Landslides (2015) 12:927–941DOI 10.1007/s10346-014-0513-xReceived: 25 February 2014Accepted: 8 August 2014Published online: 28 August 2014© Springer-Verlag Berlin Heidelberg 2014

Sujit Roy I Amiya Baruah I Santanu Misra I Nibir Mandal

Effects of bedrock anisotropy on hillslope failurein the Darjeeling-Sikkim Himalaya: an insightfrom physical and numerical models

Abstract This study investigates the role of bed-material anisot-ropy in triggering landslides in metamorphic terrains of theDarjeeling-Sikkim Himalaya. The initial disposition of foliation(planar anisotropy) with respect to the hillslopes is found to be acrucial parameter in controlling the scale of landslides. Hillslopeswith foliation dipping into the surface slope are mostly affected bydeeper-seated larger-scale landslides, as compared with those oc-curring on hills with down slope-dipping foliations. To verify ourfield observations, we performed scaled slope–failure experimentsin a tilted sandbox, simulating the foliation anisotropy in analoguemodels. Sand–mica beds with the anisotropy planes dipping intothe surface slope developed shear localisation along deep-penetrating listric zones, leading to slope failure in the form ofdown-sliding blocks of large dimensions. In contrast, models withanisotropic planes dipping down slope produced failure zonesrestricted to the shallow level. The narrow failure zones in thelatter case had little tendency to grow in depth but propagated upthe hillslope direction. Using Drucker–Prager’s failure criterion,we also ran experiments with finite element models to substantiatethe contrasting effects of bed anisotropy on hillslope failureprocesses.

Keywords Landslide . Metamorphic terrain . Foliationdip . Shear localisation . Sandbox experiments . Finite elementmodelling

IntroductionUnderstanding the mechanics of hillslope instability has been afocus of intense studies in a wide range of disciplines, such asgeotechnical engineering, geomorphology, and structural geology.Based on field evidence, various authors have proposed a numberof geological and engineering factors, such as geomorphic patterns(Agliardi et al. 2001; Avanzi et al. 2004; Dunning et al. 2009; Hoet al. 2012), seismic activities (Keefer 1984; Lenti and Martino 2012;Harp et al. 2011; Jibson et al. 1994; Chang and Taboada 2009; Alfaroet al. 2012; ; Wang et al. 2013), rainfall intensity (Keefer et al. 1987;Crosta 1998; Crosta and Frattini 2008; Martelloni et al. 2012;Sorbino and Nicotera 2013) which can trigger the process of slopeinstability (Dunnicliff 1988; Zhou et al. 2002; Weng et al. 2011),leading to landslides in mountainous regions. Under specific sur-face conditions, inherent structural features of bed materials oc-curring on varied scales, such as faults, joints and penetrativefoliations can also play a major role in controlling the hillslopestability. Model results suggest that these structures act as me-chanically weak surfaces, reduce the bulk strength of hillsloperocks and promote slope failure processes (Wang et al. 2003; Leeet al. 2002; Martel 2004; Agliardi et al. 2001).

We carried out field investigations in topographically ruggedterrains of the Darjeeling-Sikkim Himalaya (Fig. 1a). Hillslopes inthis terrain experience frequent landslides in various modes and

dimensions, ranging from shallow surface slips to compoundrock-and-debris slides. The motivation of this study was to explorethe possible roles of past bedrock rheology in dictating suchcontrasting slope failure processes in the same region. Earlierstudies show that the anisotropy of bed materials can significantlyaffect slope stability (Amadei 1996; Pietruszczak et al. 2002; Martel2004; Margielewski 2006), as well as control shapes of landslides(Bishop 1955; Hoek and Bray 1981). For example, failure surfacesdeveloping in isotropic media are nearly circular in profile buttend to non-circular when the bed materials are strongly aniso-tropic (Guzzetti et al. 1996; Zabuski et al. 1999). In this study, weshow the effects of mechanical anisotropy on the patterns of shearlocalisation in bed materials causing landslides in the Darjeeling-Sikkim terrain. This terrain is mostly underlain by PrecambrianDaling Group of rocks, comprising strongly foliated metamorphicrocks such as phyllites and schists. These foliated metamorphicrocks are mechanically anisotropic due to the presence of two-dimensional mineral fabrics and gneissic layering (Amadei 1996;Mandal et al. 2000; Dewers and Ortoleva 1990; Kocher et al. 2006).During the field study, the magnitudes and disposition of land-slides associated with relative orientations of foliation (plane ofmechanical anisotropy) were observed. Two extreme cases ofhillslopes, with foliations dipping either along or opposite to thedirection of surface slope, were observed in the study. Findingsfrom the field were verified using analogue and numerical modelexperiments. The analogue experiments were performed on me-chanically layered sand–mica models, simulating the slope failureprocesses on anisotropic bedrocks. Employing the Drucker–Prageryield criterion, we ran two series of experiments on finite element(FE) models with mechanical properties equivalent to those inanalogue experiments. Both the analogue and FE model experi-ments confirm that the presence of foliation dipping into thehillslope promote larger landslides. Another direction of the cur-rent research aims to find a quantitative approach to robust andefficient safety measures for slope instabilities, particularly thoseaffecting human habitation (Peck and Deere 1960; Chen andMartin 2002; Takahashi 1991; Iverson 1997; Crosta et al. 2003;Greco et al. 2013). In this study, we propose an effective mitigationmeasure, considering the relative orientation of bedrock anisotro-py as a factor controlling the slope failure.

