor in this study, the reference class was determined as the one with the smallest calculated frequency ratio. Different approaches exist in the literature to determine appropriate sample sizes for dependent and independent variables. For rare events (where the number of units with landslides is several orders of magnitude smaller than the number of units without landslides) it is recommended to use an equal proportion of units with and without landslides, to avoid under-predicting landslide occurrence (Can et al., 2005; Jaiswal et al., 2010a, 2010b; Yesilnacar and Topal, 2005). Many studies use unequal proportions for landslide presence and absence units (Lee and Sambath, 2006, Akgün and Bulut, 2007, Yilmaz, 2009), often considering data from the entire study area (Lee and Min, 2001; Ohlmacher and Davis, 2003). Due to the relatively small number of units (slope assets) all units both with and without landslides have been used in this study. In many of the cited studies validation is carried out by comparing the predicted susceptibility value to the locations of actual landslides and observing the distribution of actual landslides across the classes of predicted susceptibility values. However, a number of recent studies subdivide the study area into training and validation datasets (Mancini et al., 2010; Bui et al., 2015; Kritikos and Davies, 2015). The latter approach has been implemented in this study. 5. Results and discussion The entire available data (slope details and landslide records etc.) were compiled into a single database, which was then divided into a model training set (70% of assets) and a model validation set (30% of assets) using random sampling. The relatively large training dataset was chosen because of the small number of actual landslides along the network. Each of the datasets contained an equal ratio of assets where landslides had occurred and assets with no occurrence. A LR analysis was then carried out on the training set. The analysis resulted in regression coefficients βi for each factor class, shown in Table 2. The susceptibility value was then calculated for each asset using Eq. (2). The results of different statistical methods commonly used to evaluate the performance of models are summarised in Table 3. The −2 log L (L = likelihood) approach is a measure of a model's best fit deviation from the observed values. It is analogous to the residual sum of squares used in linear regression. It depends on the model size and is a less useful indicator in itself, but its comparison with the −2 log likelihood for the null hypothesis (the model with all regression coefficients except the constant set to 0) is a measure of the model's accuracy. The difference between these two values is referred to as a model chi-squared. All three of these values, presented in Table 3, indicate very good model performance. Furthermore, these values can be used to obtain the pseudo R2 value indicating how well the model fits the dataset logL Þ. A (McFadden, 1974; Menard, 2000) using the expressions 1−ð logL 0

pseudo R2 value of 1 indicates a perfect fit while a value of 0 indicates no relationship between the two. Values N0.2 represent a relatively good fit (Clark and Hosking, 1986). The model's pseudo R2 value of 0.441 demonstrates a good fit. This is complemented by Nagelkerke's

6

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

Aspect

Adjacent slope

Asset height Asset slope angle Vegetation type

Soil type

Rainfall

Condition

Constant

pseudo R2 value (Nagelkerke, 1991) computed in SPSS statistical software package, which is similar in theory to McFadden's test but accounts for sample size. Finally the model's goodness of fit is evaluated using the Hosmer and Lemeshow (1980)test which checks if the model is correctly specified by looking at the significance value of the test. If the test significance value is very low (e.g. b0.05) then the model should be rejected. The very high significance of this model (0.815) confirms its appropriateness. While a number of studies have carried out LR in a stepwise fashion discarding factors with significance below the threshold level, this study inputted all of the proposed factors simultaneously in order to observe the level of significance of each factor. A forward stepwise LR analysis was then carried out separately using a significance threshold of 0.1 (Dai et al., 2001; Regmi et al., 2014). This showed very similar results. Several interesting trends can be observed from the combined regression coefficients (Table 2) and the odds-ratios (Fig. 6), which quantify the contribution of each factor class to the susceptibility value, relative to a reference class. 1. Cuttings are far more likely to fail than embankments. 2. The slope angle was found to be the single most important factor in the analysis. This is in keeping with findings for natural slopes (Dai et al., 2001, Baeza and Corominas, 2001). In contrast an increase in slope height was found to have negligible effect on the likelihood of landslide occurrence. Table 3 LR model statistics. Statistics

Value

−2 log L0 likelihood −2 log L likelihood Model Χ2 Pseudo R2 (McFadden) Pseudo R2 (Nagelkerke) Goodness-of-fit (Hosmer-Lemeshow test)

