Original Article

Landslides (2005) 2: 8396DOI: 10.1007/s10346-005-0049-1Received: 9 October 2004Accepted: 7 March 2005Published online: 12 May 2005 Springer-Verlag 2005

Jordi Corominas Jose Moya Alberto Ledesma Antonio Lloret Josep A. Gili

Prediction of ground displacements and velocitiesfrom groundwater level changes at the Vallcebre landslide(Eastern Pyrenees, Spain)

Abstract In active landslides, the prediction of acceleration of move-ment is a crucial issue for the design and performance of warningsystems. The landslide of Vallcebre in the Eastern Pyreenes, Spain,has been monitored since 1996 and data on rainfall, groundwaterlevels and ground displacements are measured on a regular basis.Displacements observed in borehole wire extensometers have shownan immediate response of the landslide to rainfall episodes. This rapidresponse is likely due to the presence of preferential drainage ways.The occurrence of nearly constant rates of displacement in coinci-dence with steady groundwater levels suggests the presence of viscousforces developed during the movement. An attempt to predict bothlandslide displacements and velocities was performed at Vallcebre bysolving the momentum equation in which a viscous term (Binghamand power law) was added. Results show that, using similar rheo-logical parameters for the entire landslide, computed displacementsreproduce quite accurately the displacements observed at three se-lected wire extensometers. These results indicate that prediction ofdisplacements from groundwater level changes is feasible.

Keywords Translational slide . Viscous behaviour . Predictionof displacements . Eastern Pyrenees . Spain

IntroductionTraditional strategies in landslide hazard management have beenmostly oriented at avoiding dangerous sites and stabilizing unsta-ble slopes. Regional and urban planning can be powerful tools toensure that development occurs in the safest places. In that respect,planners and decision-makers have benefited from the informationprovided by hazard and risk maps. However, development in manyregions has occurred, and indeed continues to occur without hazardmaps being available. Because of this, there are numerous examplesof development built either on or near large landslides. In such cases,remedial measures are often unaffordable, while moving the popula-tion to more stable slopes can pose a considerable societal problem.As a consequence, the coexistence of human activities with naturalhazards must be considered with the risk being mitigated throughthe use of hazard management strategies.

In landslide threatened areas, solutions usually focus on the im-plementation of mitigation measures that avoid the slope failure ordivert the moving mass away from vulnerable elements, or protector reinforce the threatened elements. However, in some places, tostabilise a landslide may simply be too costly in financial and/or en-vironmental terms. When mitigation is not feasible, it is importantto consider the implementation of warning systems that may, at least,avoid damage and/or loss of human lives. To be effective and reli-able, warning systems require a sound knowledge of the behaviourof the landslide, including the mechanism, the potential triggers andtheir respective thresholds (i.e. rainfall intensity and duration), the

expected time of failure or reactivation, the expected velocity, and theareal extent including the runout distance where appropriate.

There are many uncertainties in the forecasting of when a move-ment in a landslide will occur, or when rates of movement will increaseand thus it can not be performed reliably at present. Therefore, im-proving this capability is a basic requirement for the development ofwarning systems.

The existing methods of predicting and forecasting the landslideoccurrence have mostly concentrated on first-time slope failures. Thesimplest method for predicting landslide occurrence at a regionalscale is through the establishment of empirical rainfall thresholds.This method is based on the analysis of storms that have producedslope failures. The fundamental assumption is that, in a homogeneousregion, landslides occur once a precipitation threshold has been over-come. The threshold is usually expressed as rainfall intensity-durationrelationship (Caine 1980; Cancelli and Nova 1985; Wieczorek 1987;Larsen and Simon 1993) and it has been used with some degree ofsuccess as a warning system in areas affected by widespread and re-current shallow landsliding (Keefer et al. 1987).

A more precise prediction of the time of failure can be obtained bymeasuring the displacement rates in slopes and landslides. Transla-tional and rotational movements display a range of behaviour styles,including long-term creep, catastrophic movement that is precededby long-term creep, and sudden catastrophic movement with no creepphase (Petley and Allison 1997). Forecasting of catastrophic event maybe made by analyzing the late stages before the slope failure, i.e. ter-tiary creep (Saito 1965). Time of failure can be determined by curvefitting techniques (Voight and Kennedy 1979; Picarelli et al. 2000), orfrom the linear trend of the inverse rate curve (Voight 1989; Fukuzono1990). A summary of the different methods proposed in the literaturecan be found in Federico et al. (2004).

Prediction of the failure may be also carried out by physically-basednumerical models. Significant developments have been producedover the last years in slope stability models (Matsui and San 1992;Griffiths and Lane 1999) and, in particular, in coupled hydrologicaland mechanical models (Wilkinson et al. 2002). Numerical modelscan provide a good understanding of the mechanism of failure andthey can consider complex landslide geometries, spatial variationsin soil properties and three-dimensional groundwater flow, amongother advantages. However, the applicability of these models to theprediction of slope displacements and failure conditions is still farfrom routine, is complex and time consuming, and experiences of 3Dcoupled modelling are rather limited.