Field description of landslides

Geological frameworkThe Darjeeling-Sikkim Himalaya is subdivided into distinct tec-tonic domains, separated by crustal-scale thrusts (Ganseer 1964;Acharyya 1980; Dasgupta et al. 2004; Acharyya 2007). The terrainhas undergone penetrative ductile deformation, giving rise to aregional arcuate fold pattern (Acharyya 1980) (Fig. 2). The foldcore is dominated by the Lesser Himalayan Daling Group of low-

Landslides 12 & (2015) 927

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grade metamorphic rocks (Proterozoic to Mesozoic), which isbounded by medium-to-high-grade metamorphic rocks of theHigher Himalayan Belt, called the Higher Himalayan CrystallineComplex. The Main Central Thrust separates the Lesser Himalayasfrom the Higher Himalayan belt (Ganseer 1964; Beaumont et al.,2001). Gondwana (Carboniferous–Permian) and molasse-typeSiwalik (Miocene–Pliocene) sedimentary rocks constitute the

sub-Himalayan Zone bordering the southern mountain front.The Main Boundary Thrust that separates sub-Himalayans fromthe Lesser/Lower Himalayas follows an east–west trend. In theextreme north, a thick sequence of Cambrian to Eocene fossilifer-ous sediments of the Tethyan Zone overlies the Higher HimalayanCrystalline Complex on the hanging-wall sides of a series of north-dipping normal faults constituting the South Tibetan DetachmentZone (Ganseer 1964; Burchfiel et al. 1992).

Case studiesThe terrain is characterised by tectonically controlled steep slopes,coupled with extreme weathering conditions, and its hillslopesbecome frequently unstable, leading to landslides (Bhasin et al.2002; Kanungo et al. 2006; Ghosh et al. 2012). An enormousamount of damage is caused every year due to slope-failure,heavily affecting local settlements. We investigated landslides pri-marily along the following transects of the Darjeeling SikkimHimalayas: (a) NH 31A highway leading to Gangtok; (b) roadsections in the Kurseong sub-division of Darjeeling District; (c)Gangtok–Mangan road sections; (d) Mirik sections; (e) Tistabazarhillslopes; (f) Melli-Jorthang road section; and (g) Kalimpong roadsections (Fig. 1b). These study areas are largely underlain byDaling Group of rocks. The orientation of foliation in the Dalingrocks varies considerably due to tectonic folding, and the mode ofhillslope failure is greatly influenced by the relative orientations offoliation planes and hillslopes.

Based on the geometrical relation between hillslopes and bed-rock foliations, landslides in this region broadly fall within twoextreme cases: hillslopes with foliation dipping either subparallelto the surface slope or almost perpendicular to the surface slope.Field observations undertaken upon the following transects—NH31A highway, road sections in Tistabazar and Kurseong sub-divisions, and Melli to Jorthang roadway, reveal that shallow,near-surface slope failures are common where the foliation planesdip in the direction of the hillslope. In this geomorphic setting,failure occurs along foliations that act as weak planes whichfacilitate land slippage (Fig. 3). Their failure surfaces thus tend tobe planar and predominantly occur at shallow depth. Slippingalong discrete surfaces parallel to the foliation consequently givesrise to loose masses, flowing down the hillslopes in the form ofsmall debris slides. A striking contrast in landslide geometry wasencountered where the foliation dipped steeply into the surfaceslope. For example, the failure surfaces in Ambootia slide, Deoloslide, Bara Mangwa slide and Garlang slide are generally deep-seated and curvilinear in cross-section and cut across the foliationdipping into the hillslopes (Fig. 4). They eventually develop high,vertical or near-vertical scarp faces at the head of the landslide. Inthese slides, the hanging-wall blocks underwent catastrophicdownward movements, similar to block faulting. During the slid-ing movement, these large blocks fragmented into clasts with awide range of sizes, producing debris masses. The failure processesin these locations thus involved surface instability with hugevolumes, covering areas in the order of 3×104 m2, and often occuras large debris slides (Fig. 4).

Over a span of 4 years, we specifically monitored the progres-sive development of a slide on a hillslope transacted by a streamflowing into the Tista River near Tistabazar (Fig. 5a). The slideformed and remained active within the period of the field obser-vation, enabling us to analyse a time series of the failure process at

Fig. 1 a A relief map of the studies area. Colour contours on the right barindicates elevations (in meter) with respect to the foreland plain. b A panoramicview of the Darjeeling-Sikkim Himalaya. Landslide locations under the presentstudy are shown by circles. The location of the study area in the HimalayanMountain belt is shown at the top

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Landslides 12 & (2015)928

Fig. 2 Structural patterns of the rocks in Darjeeling-Sikkim Himalayan terrain containing crustal-scale thrusts: Main Central Thrust (MCT), Main Boundary Thrust (MBT)(after Acharyya, 1980). The map reveals domes and basins, suggesting that the rocks have also undergone intense ductile deformations

Foliation parallel to hillslope

Failure along foliations

Failure along foliations

Foliation

Exposed

Foliation

Planes

Road cut0 10m

0m 100m

River Tista

Foliation

Exposed Foliation

Planes

Road cut

Road cut

Foliation dipping

parallel to hillslope

d

Foliation dipping

parallel to

hillslopeRoad cut

d

400

m

0m

30m

0m

Fig. 3 Landslides in anisotropic bed rocks with foliations dipping down the hillslopes on road sections near Likubir, NH31A highway (top) and on the Melli to Jhorthanghighway (bottom). Right-hand sketches illustrate perspective and profile views of the landslides. Foliation dips in the two landslides were 30° and 35°, respectively