502.43 280.95 221.48 0.441 0.523 0.815

3.03 2.30 1.37 1.00 0.79 0.67

a)

0.58 0.53

0

1

2

3

4

Odds ratio

1

5.50

2

4.09

0

1.00

-1

b)

0.45

0

2

4

6

Odds ratio

Bare

3.99

Grass

2.54

Shrubs

1.48

Trees

c)

1.00

0

2

4

6

Odds ratio

1200-1400 mm

2.61

1000-1200 mm

1.27

800-1000 mm

d)

1.00

0

1

2

3

Odds ratio Condition Rating

0 1.327 0 0.312 −0.405 −0.236 −0.540 0.832 −0.636 1.110 −0.797 0 1.704 1.410 0.135 0.078 1.383 0.932 0.394 0 0 −0.542 −21.393 0 0.239 0.959 0 2.000 3.284 −8.54

W SE N E NW NE S SW

Adjacent Angle Catagory

β

Embankment Cutting E N NE NW S SE SW W −1 0 1 2 Height [m] Angle [°] Bare Grass Shrubs Trees Granular till Granular material Soft clays 800–1000 mm 1000–1200 mm 1200–1400 mm 1 2 3 β0

Vegetation Type

Class

Rainfall level

Factor Object type

Aspect

Table 2 Regression coefficients.

3

26.67

2

7.39

1

e)

1.00

0

10

20

30

Odds ratio Fig. 6. Odds ratios for a) Aspect, b) Adjacent angle, c) Vegetation type, d) Annual rainfall, e) Slope condition. Reference class is in light grey and denoted with a vertical red line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3. When the adjacent natural terrain slope towards the asset, the landslide susceptibility is increased. 4. The annual rainfall was seen to be a good indicator, with the landslide susceptibility being strongly correlated to annual precipitation. 5. The type of vegetation present has a significant influence on shallow failure occurrence. 6. The asset condition was a very strong indicator of potential failure.

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

7. Although aspect was not found to be a particularly significant parameter, west facing slopes showed the highest landslide susceptibility. This is attributed to the prevailing rain-bearing winds in the region coming from the Atlantic Ocean. North facing slopes also exhibited an increased risk of failure. This is related to lower insolation and therefore reduced evapotranspiration (See Hughes et al., 2009).

7

Table 4 Confusion matrix for validation dataset. Predicted

Observed

No Yes

Correctly classified (%)

No

Yes

289 22

3 11

Overall (%)

The significance of each factor was tested using the Wald test, with a p-value of 0.1 taken as a threshold, as suggested by Dai et al. (2001) All factors except soil type were shown to be significant. Given that rock cuttings were excluded and no slopes were constructed using nonengineered fill, soft clay or peat in the Athlone division, all the assets fell into only two out of original six soil categories: glacial till and granular material. The geotechnical properties and behaviour of these two soil types (see Lehane and Faulkner, 1998) is very similar explaining the lack of bias with respect to soil type in the analyses. The LS analysis results in a predicted susceptibility value between 0 and 1 for each asset. To make a susceptibility map, these continuous values were divided into a number of groups. A range of methods have been used in the literature to classify p values (Ayalew and Yamagishi, 2005; Dai et al., 2001; Süzen and Doyuran, 2004), including natural breaks, equal intervals, quantiles, and standard deviation. In this study, five susceptibility classes were constructed after examining the patterns in the histograms presented in Fig. 7; very low (0.00–0.05), low (0.05–0.25), moderate (0.25–0.5), high (0.5–0.75) and very high (0.75–1.0). The majority of the assets (79.4%) are in the ‘very low’ susceptibility class which is unsurprising given their relative robustness over their 150 year life. The low, moderate, high and very high susceptibility class contained 13.0%, 3.9%, 2.3% and 1.4% of total assets respectively, with the percentage of assets with actual landslide records in each susceptibility class rising as the susceptibility class is increased. These are indicative of the relative accuracy of the model. 6. Validation A validation exercise was undertaken using data from 30% of the asset database comprising of randomly sampled assets not used for training the model. The validation dataset comprised of 325 assets, of which a total of 33 had experienced failure. The ratio of failures was thus the same as the training dataset. The performance of the analysis can be judged by observing the model's prediction of landslide occurrence and the actual state of each asset. This is typically observed using a confusion matrix. The confusion matrix using a typical cut-off value of 0.5 (the threshold susceptibility value differentiating between the presence or lack of a landslide) is shown in Table 4. Overall predictive performance (P) was obtained as a percentage of correctly