Suspended and dormant landslides can be reactivated in periodsof heavy rainfall while active ones may show phases of accelerationand deceleration. This variable movement pattern has been observedin slow-moving earthflows (Lateltin and Bonnard 1995), mudslides(Angeli et al. 1996), and in both rotational and translational landslides

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(Corominas et al. 1999). In some of these movements, the search forreliable rainfall thresholds has been unsuccessful (Noverraz et al. 1998;Flageollet et al. 1999) and alternative approaches are required to assessthe conditions leading to the reactivation. Petley et al. (2002) analyzedinverse rate curves and demonstrated that landslides occurring inexisting failure surfaces show an increase of the rate of deformationup to a constant rate (steady-state behaviour) for any given stress state material combination. On the other hand, the use of hydrologicaland mechanical models is restricted because of the complexity ofthese landslides. Existing models remain limited when consideringgroundwater changes and rates of displacement. Some attempts toexamine large landslides have included the use of simplified empiricalmodels that combine hydrological and stability analyses (Van Aschand Buma 1997) and the use of viscous constitutive laws for thesimulation of continuous displacement patterns (Vulliet 2000).

Continuously moving landslides require a dynamic analysis in-stead of a classical static approach. The temporal scale is fundamen-tal, and any modelling attempt should consider this. In addition tothese conceptual difficulties, the analysis of the response to both shortand medium-term rainfall scenarios with hydrological and mechan-ical models requires long records of high quality data that includerainfall, groundwater levels and landslide displacements.

In this paper we present an examination of movement of the Vall-cebre landslide, a slow-moving landslide activated by rainfall. A simu-lation of the displacement pattern in relation to groundwater recordby means of a dynamic, physical model has been attempted. Thework has been complemented by an extensive field survey and labo-ratory investigation to allow the best possible modelling of landslidebehaviour. That has included an analysis of the rheology of the slid-ing material and of the influence of the viscous component on themotion.

The Vallcebre landslideThe Vallcebre landslide is a large, active slope failure located in theupper Llobregat river basin, in the Eastern Pyrenees, 140 km northof Barcelona, Spain. The landslide is situated on the western slope ofthe Serra de la Llacuna (Fig. 1). The mobilised material consists of aset of shale, gypsum and claystone layers of continental origin glidingover a thick limestone bed, all of which are of Upper Cretaceous Lower Palaeocene age. The dimensions of the slide mass are 1200 mlong and 600 m wide. The entire landslide involves an area of 0.8 km2

that shows superficial cracking and distinct ground displacements.The age of the landslide is not known but it is known to have beenactive for several centuries at least.

From a geomorphological point of view, the Vallcebre landslide isof a translational type (Fig. 2). A longitudinal profile shows a stair-shape with three main slide units of decreasing thickness towards thelandslide toe (Fig. 3). Each unit is formed by a gentle slope surfacebounded in its downhill edge by a scarp of a few tens of meters high.At the base of each scarp an extension area develops in the formof a graben. This fact is interpreted as the lower units moving morerapidly than upper ones, which has been confirmed by the monitoringnetwork installed. The average slope of the landslide is about 10.

The toe of the landslide extends to the Vallcebre torrent bed, and ispushing it towards the opposite bank. As a result of this, the Vallcebretorrent has been shifted to the west more than ten meters and thefoot of the landslide has overridden the opposite slope to form aback tilted surface (Fig. 4). The torrent undermines the landslide toeduring floods, causing local rotational failures which decrease theoverall stability.

Most of the evidence of surface deformation is situated at theboundaries of the slide units in the form of distinct shear surfacesand tension cracks. At the base of each transverse scarp, both the

Fig. 1 General view of the Vallcebre translational slide. The movement is bounded, in the background, by the high scarp of Serra de La Llacuna (center-right), in the foreground by the Vallcebretorrent, which runs from the right to the left in an incised gully, and laterally by the light grey limestone outcrops

84 Landslides 2 . 2005

Fig. 2 A geomorphological sketch of the Vallcebre landslide

Fig. 3 Geological cross-sections of the Vallcebre landslide (the location of the profiles appears in Fig. 2)

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Fig. 4 Photograph of the toe of the Vallcebre landslide which is being continuously undermined and eroded by the Vallcebre torrent. Local slope failures are observable in the front

ground surface and the trees are tilted backwards due to the de-velopment of a graben along with a slight rotation of the head. Incontrast, within the units, the ground surface is only disturbed byminor fissures, scarps less than 50 m long, and by some crackingof the walls of farm-houses standing on the landslide. The direc-tion of both the transverse scarps and grabens, indicates a move-ment towards the north-west (see Fig. 2). A secondary direction ofmovement, towards the Torrent Llarg, is also suggested by the trendof the escarpment of the upper slide unit, but this has not beenvalidated to date. The most active area is the lower unit, which isbounded, at the south-western side, by the torrents of Vallcebre andLlarg and, at its north-eastern side, by a well developed lateral shearsurface.