Landslides 12 & (2015) 929

this location. Strongly foliated rocks of the Darjeeling Gneiss(Higher Himalayan Crystalline Complex) constitute the bed ma-terials of the Tista slide. In the landslide zone, the foliation planedips approximately 35° into the direction of the hillslope, whichhas an average slope dip of 32°. The surface instability initiatedwith the formation of large ruptures daylighting at an elevation of100 m from the landslide toe, implying a deep-seated failuresurface. The surface exposure of the rupture was marked by awell-developed scarp (Fig. 5b). This slide subsequently involved acompound failure due to the presence of small secondary fracturesperpendicular to the foliations. These fractures coalesced to form abulk failure surface and facilitated the formation of numeroussecondary failure surfaces. The process then involved localisationof a second failure surface beneath the earlier surface, resulting ina new sub-vertical scarp in the upslope direction located 100 mfrom the first scarp (Fig. 6). This new failure zone appeared to bequite deeply penetrating, as the event led to major hillslope insta-bility, and produced a huge volume of debris consisting of boul-ders, some several meters in diameter. Such large boulders seem tohave been generated by block faulting of the failed mass, whichsubsequently disintegrated into fragments of varying sizes.

Physical experiments

MethodThe landslide processes encountered in the field were investigatedthrough laboratory experiments by using scaled, analogue sand-box models. The modelling used the conventional experimentalapproach that has been extensively used in slope failure experi-ments (Mandl et al. 1977; Katz and Aharonov 2006; Roy andMandal 2009; Yamada et al. 2010). A large number of workershave used granular sand masses for such model slope experiments,as they provide good scaling of the actual shear failure behaviourof materials forming natural slopes. As an example, Yamada et al.(2010) have performed experiments with wet sand as an analogue

material to investigate submarine fans triggered by the shearfailure of slopes on the hanging walls in accretionary prisms alongsubduction margins. Their model fans show an excellent agree-ment with those observed in Nankai trough in Japan. Similarsandbox models have been employed to simulate vibration-induced shear failure on hill slopes, coupled with rain fall(Juanico et al. 2008). The results of all these experimental model-ing provides a convincing validation of the use of granular sand inthe simulation of shear failure processes on hill slopes. Based onthis consideration, we chose sand models to perform hill slopefailure experiments. An important advantage of this approach isthat one can observe the progressive stages of failure processes andundertake geometric and kinematic analyses within a three-dimensional framework. The sandbox used in this study haddimensions of 300×545×385 mm, with thick glass sidewalls(Fig. 7). The box had three movable lids at front, back and attop. The entire setup rested on a flat base with a hinge, allowingthe sandbox to be tilted as desired. In the experiments, we tookaccount of the following factors: (1) model hillslope (α) and (2)orientation of the plane of anisotropy with respect to the modelhillslope topography. Progressive slope failure processes were ob-served and photographed through the glass side walls of thesandbox under tilted conditions. For a given tilt, the sand bedunderwent failure and tended to achieve a stability of its slope. Tokeep the failure process ongoing, we progressively steepened thebasal inclination to force the surface slope always on the verge ofinstability during an experimental run.

Model material and preparationLoose silica sand was used for an appropriate scaling of analoguemodels with Coulomb (frictional) rheology, as applicable to large-scale hillslope failure processes (Roy and Mandal 2009).The bulkphysical properties of sand, e.g. porosity, frictional coefficient andcohesive strength, depend on the size, shape and packing of thesand grains. Sand grains used in our experiments were sub-

0m 100m

Exposed Scarp

d

500m

0m

Foliation dipping against hillslope

Balason River

Exposed Scarp

Foliation

Exposed Scarp

Right FlankLeft Flank

Foliation

0m 100m

0m

500m

d

Foliation dipping against hillslope

Exposed ScarpRight Flank

Foliation dipping against hillslope

Fig. 4 Landslides in anisotropic bedrocks with foliations dipping against the hillslopes at Ambootia, Kurseong (top) and Deolo, Kalimpong (bottom). Their perspectiveand profile views are shown in sketches on the right side. Foliation dips were 32° and 40°, respectively

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Landslides 12 & (2015)930

rounded and had high sphericity. To obtain a well-sorted sandmass, we sieved the sand between mesh sizes of 60 and 70 (ASTM),keeping the size distribution in a narrow range of 0.25 to 0.21 mm.The sand had an angle of internal friction ∼30°. The density of theweakly cohesive sand was in the range of 1,200–1,400 kg/m3. Thesand had a void ratio of approximately 0.6. Several workershave invoked Mohr–Coulomb failure criterion to analyze theyield behaviour in loose, granular sand materials on a con-tinuum scale (Mandl et al. 1977; Krantz 1991; Massoudi andMehrabadi 2001). However, grain scale processes can signifi-cantly influence the macroscopic failure behaviour. Shearingfailure can involve grain-scale void generation, a phenomenoncalled dilatancy, which has been shown as a major factor incontrolling the yield behaviour, especially at low pressures(Rowe 1962; Bolton 1986; Simoni and Houlsby 2006;Chakraborty and Salgado 2010). We will specifically discusslater the implications of such dilatancy factors in slope failureprocesses.

For model preparation, a small amount of water (1 % byvolume) was added to the sand to develop weak cohesion inthe models. When the sand is wet, each grain is separatedfrom the surrounding grains by a thin film of water. Thecohesion between the water molecules and the adhesion be-tween the water films and sand grains make each grain stickto its neighbour and thus introduces inherent shear strengthin the damp sand. Experiments were performed with bothisotropic and anisotropic models. The bulk planar anisotropywas produced by alternate stacking of sand layers and thinmica layers (Hubbert 1937; Horsfield 1977; Richard and Krantz1991; Cobbold and Jackson 1992; Misra and Burg 2012).