99.0 33.3 92.3

predicted assets, e.g. the ratio of “true negatives”; TN - assets with no landslide records in the database predicted as assets without landslides and “true positives; TP - assets with landslide records and predicted as such), to a total number of assets (N): P = (TN + TP)/N. The overall performance of the validation dataset was 92.3% which indicates excellent predictive capacity. This is attributed to the large number of assets in the very low susceptibility class which the model can easily identify as negatives. However this can cause the model to develop a preference for predicting the absence of landslides, with the result that only 11 of the 33 actual landslides in the validation dataset were predicted. For comparison, the results are complemented with the training dataset's confusion matrix (Table 5), where approximately half of actual landslides are identified. Sensitivity analyses were carried out using different training-validation ratios (60–40, 50–50) and yielded similar validation confusion matrix results but at the expense of the reliability and significance of the factors in the training model. The 70–30 ratio described in the paper was thus the optimal ratio as it compared well to results obtained when the analysis was carried out using the entire database as a training set (100–0 ratio). The authors therefore attribute the model sensitivity to the small number of actual failures within the database and the fact that local factors such as human interference (construction work, drainage changes) tend to be identified as contributing factors in many forensic analyses of slope failures. The authors consider that this will not be an issue for transport networks with larger datasets. Nevertheless, almost 50% of landslide affected assets were successfully predicted in the 7.7% of assets that comprise the moderate, high and very high susceptibility classes (akin to a confusion matrix with a cut-off value of 0.25), thereby effectively narrowing down the scope of critical earthwork assets on which asset managers should focus. The use of a cut-off value of 0.25 might also be justified in this case as the usual value of 0.5 results in a very uneven distribution of/susceptibility values, as only 3.7% of slopes are above this cut-off value. A confusion matrix for the validation set with a cut-off value of 0.25 is presented in Table 6. The table indicates increased potential for predicting actual failure (over 50%), with a minimal increase of false positives and a similar overall classification percentage as with the cut-off value of 0.5, justifying the use of lower value. If the asset

100

Percentage of assets [%]

90

Percentage of assets with landslide record in each susceptibility class

80 70 60

51.6

50 40

Percentage of assets without landslide record in each susceptibility class

27.8

30 20 10

5.6

6.4

2.2

1.4

1.3

0.8

0

1.1

1.0

0.5

0.3

Percentage of total assets in each susceptibility class

Susceptibility value p Fig. 7. Histograms of overall predicted landslide susceptibility and percentage of assets with and without landslides in each susceptibility class.

8

K. Martinović et al. / Engineering Geology 215 (2016) 1–9

1

Table 5 Confusion matrix for training dataset.

0.9

Observed

No Yes

Correctly classified (%)

No

Yes

667 40

13 38

Overall (%)