The geological structure of the landslide has been obtained bymeans of an intense geological and geomorphological assessment,which has included mapping of the surficial exposures, geophysicalsurveys and drilling. The mobilised material consists of a sequenceof continental sediments. From the bottom to the top it includes(Fig. 3): (i) densely fissured shales, 1 to 6 m thick, showing distinctslickensides; (ii) locally, gypsum lenses up to 5 m thick and some tensof meters width which are predominant in the southern side of thelandslide; and (iii) clayey siltstones rich in veins and micronodules ofgypsum with thickness of up to tens of meters. In addition to theselayers, the extension zones located at the toe of the scarps have beenfilled with colluvium composed of boulders and gravel with a siltymatrix.

Gypsum lenses are affected by solution processes and have devel-oped some karst features like pipes and springs. These pipes run

close to the topographical surface and frequent collapses (sinkholes)are observable in the ground surface, which are arranged followingapproximately straight paths.

The area is affected by two thrust faults and some associated folds.One of these faults runs underneath the landslide and has a verticaloffset of about 10 m (Fig. 3). The landslide also overlays and hides atightly folded syncline that forms a thick core of red clayey siltstones.This syncline has an east-west trend and its axis dips towards the west,more or less parallel to the down-slope direction.

Monitoring of the landslideThe lower unit of the Vallcebre landslide has been monitored since1987 using conventional surveying and photogrammetry (Gili andCorominas 1992). During July 1996, March 1997 and April 1998, six-teen boreholes were drilled in the landslide in order to: log the geo-logic materials of the landslide; to provide undisturbed samples forlaboratory tests; to allow in-situ hydrological testing; and to set upa monitoring network. Boreholes were equipped with inclinometers,wire extensometers and piezometers. Further details about the site,the fieldwork carried out and the monitoring scheme can be foundin Corominas et al. (1999, 2000).

The failure surface of the landslide was determined using incli-nometers. The inclinometric profiles showed that the displacementoccurs in a thin basal shear zone, with negligible deformation aboveit (Corominas et al. 1999). The shear zone develops through the fis-sured clayey siltstone layer, close to the contact with the limestone. Ithas an average inclination of 10 towards the Vallcebre torrent and it

86 Landslides 2 . 2005

Fig. 5 Wire displacements at boreholes S-2, S-5, S6, S9 and S-11

runs roughly parallel to the ground surface except in the area closeto the contact between the intermediate and lower units where thepresence of the inverse fault produces a bedrock threshold and a de-crease of the landslide thickness. The depth of the failure surface isnot constant. Inclinometric readings showed that the lower slide unithas a thickness of 10 to 15 m, whereas the intermediate unit reachesa thickness of at least 34 m in the northern side and between 14 and19 m in the southern one.

Since 1996, systematic logging of rainfall, groundwater levelchanges, and landslide displacements has been carried out every20 min. Piezometric readings have indicated that changes in ground-water levels occur quickly. The extensometer has recorded suddenchanges in displacement rates that can be directly related to the fluc-tuations of the water table governed by rainfall.

Measurements of surface displacements using differential GPS havebeen used to complement the measurements of the inclinometersand wire extensometers. A total of 30 points were positioned on thelandslide surface for periodic control. These points included reference

points, stable points adjacent of the landslide, and targets within thelandslide mass (buildings, outcropping rock blocks, steel rods andupper ends of the boreholes). Real Time Kinematics and Fast Staticwere used to analyze the GPS observations (Gili et al. 2000). FourteenGPS campaigns were carried out from December 1995 to February1998. During this period horizontal displacements up to 1.6 m andsubsidence of the landslide surface of up to 0.35 m were observed.

The wire extensometer measurements show that the landslide hasnever completely stopped moving since we started the continuousmonitoring in November 1996, although velocities reduced signifi-cantly during dry periods (Fig. 5). On the other hand, the historyof displacement of the extensometers reflects that different parts ofthe landslide mass move synchronically but with a different rate ofdisplacement. Extensometer S2 has shown the fastest displacements,with maximum recorded rates of up to 50 mm/week. The other exten-someters standing on this slide unit, the S5, S9 and S11, have exhibitedrates lower than those of S2, although they were of the same order ofmagnitude.

At borehole S6, placed on the intermediate slide unit, the velocityis significantly smaller, indicating that, compared to the lower unit,the intermediate unit is less active.

Determination of the landslide parametersTests on undisturbed samples obtained by drilling were carried outto determine parameters and soil characteristics to be used in thenumerical analyses. Special attention was paid to tests for determiningthe shear strength of the soil involved in the slip surface.

Basic identification tests and different types of shear tests wereperformed on 14 undisturbed samples. Shear tests were carried outpredominantly on samples of the fissured shale unit where the slipsurface is located; in particular, some tests were conducted on ob-served pre-existing shear surfaces (Fig. 6). Table 1 shows the locationwhere the samples were taken and the type of tests performed on eachsample.

The average Atterberg limits obtained on two samples of clayeysiltstone and seven samples of fissured shales are indicated inTable 2.