Analog models were prepared maintaining the following scal-ing ratios. The length ratio between analog models (xj

a) andequivalent natural objects (xj

n) was:

xja.

xjn ¼ 10−3 ð1Þ

(a)

(b)

Fig. 5 a A glance to the Tista landslide displaying multiple scarps developed in successive years. b Steeply dipping scarp exposed to the surface near the landslide crown.The arrow indicates the hanging wall sliding in the form of block faulting along the scarp

Landslides 12 & (2015) 931

This ratio implies that models with a length dimension of10 mm represent equivalent objects of 10 m in real space. The

sand bed thickness in our experiments was in the range of 30–40 cm, which corresponds to 300–400 m thick zones, as applicable

Horizontal Distance (m)

100 150 200 250 30050

250

300

350

400

Peswak Khola

SW NE

Surface before landslidePresent surface

Exposed scarp (1st phase of sliding)

Altitude (m)

Foliation dips against hill slope

Accumulation of debris

Exposed scarp (2nd phase of sliding)

Exposed Scarp (1st phase of sliding)

Exposed Scarp (2nd phase of sliding)

Accumulation of debris

Fig. 6 Detailed structural map (left) and a geological cross section (right) of the Tista slide, prepared based on the surface exposures. The section reveals the course oflandslide evolution through successive shear failure surfaces

Sandbox Setup

Sandbox Setup

Sand Layers

Mica Layers

Sand Layers

Mica Layers

0 20cm

0 20cm

Progressive Failure

Progressive Failure

Model Hillslope

Model Hillslope

(a)

(b)

Fig. 7 A schematic diagram of the model setup used in sandbox experiments. Layering (anisotropy planes) in sand bed dipping a down and b against the model hillslope. See text for details of the experimental procedure

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Landslides 12 & (2015)932

to landslides in our study area. Assuming the density of weatheredrocks in the order of 2400 kg/m3, the density ratio between rocksand model materials is:

ρa.ρn ¼ 0:5 ð2Þ

The stress ratio then follows:

σija.

σijn ¼ ρax j

ag.

ρnx jng ð3Þ

As the analog experiments were carried out in normal gravity,stresses are to be scaled down as the product of density and lengthdimensions. Accordingly, the cohesive strength (C) of model ma-terials must be scaled down as that of stress (Hubbert 1937;Horsfield 1977; Davy and Cobbold 1988; Cobbold and Jackson1992). The scaling ratio of cohesion thus becomes:

σija.σij

n ¼ Ca.Cn ð4Þ

Assuming the cohesion of naturally weathered rocks in theorder of Cn∼106 Pa. (cf. Zhou et al. 2004), it follows from Eqs. 1to 4 that a model material with Ca∼500 Pa is required to simulatefull-scale slope processes in analogue experiments. This value ofcohesive strength of wet granular sand used in sandbox analogueexperiments is consistent with the values widely employed byearlier workers (Krantz 1991; Eisenstadt and Sims 2005).

Isotropic models were developed by sieving sands of two dif-ferent colours alternately, forming layers with an average thicknessof 20 mm. The purpose of this passive layering was to reveal thesurfaces of shear failure in the model. In the case of anisotropicmodels, sand layers were intercalated with veneers of mica flakes(Fig. 7). The degree of anisotropy imparted by this sort of me-chanical layering is discussed later in section on “Foliated rockmaterials and their anisotropy.” Markers of different colours wereused to demarcate the anisotropic planes. Two types of anisotropicmodels were prepared; in one set of experiments, the anisotropiclayering was developed parallel to the surface slope of the sandbed, i.e. the layers dipped in the same direction as the slope whenthe sandbox had a tilt (Fig. 7a). In another set, the layers wereinclined into the tilting direction of the sandbox. To prepare thelatter models, the sandbox was initially tilted at a desired angle,and it was then filled up with alternate horizontal layers of sandand mica flakes. Finally, the whole setup was brought back to thehorizontal position, and the layering dipped into the surface slope(Fig. 7b).

The sandbox was initially kept horizontal, and the front end lidwas lifted vertically, allowing the sand bed to collapse and attainan equilibrium slope. The box was then tilted to a maximum angleof 45° by increasing the inclination at 2° intervals. During tilting,the sand bed became unstable and developed slope-failure pat-terns similar to those observed in the Darjeeling-SikkimHimalayas. Initiation and propagation of the failure surfaces wereobserved and photographed through the glass side-walls of thesand box.

Slope–failure patterns in experimentsIsotropic sandbox models always showed slope failure in the formof block faulting (Fig. 8). During the progressive stages of a modelrun, shear–failure surfaces first developed in the upper section ofthe sand bed and propagated into the deeper level with increasinginclination of the sandbox. For an inclination of ∼22°, two failuresurfaces were formed (Fig. 8). However, the frontal shear surfacehad a greater dip (74°) and became more active, resulting in slip ata higher rate, and the sliding block eventually collapsed. Thecollapse took place suddenly, producing mass movements in theform of debris avalanches down the failure surface, as observed inmany slides of the Darjeeling-Sikkim Himalaya. Another majorslip surface formed in the upslope section, which had an inclina-tion of about 55°. With a slight increase in the box tilt, the failuresurface reactivated, leading to downward block movement, as inthe previous event. The sliding motion of the block triggeredsubsidiary shear failure down the slope. Overall, the model pro-duced a failure zone consisting of several shear surfaces. The blockfinally slid over the zone and collapsed to produce debris massesin front of the sand box. The surface slope consequently attained astable angle of 48° (Fig. 8).