98.1 48.7 93.0

failure database is updated with greater regularity, the sample size might increase to a point where the choice of cut off value is less relevant to the results of the analysis. Finally the model's performance was evaluated using another metric, the receiver operating characteristic (ROC) curve. The ROC curve presents the relationship between the model's sensitivity and specificity, expressions inferred from the values from the validation confusion matrices with varying cut-off levels. The model's fit is related to the area under the curve (AUC), with an AUC value of 1 representing a perfect fit, and an AUC value of 0.5 (presented as a diagonal line) representing a completely random fit. A ROC curve was constructed for the validation dataset (Fig. 8), and an AUC value of 0.902 achieved. Such a result is viewed as an excellent performance (Kritikos and Davies, 2015). 7. Conclusions The aim of this study was to examine the suitability and effectiveness of statistical data-driven landslide susceptibility methods for engineered slopes on a major, ageing rail transport network. Due to their long linear nature engineered slopes on transport networks differ substantially from natural slopes and specific information is needed to assess their stability. A list of important factors that should be considered is presented, although in reality the analysis will depend on the data available at a network level. On this project detailed records of slope geometry, condition and landslide records were available for a significant portion of the Irish Rail network that was constructed in the mid 1800′s. Using this data a logistic regression was carried to develop a model to predict shallow translational slope failures on the network. The results were very promising with the overall performance of the validation dataset operating at 92.3% predictive capacity. Such a result is in keeping with the results of logistic regression studies undertaken on natural slopes where the state of the art is much more advanced. The majority of the assets (79.4%) were classified as having very low susceptibility to landslides, which is not surprising given that most of the slopes have been serviceable for over 150 years. Although the dataset of shallow slope failures was relatively large with 111 landslides recorded during the five years period where records were available, the overall ratio of failures to stable earthworks is low. This poses a problem for the model to predict the very small number of actual failures. More precise results might possibly be obtained by dividing the assets (and accompanying data) into smaller sections of uniform length (e.g. 100 m). Transport networks with more landslide records should be able to build a more robust and precise statistic model. Introduction of more engineered slope specific attributes in the database might also yield more precise results. For instance, more specific data on drainage type and condition is currently being collated by Irish Rail following the authors' recommendations. Table 6 Confusion matrix for validation dataset using a cut-off value of 0.25. Predicted

Observed Overall (%)

No Yes

Correctly classified (%)

No

Yes

283 16

9 17

96.9 51.5 92.3

0.8 0.7

Sensitivity

Predicted

0.6 0.5 0.4

No discrimination

0.3 0.2

p (0.902)

0.1 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1 - Specificity Fig. 8. The ROC curve obtained for the validation dataset (AUC = 0.902).

Landslide susceptibility analysis for engineered slopes results in a ranking of assets which gives asset managers indispensable information on the relative criticality of assets to each other, thereby allowing attention and budget to be shifted towards the critical assets, which can then be stabilised using engineered mitigation measures. This study proves that simple asset databases populated in part by visual surveys can be utilised to carry out landslide susceptibility analysis, resulting in proactive identification of landslide prone assets as opposed to the current reactive industry standard. This represents an important step forward in creating objective risk rating systems for transport network earthworks.

Acknowledgment The research is supported by the Irish Research Council Employment Based Postgraduate Programme and the Horizon 2020 Project Destination Rail (project no 636285). The authors would like to thank Cathal Mangan and Sharon Callanan from Irish Rail for the permission to use the data.

References Ahmed, B., 2015. Landslide susceptibility mapping using multi-criteria evaluation techniques in Chittagong Metropolitan Area, Bangladesh. Landslides 12 (6), 1077–1095. Akgün, A., Bulut, F., 2007. GIS-based landslide susceptibility for Arsin-Yomra (Trabzon, North Turkey) region. Environ. Geol. 51 (8), 1377–1387. Akgun, A., Dag, S., Bulut, F., 2008. Landslide susceptibility mapping for a landslide-prone area (Findikli, NE of Turkey) by likelihood-frequency ratio and weighted linear combination models. Environ. Geol. 54 (6), 1127–1143. Aleotti, P., 2004. A warning system for rainfall-induced shallow failures. Eng. Geol. 73 (3), 247–265. Aleotti, P., Chowdhury, R., 1999. Landslide hazard assessment: summary review and new perspectives. Bull. Eng. Geol. Environ. 58 (1), 21–44. Ayalew, L., Yamagishi, H., 2005. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan. Geomorphology 65 (1), 15–31. Ayalew, L., Yamagishi, H., Ugawa, N., 2004. Landslide susceptibility mapping using GISbased weighted linear combination, the case in Tsugawa area of Agano River, Niigata Prefecture, Japan. Landslides 1 (1), 73–81. Baeza, C., Corominas, J., 2001. Assessment of shallow landslide susceptibility by means of multivariate statistical techniques. Earth Surf. Process. Landf. 26 (12), 1251–1263. Bednarik, M., Magulová, B., Matys, M., Marschalko, M., 2010. Landslide susceptibility assessment of the Kraľovany–Liptovský Mikuláš railway case study. Phys. Chem. Earth Parts A/B/C 35 (3), 162–171. Brenning, A., 2005. Spatial prediction models for landslide hazards: review, comparison and evaluation. Nat. Hazard. Earth Syst. Sci. 5, 853–862. Budetta, P., 2004. Assessment of rockfall risk along roads. Nat. Hazard. Earth Syst. Sci. 4 (1), 71–81. Budimir, M., Atkinson, P., Lewis, H., 2015. A systematic review of landslide probability mapping using logistic regression. Landslides 12 (3), 419–436. Bui, D., Tuan, T., Klempe, H., Pradhan, B., Revhaug, I., 2015. Spatial prediction models for shallow landslide hazards: a comparative assessment of the efficacy of support vector