Table 1 Location of samples and tests performed

Borehole Depth of slip surface (m) Depth of sample (m) Material Type of test and specimenDirect shear test Ring shear test CU triaxial test

S-2 15 15.2 Fissured shale Existing shearsurface

Remoulded Undisturbed

19.6 Fissured shale Undisturbed S-3 9.5 10.3 Fissured shale Undisturbed Remoulded

10.7 Fissured shale UndisturbedS-4 9.5 4.0 Clayey siltstone Undisturbed Remoulded

8.9 Clayey siltstone Undisturbed Remoulded S-6 44.5 44.1 Fissured shale Existing shear

surfaceRemoulded

S-7 3 4 25.4 Fissured shale Undisturbed Remoulded 34.2 Fissured shale Undisturbed Undisturbed

S-9 14.5 15.2 Fissured shale Undisturbed Remoulded S-11 8 6.5 Clayey siltstone Undisturbed S-12 17.5 11.2 Clayey siltstone Undisturbed Remoulded S-13 13.5 11.4 Clayey siltstone Undisturbed Remoulded S-14 13.5 8.7 Clayey siltstone Remoulded

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Fig. 6 Slickensided shear surface withinthe fissured shales

Table 2 Average Atterberg limits

Liquid limit Plastic limit Plasticity index

Fissured shales 41.8 22.1 19.7Clayey siltstones 54.5 35.2 19.3

Using a conventional direct shear box apparatus, a displacement,totalling 30 mm was applied in three steps, consisting of an initialdisplacement of 7.5 mm followed by a return displacement of 15 mm,and finally a displacement of 7.5 mm to return to the starting posi-tion. A minimum of three different vertical stresses were applied oneach specimen (50 or 60 mm diameter, 25 mm high). The rate of dis-placement was 7.5 mm/day ensuring that shear occurred under fullydrained conditions. For two samples of fissured shale, taken from adepth of 15.2 m from borehole S2 and from a depth of 44.1 m from

Table 3 Peak shear strength parameters of fissured shale and clayey siltstone

Range of normal stress (n) c (kPa) ()0

Fig. 7 Minimum shear strength obtainedin different types of tests and samples

were performed on four specimens (50 mm diameter, 100 mm high)extracted from three undisturbed samples of fissured shale.

Peak shear strength envelopes obtained from direct shear tests andtriaxial tests are similar for fissured shale and clayey siltstone. Theresulting failure envelopes are non linear and may be defined by theparameters shown in Table 3.

Figure 7 shows for all three types of experiment the minimum shearstrength measured for each sample. In fissured shale the differencesbetween the minimum shear strength measured in direct shear, intriaxial tests or in ring shear tests are small and are comparable todifferences between samples of the same material. The minimumstrength measured from direct shear tests on clayey siltstone is lightlygreater than the same type of strength obtained for fissured shale.Nevertheless, the minimum strength of clayey siltstone, obtained

Fig. 8 Piezometric records of boreholes S2, S4, S5, S6, S9 and S11

from ring shear tests, is similar to the minimum strength measuredfor the fissured shale.

The strength measured on pre-existing shear surfaces is smallerthan the minimum strength obtained from direct shear tests and ringshear tests, indicating that the residual state has not been reached inthese tests. Therefore, for the fissured shale, the residual strength maybe overestimated if it is assumed to be equal to the minimum strengthmeasured in direct shear box or in the Bromhead ring shear appa-ratus. Table 4 shows the parameters that define the failure envelopeassociated to the minimum strength measured. Those parameterscorrespond to the straight lines depicted in Fig. 7.

From volumetric changes recorded during consolidation phasein shear box tests, the variation with applied vertical stress of theconfined elastic modulus, the consolidation coefficient, the hydraulicconductivity, and, the secondary consolidation coefficient were deter-mined. Typical values of confined elastic modulus are about 100 MPaand hydraulic conductivities range between 107 and 109 cm/s.

Hydrological changes and landslide responseGroundwater variations for the period November 1996 to October1997, measured using six piezometers (see Fig. 2 for the locations) areshown in Fig. 8. All piezometers were open from top to bottom, whichgives an average position of the water table in the borehole. A parallelgroundwater flow was assumed in all analyses. Table 5 shows the depthof the piezometers and the position for low and high groundwaterlevel.

The data show that groundwater reacts almost immediately to rain-fall inputs, suggesting that water infiltration is controlled by fissures

Table 5 Depth of piezometers and range of groundwater level position in boreholes S2,S4, S5, S6, S9 and S11

Depth to groundwater level (m)Borehole Piezometer depth (m) Minimum Maximum

S2 8.7 0.63 6.28S4 7.7 0.96 4.47S5 8.8 3.50 6.2S6 19.8 3.59 11.71S9 9.9 1.28 5.81S11 7.9 0.96 5.05

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Fig. 9 Piezometric record (blue line) and landslide velocity (black line) at borehole S2

and pipes rather than by soil porosity. The role of the karstic net-work in the gypsum lenses is unclear but all the observed features arevery shallow (up to 3 m depth), which is well above of the normalgroundwater level fluctuation. Thus it might play only a secondaryrole.

