Landslides (2013) 10:729–736DOI 10.1007/s10346-012-0360-6Received: 4 June 2012Accepted: 2 October 2012Published online: 19 October 2012© Springer-Verlag Berlin Heidelberg 2012

Mihail Garevski I Zeljko Zugic I Vlatko Sesov

Advanced seismic slope stability analysis

Abstract The objective of this study was to present an advancedmethodology for assessing seismic slope stability by taking intoaccount the uncertainties related to the main input parameters.The methodology was applied on a real landslide in order to showthe advantages of using the proposed procedure and establish thebaseline trends of dynamic response and calculated permanentseismic displacements. It involves the following steps: preliminaryanalysis, probabilistic static and seismic factor of safety analysis,and permanent seismic displacement analysis. Estimating post-failure maximum seismic deformation of landslide mass andsounding properties is the most important part of this study. Itinvolves both Newmark sliding block method and continuummechanics approach, applied for characteristic set of input valuesin order to have more accurate assessment of slope performanceand determine the relative importance of input parameters. Theresults of the analysis showed the benefits of using the proposedstep-by-step methodology. The obtained difference in the resultsbetween the two methods depends strongly on the set input datafor a particular analysis.

Keywords Seismic slope stability . Uncertainties . Probabilisticapproach . Permanent displacement . Sensitivity analysis

IntroductionThe uncertainties related to input parameters that one faceswhile analyzing seismic slope stability make sensitivity andreliability methods very suitable for application in assessmentof active and potential landslides as well as evaluation ofdesign solutions projected to prevent sliding processes. Thereare different methods for probabilistic and pseudo-probabilisticseismic slope analysis and only a limited number of them dealwith seismic permanent displacement. Most of the displace-ment-based methods are adopted and verified for regions ofhigh seismicity. They are based on significant seismic data andrequire a large number of simulations (Rathje and Saygili 2009;Bray and Rathje 1998). Some of them require advanced knowl-edge of the probabilistic theory (Kim 2001). Nowadays, most ofthe probabilistic displacement assessment procedures are basedon the sliding block (Newmark 1965) procedure. Continuummodelling is still not widely used due to its complexity andtime required for analysis (Rathje and Bray 2000). 2D modelassumption is quite common even for important projects.Therefore, in addition to all other uncertainties, one of thebiggest sources of uncertainty is the slope model. Just a fewresearchers take into account the uncertainties related to soilproperties (Rathje and Saygili 2009; Murphy and Mankelow2004; Kim 2001). However, there is still no consensus in engi-neering community and therefore probabilistic methods are stillnot widely used in practice. The challenge is to develop amethodology that will be complex enough to take into accountthe uncertainties associated with the main input parametersand simple enough to provide results within a reasonable time,without complex probabilistic computation, being applicable in

case of having an average amount and quality of seismic andgeotechnical data. Developing a procedure to perform seismicslope stability analysis, learning about the relative importanceof input parameters and comparison of results obtained usingdifferent methods for seismic slope deformation assessment,have been the objectives of this study.

Motivation for researchAccording to both general and preliminary designs of the mo-torway running from Belgrade to the South Adriatic, i.e. E-763, atthe exit from Belgrade—the capital of Serbia, the road facilitycorridor is located on the right bank of Sava river, at the mean-dering apex (Fig. 1). Along a length of 3 km, it crosses “Umka-Duboko”, the large active landslide with a depth of 10–26 m, withdominant presence of Marly clays, covering an area of 1.8 km2

(Fig. 2). Having in mind the importance of the project and theincreased risk in the landslide area, extensive geotechnical inves-tigations were conducted in 2005. Some of the results importantfor this paper are summarised in Fig. 3. where one can noticequite a large scatter of soil parameters. They are related for themost critical slope “Duboko” (Fig. 4). Based on analyses and aseries of iterative procedures, it has been decided to widen up theSava river channel on the left bank, build a parallel protective–retaining structure made of crushed stone on the right bank, andset the motorway road base on a high embankment (made ofdredged sand) behind the mentioned structure (Fig. 5). In addi-tion, it has been envisioned to carry out works for drainage,levelling and aforestation of the unstable terrains. Consideringthat a motorway of such an importance is going to be built abovethe presented landslide, the necessity for assessing the static andseismic performance of such repair solution using advancedmethods became obvious. The landslide is located in a seismicactive area and the impact of possible seismic movement of thelandslide on the structure of the future motorway is a veryimportant issue of this project.

Proposed methodologyThe general rule which is followed while defining the methodologyis going from simple to complex analysis and not to combine thecomplex probabilistic framework with computation demandingseismic analysis. Therefore, it includes three steps, by increasingcomplexity and the final goal is to assess the slope permanentseismic displacement. The proposed methodology can be imple-mented in any commercial software. For analysis of the case studypresented in this paper, commercially available programs SLOPE/W, QUAKE/W (Krahn 2004) and FLAC (Itasca Consulting Group2000) are used.