K. Martinović et al. / Engineering Geology 215 (2016) 1–9 machines, artificial neural networks, kernel logistic regression, and logistic model tree. Landslides 1–18. Can, T., Nefeslioglu, H., Gokceoglu, C., Sonmez, H., Duman, T., 2005. Susceptibility assessments of shallow earthflows triggered by heavy rainfall at three catchments by logistic regression analyses. Geomorphology 72, 250–271. Carrara, A., Cardinali, M., Detti, R., Guzzetti, F., Pasqui, V., Reichenbach, P., 1991. GIS techniques and statistical models in evaluating landslide hazard. Earth Surf. Process. Landf. 16 (5), 427–445. Cascini, L., 2008. Applicability of landslide susceptibility and hazard zoning at different scales. Eng. Geol. 102 (3), 164–177. Clark, W., Hosking, P., 1986. Statistical Methods for Geographers. John Wiley and Sons, New York (518 pp). Corominas, J., Van Westen, C., Frattini, P., Cascini, L., Malet, J.P., Fotopoulou, S., Pitilakis, K., et al., 2014. Recommendations for the quantitative analysis of landslide risk. Bull. Eng. Geol. Environ. 73 (2), 209–263. Cruden, D.M., Varnes, D.J., 1996. Landslides: investigation and mitigation. Chapter 3-landslide types and processes. Transportation Research Board Special Report (247). Dai, F.C., Lee, C.F., Li, J., Xu, Z.W., 2001. Assessment of landslide susceptibility on the natural terrain of Lantau Island, Hong Kong. Environ. Geol. 40 (3), 381–391. Dai, F.C., Lee, C.F., Ngai, Y.Y., 2002. Landslide risk assessment and management: an overview. Eng. Geol. 64 (1), 65–87. Das, I., Sahoo, S., van Westen, C., Stein, A., Hack, R., 2010. Landslide susceptibility assessment using logistic regression and its comparison with a rock mass classification system, along a road section in the northern Himalayas (India). Geomorphology 114 (4), 627–637. Devkota, K.C., Regmi, A.D., Pourghasemi, H.R., Yoshida, K., Pradhan, B., Ryu, I.C., Althuwaynee, O.F., et al., 2013. Landslide susceptibility mapping using certainty factor, index of entropy and logistic regression models in GIS and their comparison at Mugling–Narayanghat road section in Nepal Himalaya. Nat. Hazards 65 (1), 135–165. Donohue, S., Gavin, K., Tolooiyan, A., 2011. Use of geophysical techniques to examine slope failures. J. Near Surf. Geophys. Vol 9 (1). http://dx.doi.org/10.3997/1873-0604. 2010040 (February, pp 33–44). Ermini, L., Catani, F., Casagli, N., 2005. Artificial neural networks applied to landslide susceptibility assessment. Geomorphology 66 (1), 327–343. Fealy, R., Green, S., 2009. Teagasc-EPA Soils and Subsoils Mapping Project: Final Report V. 1. Teagasc; Environmental Protection Agency. Fell, R., Ho, K.K., Lacasse, S., Leroi, E., 2005. A framework for landslide risk assessment and management. Landslide Risk Manag. 