Despite the rapid response of the piezometers, peak water levelsare attained at slightly different times depending on the permeabilityof the adjacent material. Two basic types of responses to rainfallhave been observed, depending on the location of the piezometers.These located in tension zones, such as S5, show a smaller variationin groundwater level (ranging between 0.5 and 2 m) and a fasterdrainage compared to the piezometers located elsewhere (for exampleS2, S4 and S11). The latter piezometers experience changes of 2 to 5 mand a slower rate of groundwater level decrease. The behaviour ofpiezometer S5 is consistent with the presence of high permeabilitycracks in the tension zone (graben). Consequently, it can be inferredthat cracks act as preferential drainage paths within the landslide.

In addition to the rapid response to precipitation inputs, allpiezometers show a defined level below which the groundwater tabledecreases very slowly. This level may be observed during the periodsFebruaryApril 1997 and SeptemberOctober 1997, in which no ornegligible rain was recorded in the area (Fig. 8).

A close relationship between the groundwater level changes andlandslide activity was measured using a wire displacement meterat borehole S2 (Fig. 9). There exists a strong level of synchronismbetween the two records. In addition, the rate of displacement isstrongly correlated with the water table data. The exception to this isthe event of January 1997 (increment of velocity without incrementof water table), which may be caused by other factors (i.e. toe erosionby the Vallcebre torrent).

Stability conditionsAn analysis of the stability of the landslide was performed using 2-Dlimit equilibrium method. This gives a global safety factor which isdifficult to relate to the creep behaviour seen in Vallcebre, wheremovements occur almost continuously. However the determinationof both driving and resisting forces provides an insight into the mag-nitude of the unbalanced force and the degree of stability of thelandslide.

For this analysis, the Bishop and Janbu methods of slices havebeen used by means of the STABL code, which was developed atPurdue University, USA (Lovell 1988). The stability analyses have beenperformed considering the two extreme groundwater levels recordedin the piezometers. In this case the observed groundwater depthsranged between 1 and 6 m in the lower unit and 10 and 12 m in theintermediate unit. A flow parallel to the slope surface was assumedto compute pore water pressures from water table depth. Finally,a direct relation between water table position and global factor ofsafety is defined. We have determined the factor of safety for a rangeof strength parameters and water table positions. Four groups of limitequilibrium analyses were performed:

Case 1. Analyzes the stability of both the lower and intermediateunits of the landslide, i.e. the slip surfaces can include both units.

Case 2. Only the stability of the lower unit has been considered. Case 3. Only the equilibrium of the intermediate unit has been

analyzed. Case 4. The stability of the intermediate unit, in the absence of

the lower unit has been considered. In this case the toe of the slipsurface could exit through the crack zone, so as to avoid passiveearth pressures from the lower unit affecting the stability of theintermediate one.

In each case, two positions of the ground water table have beenconsidered, corresponding to the maximum and minimum situationsmeasured in the piezometers within the period analyzed (Table 5).Finally, a variation of the soil strength parameters has been adopted,in order to perform a sensitivity analysis of the global factor of safety.

Three types of materials have been used as different layers, inthe same way as the hydrological model, with the following natural(saturated) unit weights (n):

Fissured shales n = 22 kN/

m3

Clayey siltstone with gypsum n = 20 kN/

m3

Gravel + silty matrix n = 22 kN/

m3

Table 6 summarises the main results of these analyses. These resultsshow that in some particular cases, the global factor of safety is closeto unity. This explains the activity of the landslide, i.e. small changesin stresses or pore water pressures produce a significant decreasein factor of safety and therefore a change in movement rate. Thegeometry used in the analyses coincides with that presented in Fig. 3(cross section A-A). The slip surface considered in the computationsis based on the information provided by the inclinometers.

The computed factors of safety show that the lower unit of thelandslide is less stable than the intermediate one. Note that parametervalues of cohesion (c) and friction angle () used in the calculationscorrespond to feasible values, taking into account the laboratorytests performed. It has been assumed that representative strengthparameters are those of the shear surface. For the low groundwa-ter position, displacement records at S-6 show no movement whiledisplacements at S-2 and S-8 are very low. This is consistent withthe results of Cases 1 and 4 which indicate that rapid movementof the lower landslide unit removes support to the intermediateone.

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Table 6 Global Factors of Safetycomputed for the different cases(see text)

Clayey siltstone Fissured shale Colluvium Factor of safetyc c c Position of water table

Low High

Case 1 (Both Landslide units)0 14.7

0 11.8 0 14.7 1.19 1.140 14.7 0 7.8 0 14.7 1.02 0.98Case 2 (Lower Landslide unit)0 14.7 0 11.8 0 14.7 1.17 1.070 14.7 0 7.8 0 14.7 0.79 0.72Case 3 (Intermediate Landslide unit)0 14.7 0 11.8 0 14.7 1.18 1.130 14.7 0 7.8 0 14.7 1.05 1.01Case 4 (Intermediate unit without lower unit)0 14.7 0 11.8 0 14.7 1.14 1.100 14.7 0 7.8 0 14.7 1.02 0.99

These results also agree with the field measurements, which showhigher velocities for the lower part. In fact, it is assumed that move-ment starts on the lower unit, which has a factor of safety close to 1,and then a tension area and some cracks develop at the head scarp ofthis unit, which is actually the toe of the medium part of the land-slide. This movement of the lower unit generates, after some days, amovement increase on the intermediate part as well. This behaviourhas been considered in the group of analyses in which the equilib-rium of the intermediate part without the lower unit has been studied(Case 4).