The first step (Fig. 6) is evaluating the most criticalfailure mechanism by solving equilibrium and constitutiveequations for full solution of the coupled stress/displacementstate in the slope corresponding to the point of instabilitywhile performing a series of calculations with different prop-erties. It should be taken into account that, in some cases, the

Landslides 10 & (2013) 729

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mechanism for horizontal dynamic loads can be differentfrom the failure mode induced by static loading. There arestrong reasons why such an analysis is recommended in theearly stage of analysis of complex slopes like possibility todetect simultaneous failures, soil structure interaction, etc. Allof these are explained in literature (Dawson et al. 1999). Forpreliminary analysis, deterministic input parameters (best es-timate values) should be used. Nevertheless, it is recommen-ded to have an insight into the main uncertain parametersand their upper and lower bound values because this isnecessary for the next two steps. The second step is theprobabilistic limit equilibrium factor of safety analysis usingthe Monte Carlo simulation for the sliding mechanism definedas the most critical in the preliminary analysis. One of themain recommendations in this stage analysis is sampling thesoil properties of the sliding mass in several ways. The soilproperties can be sampled: for each slice along the slip sur-face, at a specified distance along the slip surface, or onlyonce for each soil for the entire slip surface. This could be avery important issue for huge landslides and according togeotechnical investigations, different sampling can be used.The obtained results (first of all, the probability of failure)provide an answer as to whether there is a necessity to

perform a displacement analysis. As the third step, slidingdisplacement analysis is proposed to be made using bothsliding block (Newmark 1965) and continuum mechanics ap-proach. The first benefit of this analysis is comparison of theresults by using different approaches. Another advantage isrelated to the time necessary to perform sensitivity analysisfor both methods. For many slope cases, the Newmark slidingblock procedure is just an index of slope behaviour, but veryuseful in the case when analysis should be run many timesfor various sets of input values. The results from the New-mark sliding block analysis help us detect which of the un-certain parameters are less important so that they can beexcluded from the continuum approach sensitivity analysis.Plenty of time can be saved if consideration is employed.The analysis, similar to the one performed by Chugh andStark (2006), is proposed to be repeated for a predefined setof inputs in order to perform sensitivity analysis. Sensitivityanalysis is a technique for systematically changing parametersin a model to determine the effects of such changes. Tornadodiagrams, also called tornado plots or tornado charts, areused for visualisation of the results from the sensitivity anal-ysis. This technique was applied in earthquake engineering byPorter et al. (2002). The first input is then set to its bestestimate value and the process is repeated for the next inputin order to determine the swing associated with the variabilityof that input. One can then rank the input variables accordingto their swing. A larger swing reflects a more important inputuncertainty.

Application of methodologyBefore the application of the above-described procedure, pre-vious geotechnical analyses and selection of design parameterswere consulted. For the established landslide models, along 15geotechnical profiles, the natural stability of the slope inter-cepted by the landslip has been analysed by Mitrovic andJelisavac (2006) in a recurrent mode; for the design condi-tions of equilibrium Fs01, a tentative angle has been lookedfor at average water of Sava the river and maximum watersaturation of the slope. The laboratory residual resistance andtentative angles for the design conditions of equilibrium arecorrelative. It has been recommended for the purpose ofchecking up the effect of repair to utilise the design residualparameters for the Duboko landslide which are φr011 degreesand cr00 kPa. In the past, analysis was performed on all the

Fig. 1 Location map of study area

Fig. 2 Umka–Duboko landslide

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defined profiles. It was detected that cross-section 12–12 of the“Duboko” slope located at 9+611 m (Fig. 5) gives the lowestfactor of safety wherefore the proposed methodology wasapplied on this particular slope. Slope “Duboko” is of afrontal type, with a length of 1.45 km along the river, whereasalong the slope, it is 300 m long, thus amounting approxi-mately to 40 ha (Fig. 2). The volume of the landslide is6,000,000 m3 with an average depth of 15 m. So far, observa-tions have been made at the installed 19 inclinometers, 15piezometers, and 3 exploratory shafts. In accordance withthe morphology and the sliding mechanism, three blocks havebeen singled out: D, E and F. The length of the blocks alongthe river is 350–550 m, whereas the maximum depths ofsliding were recorded in block D—up to 25 m, in block E—up to 16.5 m, and in block F—up to 10 m. The analyses werefocused on block D presented in Figs. 3 and 5. The soilproperties evaluated from the geological investigations, thedesigned repair measures and iterative calculations are pre-sented in Table 1. More information can be found in thereferences (Mitrovic and Jelisavac 2006).