The failure pattern described above drastically changed whenthe model was mechanically anisotropic with the plane of anisot-ropy dipping in the same direction as the surface slope (Fig. 9).The anisotropy planes tended to arrest penetration of the failuresurface deeper into the slope and caused localisation of slopeinstability at a shallow depth. The failure zone grew in size withan increase in the box tilt. For a tilt of 14°, a minor, weakly curvedfracture surface formed in the front part of the sand bed and hadan inclination of around 61° in the upper section. When the slopeangle reached 26° a major shear surface formed at an inclination of∼10° to the anisotropic plane. With further tilting (32°), the modeldeveloped discrete shear fractures with a spacing of 5 cm close tothe surface, forming domino-like blocks (Fig. 9). The blocks had atendency to rotate independently while sliding on a principalshear–failure surface. Consequently, the slip surfaces locally

Fig. 8 Progressive slope failure patterns in isotropic sand models. Note that the colour layering in this model was passive in nature, and the values shown in the figurescorrespond to the inclinations just after the moments of failure initiation in successive stages

Landslides 12 & (2015) 933

formed wavy geometry due to interactions with the rotating dom-ino blocks. On a long run, these small scale blocks collapsed downthe slope along the anisotropic planes, similar to that observed inthe field. When the box was tilted to more than 40°, another twofailure surfaces formed at horizontal angles of 35° and 20° in theupslope direction. They showed listric (spoon-shaped) geometry,tending to be tangential to the anisotropic plane (Fig. 9). Overall,the failure zone was restricted to a shallow level (d/H=0.2, where dis the maximum depth of failure zone, normalised to bed thick-ness, H) and propagated to a large extent in the upslope direction.The depth of failure zone, d/H, however, increases from nearly 0.2to 0.6 as the tilt increased from 30° to 45° (Fig. 10).

Anisotropic models with the same rheology but with the planeof anisotropy dipping into the surface slope produced strikinglydifferent failure patterns when compared with the models withplanes of anisotropy parallel to the slope. In this case, the failureinvolved block faulting along deep-penetrating listric surfaces(Fig. 11). For a tilt of 12°, a failure surface formed at an angle of

38° with the base. The anisotropy plane showed weak drag effectson either side of the fracture. With increasing basal slope, thefailure surfaces multiplied at regular intervals but tended to betangential to the base. When the tilt was increased to ∼35°, themodel developed a large shear–failure surface localised in theupslope section, which propagated by cutting the earlierdown-slid blocks. In addition, the model developed minorclosely spaced shear surfaces at a deeper level in the frontalpart. They intensified the failure process at a greater depth.The anisotropic layering was locally obliterated due to intenseshearing along these slip planes. Primarily, the models haddeep-penetrating failure surfaces with strong listric geometry,resulting in large fault blocks sliding down the slope (Fig. 11).The upwardly concave failure surface transacted the olderfailed blocks at the toe portion. These models finally pro-duced thick failure zones; their relative depth d/H was sensitive tothe tilt and varied from 0.4 to 0.9, with the tilt increasing from 25° to45° (Fig. 10).

Fig. 9 Development of slope failure in anisotropic sand models with the anisotropy plane dipping towards the hill slope direction. Dashed black lines indicate thesurfaces of shear failure produced in successive phases

0.00

0.20

0.40

0.60

0.80

1.00

20 30 40 50

Opposite to Slope

Parallel to Slope

Hillslope Gradient

d/H

Hd

Fig. 10 Variations in the maximum penetration depth (shown inset) of failure surface in model landslides with the anisotropy planes dipping down (violet line) andagainst (green) the hill slope

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Landslides 12 & (2015)934

The principal findings of our physical experiments were:(1) mechanical anisotropy significantly influences slope-failure patterns; (2) anisotropic planes dipping down theslope result in the development of shallow failures, whereasthose dipping against the surface slope produce large, deeplypenetrating failure zones, characterised by listric shear sur-faces (Fig. 12).

Finite element analysis

Modelling approachA finite element method (cf. Griffiths and Lane 1999; Zheng et al.,2005; Roy and Mandal, 2009; Crosta et al., 2003) was used tosimulate slope–failure patterns in numerical experiments and tosubstantiate observations from the physical experiments. The me-dia considered for numerical modeling were rate-independentelasto-plastic continua, undergoing failure by Drucker–Prageryield criterion (Regueiro and Borja 1999). According to this yieldcriterion, an equivalent stress is defined,

σe ¼ 3βσm þ 12

Sf gT M½ � Sf gh i 1

2 ð5Þ

where σm is the mean or hydrostatic stress,

σm ¼ 13

σx þ σy þ σz� �

and {s}T represents all the stress components, and Sf g is thedeviatoric stress matrix. [M] is a matrix with the following form:

M½ � ¼

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 2 0 00 0 0 0 2 00 0 0 0 0 2

26666664

37777775

β is a material constant, expressed as:

β ¼ 2 Sin ∅ffiffi3

p3−Sin∅ð Þ ð6Þ

The material yield parameter is defined by:

σy ¼ 6c Cos ∅ffiffi3

p3−Sin∅ð Þ ð7Þ

where ∅ is the angle of internal friction and c is cohesionof the material. The material remains elastic and the stressesdevelop following the elastic stress–strain relations until σe<σy. The material yields when the value of σe becomes morethan σy. From Eq. 5, the yield criterion follows

F ¼ 3 βσm þ 12

Sf gT M½ � Sf gh i 1

2− σy ¼ 0 ð8Þ

The criterion in Eq. 8 is close to the von Mises yieldcriterion, but it takes into account the effect of hydrostaticstress. The equation defines the yield surface as a circularcone in the stress space. Equations 6 and 7 are chosen insuch a manner that the yield surface encloses rightly thehexagonal Mohr-Coulomb yield surface. There is no hard-ening rule, as the yield surface does not change with pro-gressive yielding, and the material is considered perfectlyplastic.