However, the analysis of the lower unit (Case 2) also shows that for alow groundwater level, the factor of safety is still very low (F.S. = 0.79),which does not correspond with the very low rate of displacementobserved. This suggests that either the analysis is not appropriate orother forces must be taken into account.

On the other hand, Fig. 10 shows an interesting relationship be-tween observed velocities and the depth of water table at borehole S2for the period considered (modified from Fernandez-Pombo 1998).A cubic curve can be fitted to the data, giving a good regressioncoefficient. The points at a water table depth of 5 m and velocitiesover 5108 m/s refer to the event of December 1996January 1997mentioned above.

Fig. 10 Velocities versus water table depths at borehole S2 for November 1996 to October1998. Data correspond to mean daily values (modified from Fernandez-Pombo 1998)

The position of the groundwater level at a depth of 6.22 m approxi-mately, corresponds to a stable situation. If a back analysis of stabilityis performed for this case in the lower unit, values of the effectivefriction angle of = 14 and of cohesion c = 0 for the fissured shaleare obtained. This, again, does not agree with the value obtained fromlaboratory tests, which range from 7.8 to 11.8. Note that this smallrange of friction angle provides a change in factor of safety from 0.79to 1.17.

The value of = 14 obtained assuming limit equilibrium forthat position of water table is difficult to explain if only static condi-tions are considered. Although laboratory data could include someuncertainties (i.e. due to sampling) we do not have any evidence ofsuch high strength for the slip surface. Consequently, we understandthat beside frictional resisting forces, additional resisting forces (i.e.viscous forces) are necessary to stop the movement. Overall, a limitequilibrium analysis can not simulate the continuous movement ofthe landslide, and a different mechanical analysis must be used in-stead.

Modelling of landslide displacementsThe close relationship existing between landslide velocity and posi-tion of groundwater level at borehole S2 suggests that it is possibleto perform a simulation of the landslide displacements from datarecorded in the piezometers. Figure 10 shows that a black box regres-sion analysis is feasible for the simulation of displacements, but wepreferred to adopt a physical approach using the momentum equa-tion. We analysed the dynamics of local points of the landslide inwhich uniform conditions for the geometry (i.e. infinite slope con-ditions) can be reasonably assumed. In addition to that, a viscouscomponent has also been taken into account. A brief description ofthe model and its application to Vallcebre is presented in this section,which also includes a critical appraisal of the approach considered.

Viscous behaviour of the landslideThe dynamics of the landslide are governed by the difference betweendestabilising forces (F), that depend basically on weight and slope,which are constant, and resisting forces (F r), that are sensitive towater pressure at the slip surface. The momentum equation can bewritten as:

F Fr = ma (1)

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where m is the mass and a the acceleration. For a local point of thelandslide where infinite slope conditions apply, resisting forces canbe estimated using Mohr-Coulomb criterion, depending on cohesionand friction. Forces are computed over a unit surface, and thereforeshear stresses are considered in what follows:

[c + ( pw) tan ] = ma (2)

where is the destabilising shear stress, c is the cohesion, is thenormal stress, p w the groundwater pressure and the friction angle,all magnitudes referred to the slip surface. Some general predictionson landslide behaviour can be inferred from Eq. (2) , and they will becompared with the observations made in the Vallcebre landslide.

The groundwater pressure is the only temporal variable in the lefthand side of Eq. (2). Therefore this equation predicts a unique valueof the acceleration for each value of groundwater pressure. A one toone relationship should also exist between acceleration and positionof the groundwater level, if parallel flow is assumed. However, theanalysis of Fig. 9 shows that the acceleration is positive when thegroundwater level rises whereas it is negative when the water tabledecreases. Thus, different values of acceleration were recorded at thelandslide for the same groundwater level. This fact suggests that otherterms should be included in the momentum equation.

Another evidence of this behaviour is presented in Fig. 11. Thisfigure shows groundwater level changes and wire displacements atborehole S2. Note that during dry periods, for example April andMay 1997, the movement has constant velocity. However, if there isan unbalanced force in the system, a value of acceleration shouldbe expected. If this is not the case, other resisting forces should betaken into account in Eq. (2). Therefore, an additional force thatwe interpret as being a viscous component, appears to be importantand should be considered in further analyses. After a rain event,the velocity changes, and from a total displacement BC, part canbe attributed to the rainfall (AB) and part is due to the viscous

Fig. 11 Water table depths and displacements measured by the wire extensometer, plottedagainst time at borehole S2 during spring and summer 1997

component (AC). In fact viscous component depends on velocity,and AC is not exactly that part, but from a conceptual point of viewit becomes evident that apart from inertial terms, other forces shouldbe considered in Eq. (2).