3–25. Fell, R., Corominas, J., Bonnard, C., Cascini, L., Leroi, E., Savage, W.Z., 2008. Guidelines for landslide susceptibility, hazard and risk zoning for land-use planning. Eng. Geol. 102 (3), 99–111. Fitzgerald, D., Forrestal, F., 1996. Monthly and Annual Averages of Rainfall 1961–1990. Climatological Note No. 10. Irish Meteorological Service. Gavin, K., Reale, C., Xue, J., 2014. Geotechnical Challenges for the European TEN-T Network, Keynote Paper at the 3rd International Conference of Road and Rail Infrastructure. CETRA, Split, Croatia. Godt, J.W., Baum, R.L., Savage, W.Z., Salciarini, D., Schulz, W.H., Harp, E.L., 2008. Transient deterministic shallow landslide modeling: requirements for susceptibility and hazard assessments in a GIS framework. Eng. Geol. 102 (3), 214–226. Guzzetti, F., Carrara, A., Cardinali, M., Reichenbach, P., 1999. Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy. Geomorphology 31 (1), 181–216. Hosmer, D.W., Lemeshow, S., 1980. A goodness-of-fit test for the multiple logistic regression model. Commun. Stat. A10, 1043–1069. Hughes, P.N., Glendinning, S., Mendes, J., Parkin, G., Toll, D.G., Gallipoli, D., Miller, P.E., 2009. Full-scale testing to assess climate effects on embankments. Proceedings of the Institution of Civil Engineers-Engineering Sustainability Vol. 162. Thomas Telford Ltd., pp. 67–79 No. 2. Jaiswal, P., van Westen, C.J., 2009. Estimating temporal probability for landslide initiation along transportation routes based on rainfall thresholds. Geomorphology 112 (1), 96–105. Jaiswal, P., van Westen, C.J., Jetten, V., 2010a. Quantitative landslide hazard assessment along a transportation corridor in southern India. Eng. Geol. 116 (3), 236–250. Jaiswal, P., Van Westen, C.J., Jetten, V., 2010b. Quantitative assessment of direct and indirect landslide risk along transportation lines in southern India. Nat. Hazards Earth Syst. Sci. 10 (6), 1253–1267. Jaiswal, P., van Westen, C.J., Jetten, V., 2011. Quantitative assessment of landslide hazard along transportation lines using historical records. Landslides 8 (3), 279–291. Kavzoglu, T., Sahin, E.K., Colkesen, I., 2014. Landslide susceptibility mapping using GISbased multi-criteria decision analysis, support vector machines, and logistic regression. Landslides 11 (3), 425–439. Klose, M., Damm, B., Terhorst, B., 2015. Landslide cost modeling for transportation infrastructures: a methodological approach. Landslides 12 (2), 321–334. Komac, M., 2006. A landslide susceptibility model using the analytical hierarchy process method and multivariate statistics in perialpine Slovenia. Geomorphology 74 (1), 17–28.