For numerical modelling, we used a commercial finiteelement code (ANSYS® Academic 2007) imposing the rheo-logical formulations described above. The Drucker–Prageryield criterion (Eq. 8) can be implemented by this code interms of either the associated or non-associated flow rule. Toavoid plastic dilations in the medium, inputs were consid-ered with a dilatancy constant of 0, which in turn definesadoption of the non-associated flow rule. To determine theplastic yielding, a parameter, called stress ratio is used,

Fig. 11 Progressive slope failure patterns in anisotropic sand models with the plane of anisotropy dipping against the hill slope direction. Note that the shear failureoccurs as block faulting along deep-penetrating shear surfaces (dashed black line)

Landslides 12 & (2015) 935

expressed as:

N ¼ σe

σyð9Þ

Yielding takes place in an elasto-plastic body when N≥1. Thebody remains in an elastic state if N<1. We mapped the zones withN≥1 to reveal the pattern of slope failure under gravity. Thesevalues were used to map the plastic yield zones in the deformingmedium. However, such numerical analysis of progressive defor-mation does not take into account the instantaneous elastic toplastic transformation of the media, rather it assigns N>1 to thezones of plastic yielding, which can be contoured and mapped toshow the progressive development of yield zones under a givenstress. The finite-element experiments were run with nonlinearstatic conditions to simulate the progressive development of fail-ure zones.

We designed two-dimensional finite element models usingANSYS plane strain elements (Plane 82).The element Plane 82 isdefined by eight nodes with two degrees of freedom, i.e.

displacements along the nodal x and y directions. Experimentalrun time was divided into a number of time sub-steps; for eachtime sub-step, the stress ratio factor N (Eq. 9) was estimated foreach node and then contoured and mapped in the xy space.

The elastic properties of the model material were given in termsof Young’s modulus and Poisson’s ratio with values in the order of2×106 Pa and 0.25, respectively. Considering the density of naturalsand used in analogue experiments, the material density in thenumerical model was chosen to be around 1,400 kg/m3. To de-scribe the Drucker–Prager Criterion employed in the model, wechose the cohesive strength and friction angle in the order of500 Pa and 30°, respectively, conforming to the properties of sandbeds in the physical experiments. To simulate the mechanicalanisotropy, the models were inter-layered with weak layers, me-chanically equivalent to the mica veneer in the sand models. Forthis, an elasto-plastic material was chosen with lower cohesion(100 Pa) and frictional angle (25°). To simulate strain localisationunder varied hill slope conditions, all the nodes in the finite-element model were attributed to a global gravity load. Themodel boundary conditions (Fig. 13) were chosen to replicatethose employed for the sandbox experiments. It may benoted that we deliberately designed the numerical modelscommiserating the sandbox models as the later is wellconstrained with respect to the material parameters as wellas boundary conditions, which were not possible to collectand measure reliably from natural examples to fit into thenumerical model. In fact, our numerical models aimed atvalidating the analogue experimental results, which were ingood agreement with natural hillslopes in the Darjeeling-Sikkim Himalaya.

Progressive failure patterns in finite-element modelsThe numerical results obtained from anisotropic models show anexcellent agreement with those observed in the physical experi-ments. Models with anisotropic planes sloping in the same direc-tion as the surface did not produce distinct failure zones, incontrast to that in isotropic models (Fig. 14a). It appears that theplanar mechanical anisotropy acts as a barrier to downward pen-etration of material failure into the slope. The stress–ratio mapshows that the failure (N>1) localises at a shallow depth along thetopographic surface, with little or no penetration downward (d/H=0.18), as observed in the sandbox experiments. The failurezones localise at a higher level in the up-slope direction andprogressively propagated down the surface slope, withoutshowing much penetration into the deeper level. However,models with planar mechanical anisotropy dipping into thesurface slope produce distinct failure zones (N>1) in thedeeper part of the model (Fig. 14b). The failure pattern issimilar to that in isotropic models. However, the failure zonepenetrates further into the deeper section of the slope (d/H=0.65), causing large slope instability, which was also observedin the sandbox experiments.

To summarise, the presence of planar anisotropy significantlyinfluences the failure pattern as well as the intensity of damage. Inthe case of anisotropy planes dipping along the surface slope, theshear failure is weak and restricted to shallow levels. In contrast,anisotropy planes dipping into the surface slope produce deeplypenetrating shear bands, leading to slope instability in the form ofa fault block.

Fig. 12 Line diagrams of the model landslides showing contrasting failurepatterns for isotropic and anisotropic sand beds with layering down and againstthe surface slope

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Discussion

Implications of model resultsSandbox experiments were conducted to study the pattern offailure in hillslopes as a function of the angle of slope and theorientation of mechanical anisotropy in the bed materials.Some of these experimental results were complemented bynumerical simulations, which yielded similar patterns ofhigh-strain localisations. The experimental results indicatethat the relative orientation of mechanical anisotropy withrespect to surface slope has an enormous effect on the local-ization of high-strain zones. Both the physical and numericalmodel experiments confirm that hillslopes with foliations dip-ping at the slope angle produce little or no shear localisationat deeper levels. Slope failures in such settings are likely to berestricted to shallow depths. On the other hand, anisotropyplanes dipping into the hillslope cause pronounced shearlocalisation in the form of narrow, sharp bands, which actas the potential zones of slope failure. The failure zones

therefore penetrate to deeper levels, and the landslides be-come large in magnitude.