Viscous models used and simulation procedureThe mentioned evidences suggest that a viscous term should be in-cluded in Eq. (2), as it is considered in dynamics. That is:

(c + ( pw) tan ) v = ma (3)

where v is a viscous component depending on velocity.Expression (3) has been already used to analyze landslide dynamics

by Angeli et al. (1996). They used a viscous model for a local pointanalysis, assuming infinite slope conditions. A similar procedure hasbeen considered here. Figure 12 presents the variables used in thisapproach.

The corresponding momentum Eq. (3) becomes, for infinite slopeconditions (Fig. 12):

l sin cos

[c + ( l cos2 pw) tan ] v = ma (4)

where is the specific weight of the sliding mass. Note that in Eq. (4),

forces are expressed per unit area of slip surface.Viscous forces are usually dependent on the strain rate of the shear

zone. For a Bingham type model, this relation is linear and becomes:

v = v/z (5)

where, is the viscosity, v the velocity and z the thickness of theshear zone. Expression (5) can be introduced in Eq. (4) to give adifferential equation for a single point, assumed representative of thewhole landslide:

l sin cos [c + (cos2 pw) tan ]

Fig. 12 Geometry and variables used in the local analyses

92 Landslides 2 . 2005

= ma + vz

= m dvdt

+ vz

(6)

Pore water pressure was not measured directly, but it was estimatedfrom readings of depth of groundwater level. Assuming a parallel flowto the slope surface:

pw = w cos2 h = w cos2 (l Dw) (7)

where w is the specific weigth of water, l the thickness of the slidingmass and D w the depth of groundwater level.

An alternative to the Bingham model based on a power law wasconsidered as well. In such model the velocity (v) is obtained fromthe excess of driving forces 0 (Leroueil et al. 1996):

v = A(

0

)x, > 0 (8)

where A and x are material parameters to be calibrated by backanalysis.

In (8), 0 corresponds to the viscous component v, and thatexpression can be written as:

v(power) = ( v

A

) 1x

(9)

By replacing in the momentum Eq. (4):

l sin cos [c + (cos2 pw) tan ]

= ma + ( v

A

) 1x

(10)

with = l sin cos Equations (6) and (10) have been solved numerically in terms of

displacements, using a classical finite difference scheme. Using thesame numerical approach, it is possible to derive directly the velocityand the acceleration in the slope. After the numerical integration ofEqs. (6) and (10), we obtained the values of the material parameters(viscous parameters and the friction angle ) by non linear regressionto minimize differences between the measured and the computeddisplacements.

The landslide displacements used for comparison with model pre-dictions were assessed from the displacements measured in wire ex-tensometers. Wire displacements depend on the slope and thicknessof the basal shear zone. The slope of the shear zone was determinedfrom profiles including several inclinometric boreholes (see Fig. 3).The thickness of the shear zone was obtained independently calibrat-ing wire extensometer displacements with landslide displacementsmeasured with GPS. The procedure to obtain the shear zone thicknessand landslide displacements from wire extensometer displacementsis detailed in Corominas et al. (2000).

Simulated landslide displacementsAn attempt to simulate the measured landslide displacements hasbeen performed using data recorded in several piezometers. We haveused three boreholes located in the lower unit of the landslide (bore-holes S2, S9 and S11), which are considered to be representative ofdifferent parts of the whole unit and where infinite slope assumptions

Fig. 13 Measured and predicted displacements and velocities at borehole S2 using Binghamand power law models. The results of the two models are represented by a same line becausethey are almost the same and indistinguishable at the scale of the graphs

could apply. A fourth borehole, S5, located close to the graben andaffected by some rotational component was also used. The parame-ters of the viscous models and the angle of friction were estimatedindependently for each borehole.

Figure 13 presents a comparison between measured and predicteddisplacements and velocities, using the Bingham and power law mod-els for borehole S2. It can be observed that both models provide agood simulation of the measured behaviour. Table 7 shows the esti-mated values of material parameters. The values predicted by the twomodels are almost the same, because when the exponent in the powerlaw is near one, as occurs in this case, the two models are equiva-lent, and the value of /z is equal to /A. Table 7 also indicates thegoodness of fit. The latter is expressed as the root mean squared error(RMSE).

Simulated displacements and velocities for the other two analysedboreholes are not as good as for borehole S2. Power law model pro-vides better fits than the Bingham model for the borehole S9, althoughthe difference between the velocities predicted by the two models issmall (Fig. 13 and Table 7). For borehole S11, the predictions of themodels are very similar.