9

Kritikos, T., Davies, T., 2015. Assessment of rainfall-generated shallow landslide/debrisflow susceptibility and runout using a GIS-based approach: application to western Southern Alps of New Zealand. Landslides 12 (6), 1051–1075. Lee, E.M., Jones, D.K., 2004. Landslide Risk Assessment. Thomas Telford Publishing, London. Lee, S., Min, K., 2001. Statistical analysis of landslide susceptibility at Yongin, Korea. Environ. Geol. 40 (9), 1095–1113. Lee, S., Sambath, T., 2006. Landslide susceptibility mapping in the Damrei Romel area, Cambodia using frequency ratio and logistic regression models. Environ. Geol. 50 (6), 847–855. Lehane, B., Faulkner, A., 1998. In: Evangelista, Picarelli (Eds.), Stiffness and Strength Characteristics of a Hard Lodgement Till. The Geotechnics of Hard Soil & Soft Rocks, pp. 637–646. Mancini, F., Ceppi, C., Ritrovato, G., 2010. GIS and statistical analysis for landslide susceptibility mapping in the Daunia area, Italy. Nat. Hazard Earth Syst. Sci. 10 (9), 1851–1864. Martinovic, K., Gavin, K., Reale, C., 2016. Assessing the vulnerability of Irish rail network earthworks. Transp. Res. Procedia 14, 1904–1913. McFadden, D., 1974. Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (Ed.), Frontiers in Econometrics. Academic Press, pp. 105–142. Menard, S., 2000. Coefficients of determination for multiple logistic regression analysis. Am. Stat. 54, 17–24. Michoud, C., Derron, M.H., Horton, P., Jaboyedoff, M., Baillifard, F.J., Loye, A., Queyrel, A., et al., 2012. Rockfall hazard and risk assessments along roads at a regional scale: example in Swiss Alps. Nat. Hazards Earth Syst. Sci. 12 (3), 615–629. Nagelkerke, N.J.D., 1991. A note on a general definition of the coefficient of determination. Biometrika 78, 691–692. Nefeslioglu, H.A., Gokceoglu, C., Sonmez, H., 2008. An assessment on the use of logistic regression and artificial neural networks with different sampling strategies for the preparation of landslide susceptibility maps. Eng. Geol. 97 (3), 171–191. Nelder, L.M., Gunn, D.A., Reeves, H., 2006. Investigation of the geotechnical properties of a Victorian Railway Embankment. Proc. 1st Int. Conf. Railway Foundations, pp. 34–47. Oh, H.J., Pradhan, B., 2011. Application of a neuro-fuzzy model to landslide-susceptibility mapping for shallow landslides in a tropical hilly area. Comput. Geosci. 37 (9), 1264–1276. Ohlmacher, G.C., Davis, J.C., 2003. Using multiple logistic regression and GIS technology to predict landslide hazard in northeast Kansas, USA. Eng. Geol. 69 (3), 331–343. Park, S., Choi, C., Kim, B., Kim, J., 2013. Landslide susceptibility mapping using frequency ratio, analytic hierarchy process, logistic regression, and artificial neural network methods at the Inje area, Korea. Environ. Earth Sci. 68 (5), 1443–1464. Quinn, P.E., Hutchinson, D.J., Diederichs, M.S., Rowe, R.K., 2010. Regional-scale landslide susceptibility mapping using the weights of evidence method: an example applied to linear infrastructure. Can. Geotech. J. 47 (8), 905–927. Regmi, N.R., Giardino, J.R., McDonald, E.V., Vitek, J.D., 2014. A comparison of logistic regression-based models of susceptibility to landslides in western Colorado, USA. Landslides 11 (2), 247–262. Remondo, J., Bonachea, J., Cendrero, A., 2008. Quantitative landslide risk assessment and mapping on the basis of recent occurrences. Geomorphology 94 (3), 496–507. RSC Railway Safety Committee, 2014. Post Incident Inspection - Collision of Train With a Landslip at the 38 ¼ Milepost on the Kilkenny to Waterford Line (Irish Rail). Süzen, M.L., Doyuran, V., 2004. A comparison of the GIS based landslide susceptibility assessment methods: multivariate versus bivariate. Environ. Geol. 45 (5), 665–679. Van Westen, C.J., Van Asch, T.W., Soeters, R., 2006. Landslide hazard and risk zonation—why is it still so difficult? Bull. Eng. Geol. Environ. 65 (2), 167–184. Van Westen, C.J., Castellanos, E., Kuriakose, S.L., 2008. Spatial data for landslide susceptibility, hazard, and vulnerability assessment: an overview. Eng. Geol. 102 (3), 112–131. Varnes, D.J., 1984. Landslide Hazard Zonation: A Review of Principles and Practice (No. 3). Walsh, S., 2012. A Summary of Climate Averages 1981–2010 for Ireland, Climatological Note No.14. Met Éireann, Dublin. Yalcin, A., 2008. GIS-based landslide susceptibility mapping using analytical hierarchy process and bivariate statistics in Ardesen (Turkey): comparisons of results and confirmations. Catena 72 (1), 1–12. Yesilnacar, E., Topal, T., 2005. Landslide susceptibility mapping: a comparison of logistic regression and neural networks methods in a medium scale study, Hendek region (Turkey). Eng. Geol. 79 (3), 251–266. Yilmaz, I., 2009. Landslide susceptibility mapping using frequency ratio, logistic regression, artificial neural networks and their comparison: a case study from Kat landslides (Tokat—Turkey). Comput. Geosci. 35 (6), 1125–1138. Yilmaz, I., 2010. Comparison of landslide susceptibility mapping methodologies for Koyulhisar, Turkey: conditional probability, logistic regression, artificial neural networks, and support vector machine. Environ. Earth Sci. 61 (4), 821–836. Zêzere, J.L., Garcia, R.A.C., Oliveira, S.C., Reis, E., 2008. Probabilistic landslide risk analysis considering direct costs in the area north of Lisbon (Portugal). Geomorphology 94 (3), 467–495.