The model results from this study have significant implicationsin the finer interpretation of landslide activities in tectonicallydeformed terrains, such as the Darjeeling-Sikkim Himalaya. Thebedrock in this kind of terrain is generally foliated, resulting instrong mechanical anisotropy (Mandal et al. 2000). The orienta-tion of rock foliations relative to the hillslopes are an additionalfactor in determining the scale of landslides. Under the same set ofgeological conditions, hillslope surfaces cutting across the rockfoliation are likely to be unstable on a large scale, in contrast tothose surfaces sloping along the foliation. In the latter case, theslopes can frequently be unstable due to localisation of slipsparallel to the foliation but on a small scale.

Natural slope failures in the Darjeeling-Sikkim Himalayashowed deposition of large volume of debris in their toe region(Fig. 6). These frontal materials were produced by collapse of thesliding blocks down the hillslopes. Some of our sandbox experi-ments produced similar collapse of the sliding blocks in the frontalregion (Fig. 12). In case of natural landslides, these loose materialsare generally washed away by flowing streams and rain water.However, they would influence the stability of slopes if they wereallowed to accumulate and accrete in volume through successivestages of slides. Understanding of such complex landslide process-es needs further investigations.

Sandbox model results described above are concerned with theeffects of planar mechanical anisotropy on the failure patterns ofhill slopes, as observed in our field study area. There are otherfactors that can influence the failure behaviour in sand models. Ithas been demonstrated from theoretical studies that shearingdeformations in granular sand can involve inter-granular voidgeneration, leading to dilatancy during the flow. The effects ofsuch dilatancy on the macroscopic failure have been studied ingreat detail (Desrues et al. 1985; Bolton 1986; Oda and Kazama1998; Du Bernard et al. 2002; Iverson 2005). Some of the theoreticalmodels are capable of complying with a specific form of the Mohr–Coulomb criterion to account for the dilatancy effects (Cowin1974; Rajagopai and Massoudi 1990; Massoudi and Mehrabadi2001). It has been shown that the inclination of shear failure

Fig. 13 Consideration of boundary conditions used in finite element (FE)modelling. ux and uy are displacement components along x and y direc-tions, respectively. All elements are subjected to gravity forces (g=9.81 m/s2) in thevertical direction

Fig. 14 Patterns of slope failure in finite element models with the planes of anisotropy dipping a down and b against the hill slope. Note that the model in (b) hasproduced spectacular shear localization at a deeper level, in contrast to the model in (a) showing a weak failure zone at the shallower level

Landslides 12 & (2015) 937

surfaces with the principal compression is a function of the dilat-ancy angle. In our sand experiments, this dilatancy factor mighthave influenced the inclinations of shear failure on model slopes.However, the results obtained from sandbox provide qualitativelya good correlation with those observed in natural hill slope failure.

Foliated rock materials and their anisotropyThis section discusses the common petrological elements thatinduce mechanical anisotropy in the inherent rock materials andalso the possible role of surface processes in amplifying the degreeof anisotropy in them. Different types of structural elements, suchas bedding, stratification, lamination, planar mineral fabrics, andsystematic joints may cause mechanical anisotropy in rocks(Amadei 1996; Mandal et al. 2000; Misra et al. 2009). A commonvariety of layered anisotropy is induced by alternate laminationsof weak and stiff mineral constituents. For example, many foliatedrocks show alternate quartzo-feldspathic and mica-rich layers.Such foliated rocks can be compared with layered compositeswidely used in material sciences. The degree of mechanical anisot-ropy of a layered composite depends on the contrasts in stiffnessand thickness across the layering (Biot 1965). To express the degreeof anisotropy, consider the following theoretical model. The bulkrigidities of a layered composite under stresses normal and tan-gential to the anisotropy plane are:

μN ¼ μ1α1 þ μ2α2 ð10Þ

μT ¼ 1α1

μ1þ α2

μ2

� � ð11Þ

where αi ¼ tit1þt2

; i ¼ 1t and μ represent the thickness and the shear modulus of

individual layers. Several authors have used the ratio of μN andμT to express the degree of bulk mechanical anisotropy, termed δ(Biot 1965; Weijermars 1992; Ramsay and Lisle 2000; Mandal et al.2000). For isotropic materials δ=1, and δ>1 in the case of aniso-tropic materials. From Eqs. 10 and 11,

δ ¼ 1þ R−1ð Þ2R

TT þ 1ð Þ2 ð12Þ

R is the ratio of shear moduli of the stiff and weak layer units inthe composite material, and T is their thickness ratio. Equation 12shows that δ =1 when R=1, i.e. isotropic rheology. δ increases withincreasing R, implying increasing bulk anisotropy in the compos-ites (Fig. 15). On the other hand, δ shows a nonlinear increase withthe thickness ratio T (Fig. 15).

In Darjeeling-Sikkim Himalaya, the terrain is mostly com-posed of foliated rocks which are comparable to the layeredcomposites described above. These gneissic rocks are macro-scopically banded with alternating layers of quartzo-feldspathic and micaceous materials. Both natural and exper-imental evidence suggest that quartzo-feldspathic materials aremechanically stiffer than micaceous materials. Differentworkers have analyzed the δ factor for rocks showing com-posite character imparted by various factors, such as sedimen-tary bedding, metamorphic segregation (Dewers and Ortoleva

1990), and the presence of inclusions in a homogeneousmatrix (Mandal et al. 2000). Bayly (1970) estimated δ in therange of ∼2.0 for mica-poor phyllites and ∼12.5 for the samerock type rich in mica. Using these analytical data fromnatural examples, together with analogue experimental data,Bayly proposed a high δ value of 25 or more for natural rocktypes. However, available literature suggests that the degree ofanisotropy can be as high as 50 (Lan and Hudleston 1996;Kocher et al. 2006), and 100 (Weijermars 1992). This theoret-ical analysis indicates that the rocks in metamorphic terrains,i.e. the Himalayan Gneissic Complex, can be strongly mechan-ically anisotropic. This supports this paper’s proposition thatmechanical anisotropy plays a crucial role in governing thelandslide process in this terrain.