Landslides 2 . 2005 93

Original Article

Table 7 Parameters obtainedfrom back analysis and goodnessof fitted displacements and velocities(expressed as root mean squarederrors, RMSE's)

Borehole S2 S9 S11

Thickness of shear zone (cm) 31.5 21.5 32.0

Friction angle () 7.3 6.1 6.2Bingham model (kPa s) 1.51 107 1.52 107 1.60 107Power law model A (m/s) 0.55 106 0.44 106 4.06 106

x 1.0023 1.39 1.83Goodness of fit

RMSEBingham model Displacement (mm) 12.7 21.2 36.4

Velocity (m/s) 1.05 108 1.48 108 1.69 108

Power law model Displacement (mm) 12.7 14.7 36.2

Velocity (m/s) 1.05 108 1.36 108 1.59 108

Fig. 14 Measured and predicted displacements and velocities at borehole S9 using Binghamand power law models (dashed line corresponds to a period without measured data)

Note that the parameters obtained through back analysis are similarin all boreholes. On the one hand, friction angles of 6 to 7 are closeto the residual value measured in the laboratory for the fissured clay(7.8 degrees). On the other hand, the thickness of the shear zone, aparameter difficult to estimate in practice, is around 0.3 m, a valueobtained by analysing the behaviour of the wire extensometer records(Corominas et al. 2000).

For the Bingham model, the viscosity calibrated was around1.5107 kPa-s in the three boreholes. These values are within the

Fig. 15 Measured and predicted displacements and velocities at borehole S5 using Binghamand power law models

range of the viscosities obtained in other studies (Vulliet and Hut-ter 1988; Angeli et al. 1996). However, parameters estimated for thepower law provide small variations in the three boreholes, in par-ticular the value of parameter A in borehole S11 is almost an orderof magnitude higher than the same parameter obtained in otherboreholes.

The agreement between computed and predicted displacements us-ing the estimated parameters is generally good, particularly for bore-hole S2. Nevertheless at that particular point, some of the events have

94 Landslides 2 . 2005

not been reproduced by the model. This is the case of the peak of veloc-ity in January 1997 without rising of water table, already mentioned.

A condition that seems to have a strong influence on the qualityof the simulation is the assumption of infinite slope. In that respect,at borehole S2, located in the centre of the lower unit and, in a lesserextent, at boreholes S9 and S11, these conditions may apply (Figs. 2and 3).

Instead, for borehole S5, the infinite slope conditions are clearlynot valid. This borehole is located near the head scarp of the lowerunit where the ground surface has some rotational component ofmovement. We obtained spurious results, as negative velocities ornull displacements for periods in which the landslide was moving(Fig. 15).

The former shows that extension of the results to other local pointsmust be always performed carefully. The use of local models seemsto be more interesting for conceptual purposes, when the mechanicalbehaviour is not known in advance and general trends are investi-gated as a first step for developing future global models. In this case,the use of a viscous component in the dynamics of the landslidehas proved to be useful for a consistent analysis of the records ofdisplacements and water pressures. Obviously these analyses are lim-ited to local conditions and thus, a representative set of boreholesmust be selected. For a particular landslide, those types of recordsand the kind of analyses described here may become a promisingtool to develop alarm systems and to develop future procedures forpredicting landslide behaviour at a global scale (i.e., using coupledfinite element models including flow and mechanical equations).

ConclusionsThe nearly continuous monitoring of the Vallcebre landslide hasallowed the observation of some characteristics of the landslide be-haviour that would otherwise have gone unnoticed. The landslide isvery sensitive to rainfall, and cracks have been shown to be preferen-tial infiltration and drainage pathways.

Our monitoring network has shown the dependence of the rate ofdisplacement on groundwater level; from this we infer the existence ofa viscous component in the landslide behaviour. On the other hand,the continuous records have been used to both calibrate and validatethe analyses performed.

From the point of view of the limit equilibrium stability conditions,the Vallcebre landslide has a factor of safety of about one. However,when critical conditions are reached, failure does not occur instan-taneously, because only a small acceleration of the mass is produced.Thus, a full analysis needs to consider the dynamics of the land-slide, instead of assuming a binary approach: stability versus failure.The models used in the time dependent simulations are based onthis dynamic approach, rather than just considering static limitequilibrium.

The simulations of the landslide dynamics by taking into accounta viscous component were performed using parameters obtainedby back-analysis of the recorded data. This simulation is successfulbecause the parameters back-analyzed are consistent with field andlaboratory data obtained in an independent manner. Moreover, thosevalues obtained were similar for all the boreholes considered. Thus,the landslide behaviour at selected locations seems to be well repro-duced using the procedure outlined in the paper. Next steps in thisanalysis will include the examination of the behaviour of the land-slide from a global perspective, instead of considering only motionin individual boreholes. That approach, however, will likely requirea considerable computational effort, because a 3D analysis and a

coupled hydrological and mechanical model may be required. Theexistence of well-instrumented landslides to implement and validatecomplex numerical models is thus seen to be highly beneficial.

AcknowledgementsThe financial support of this work has been provided by CEC throughthe NEWTECH project (Contract ENV-CT96-0248), the Spanish CI-CYT (Contract AMB96-2480-CE) and the Institute of Geomodels(IGME-DURSI-UPC-UB). The authors are indebted to David N.Petley who has reviewed and made some valuable suggestions to thispaper

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J. Corominas () J. Moya A. Ledesma A. Lloret J. A. GiliDepartment of Geotechnical Engineering and Geosciences, Technical University of Catalonia, UPC,Jordi Girona 1-3, D-2 Building,E-08034 Barcelona, Spaine-mail: Jordi.Corominas@upc.eduTel.: +34-93-401-6861Fax: +34-93-401-7251

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