The inherent anisotropy of such bedrock may undergomodification due to near-surface chemical weathering bygroundwater. Preferential percolation of groundwater can sig-nificantly promote the degree of mechanical anisotropy. It hasbeen shown that foliated rocks exhibit strong anisotropichydraulic conductivity, as water tends to flow along the layerinterfaces, i.e. foliation (Wang et al. 2002). During watertransport parallel to the foliation, the rocks undergo hydro-lytic chemical reactions, producing phengitic or sericitic min-erals along the foliations. These new materials are muchweaker than the original minerals, reducing the bulk shearmodulus and shear strength along the foliation, and therebyincreasing the degree of anisotropy in the rocks seated be-neath surface. It then follows that the landslide activities in aterrain can intensify due to the effect of mechanical anisotro-py via surface weathering processes.

Fig. 15 Variations in the degree of bulk anisotropy factor (δ) with the thickness(T) and shear moduli (R) ratios of composites consisting of layers with contrastingthicknesses and rigidities. The shaded region indicates the range of δ values fornatural rocks

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Implications in mitigation measuresThis study provides a scientific framework for developing mitiga-tion measures to tackle landslide-associated natural disasters inDarjeeling-Sikkim Himalaya and similar terrains elsewhere. Ac-cording to field observations and model test results, mitigationmeasures must take into account bedrock anisotropy and itsorientation relative to the surface slope. Both the physical andnumerical experiments confirm that hillslopes with foliation dip-ping in the same direction as the surface slope are unlikely toproduce deep-seated high-strain zones or shear failure surfaces.Slope failures in such settings are likely to be restricted to shallowdepths. Based on this finding, this paper proposes that retainingwalls commonly used for arresting landslides need not have deep-penetrating foundations on these slopes. Conversely, anisotropyplanes dipping into the hillslope cause pronounced shearlocalisation, forming narrow, sharp bands that may form the zonesof potential shear failure. The failure zones therefore lies at a muchdeeper level, and the landslide becomes quite large in magnitude.Evidently, the mitigation measures have to be designed in such amanner that the stabilisation structures (e.g. toe walls, toe piles,etc.) extend beyond the likely depth of the failure zone, whichforms at some location on the hill slope and propagates upward,maintaining a maximum depth of penetration, as predicted in thenumerical and physical experiments (Fig. 10). Otherwise, the entirestabilisation structure might move with the down sliding blockalong the deeper-level shear failure surfaces (Fig. 16a).On the otherend, a series of retaining walls with shallow foundations would beeffective for maintaining the stability of hillslopes with foliationsdipping along the slope, where the failure zones are likely tolocalise at the shallow depth (Fig. 16b).

LimitationsThere are some limitations in the sandbox modelling. (1) Granularsand materials used in the experiments provide an approximaterheological correlation with natural hill slope materials, excludingphysical factors, such as dilatancy, heterogeneity in suction andtime-dependent rheological variations. Despite these limitations,sandbox experiments are found to be effective in order to dem-onstrate natural shear failure processes convincingly in the

laboratory. (2) Natural slope processes generally involve timevariability of the physical settings, which has not been taken intoaccount in the modeling. Where the groundwater level occurs atmuch deeper levels, it has little effect on surface failure processes.However, during the monsoon season, the water table can lie closeto the ground surface and markedly influence slope stability. (3)Steepening of the hill slopes is considered to be the driving factorfor slope failure. However, there are other physical factors thatoften lead to landslides under the same topographic slopes. Me-chanical attributes of such factors, e.g. ground vibration, thermalexpansion, soil creep and vegetation and weathering were notconsidered in this study. However, the principal objective of thisstudy is to demonstrate the probable effects of mechanical anisot-ropy on the gravity-induced slope failure patterns.

ConclusionsMechanical anisotropy in the rock mass can influence the patternof strain localisation in the hillslope and thereby control thelandslide processes in terrains with large topographical variability.Foliations dipping into the surface slope promote shear failure atdeeper levels, resulting in landslides of large dimensions. On theother hand, foliations dipping down the hillslopes induce strainlocalisation near the surface and cause frequent shallow landslidesof smaller dimensions. As a mitigation measure, we propose for asingle retaining wall with deep foundation on hillslopes withfoliations into the surface slope, whereas a set of a multipleretaining walls with shallow foundations in case of hillslopes withfoliations along the hillslope.

AcknowledgementsCSIR, India, is gratefully acknowledged for providing a researchfellowship to SR. AB thanks DST, India, for awarding theINSPIRE AORC fellowship. A part of this study has beensupported by the SERB project, and J. C. Bose Fellowship ofDST, India, awarded to NM. SM acknowledges an SDF grantfromGNS Science. Themanuscript benefited from critical commentsby Mauri and Eileen McSavney. We thank the two anonymousreviewers and the Editor for their insightful, thought-provokingand thorough reviews.

Fig. 16 Proposed designs for the mitigation of landslides on hill slopes with foliated bed rocks. a Retaining wall with a deep foundation for hill slopes with foliationsdipping against the slope and b placement of multiple retaining walls with shallow foundation for hill slopes where the foliations dip down the hill slope

Landslides 12 & (2015) 939

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