Definition of uncertain input parametersThe most of important soil parameters are given in Table 1.The uncertainties of soil properties, water level and slopeangle are defined by probability distribution functions (Ta-ble 2). The mean values are determined according to themeasurements from the site and laboratory tests. The stan-dard deviations and types of probability distributions aredefined according to the detected scatter of the data andrecommendations presented by other authors (Jones et al.2002; Lacasse and Nadim 1996) except the value of the waterlevel which is adopted according to the available hydro-geo-logical measurements. Geometry changing is achieved simplyby moving the material boundary up and down in order toachieve the lower and upper bound of the slip surface anglein the observed models.

Definition of seismic inputOn the basis of the available seismic data from the seismichazard maps, the location of Umka–Duboko is within thezone of maximum intensity of VII MSK PGA00.1 g, T0475 years. Figure 7 shows the hazard curve approximatedaccording to seismic maps and historical data. More detailsabout seismic hazard assessment for this region are given in

Fig. 5 Remedial design solution—the most critical engineering geologic profile 12(block D)

Newmark method (Slope/W, Quake/W)

Preliminary analysis (FLAC/Slope) Verification of most critical sliding mechanisms

Probabilistic (Monte Carlo Simulation)

FOS analysis (SLOPE/W)

Sensitivity analysis of

Slope seismic permanent displacement

Continuum modeling

(FLAC 5.0)

Fig. 6 Proposed methodology for seismic slope stability assessment

Fig. 3 Parameters obtained byinvestigation works and previousanalysis

Fig. 4 Slope Duboko

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literature (Mitrovic and Jelisavac 2006). Considering there isno valuable data, a set of accelerograms for dynamic anal-yses should be spectrum compatible, meaning that the averageresponse spectrum computed from all the accelerogramsshould match a target spectrum prescribed by a seismiccode Eurocode 8 EN 1998–5:2005 (2005) within a certaintolerance, over a specified range of periods. Spectral com-patibility is not simply achieved when recorded accelero-grams are used; however, it is an important requirementin order to avoid using records that are inconsistent withcode prescriptions.

In this work, the 20 accelerograms to be adopted fordynamic analyses were selected from strong motion recorddatabases (Fig. 8), by imposing the constraint of spectrumcompatibility with a code-based target spectrum. The spec-tral shape of Eurocode 8 type 2 (Fig. 9) was used (M<5.5),considering ground type A (rock site Vs30≥800 m/s). Thedeconvolved accelerograms are calculated by using the com-puter program SHAKE91 (Idriss and Sun 1992) based onone-dimensional wave propagation theory and applied tothe bottom of the model.

Definition of inputs for tornado diagramsIn order to construct a tornado diagram, the range of seismicevents needed to be defined from seismic hazard curve (Fig. 7).Considering that the serviceability of the motorway has beenadapted to 100 years, the used values of seismic intensity havebeen: 10 % in 100 years corresponding to T043 years, PGA00.04 g50 % in 100 years corresponding to T0144 years PGA00.064 g90 % in 100 years corresponding to T0950 years, PGA00.13 g(Table 3).

For defining the input for seismic records, all therecords have been scaled to the best estimation PGA valueof 0.064 g. Having 20 records and 20 calculated displace-ments simply by sorting in a decreasing array, we havedefined 2/20 value as a 90 % percentile and 18/20 as 10 %value. These are record no. 3 and record no. 17. (see Table 3).The best estimation (10th largest displacement) has beenobtained for record no. 10 and has been used as the bestestimation value for ground motion record. A similar ap-proach was used by Porter et al. (2002) related to damagefactor in structural engineering. Another remark should begiven that the meaning of the upper bound and lower boundvalues of the variables in Table 3, addresses the upper boundvalues of the calculated displacement. All other inputs pres-ent in Table 3 are determined as mean values and 90 and10 % percentiles of the variables defined in Table 2. Uncer-tainties of the mass and damping parameters are not includ-ed. It was detected that mass variation has no significantinfluence. Damping variation was excluded because different

Table 1 Soil strength and stiffness parameters

Soil Density[kg/m3]

Material strength Stiffness parametersGmax/damping curve(shear and normalstiffness for interface)

Name Class c′ [kPa] ø′ [deg.]

Colluvium Marly clay 1,790.0 30 23.0 6,200 kPa (Hardin and Black 1968)

Rock Marlstone 1,890.0 290 25.2 1.2 GPa—constant

Mini dam Crushed stone 2,600.0 0 45.0 13,000 kPa (Kokusho and Esachi 1981)

Embankment Refuelled sand 1,700.0 0 25.0 8,400 kPa (Kokusho and Esachi 1981)

Slip surface Marly clay 1,790.0 0 11 Kn03×10e5kPa/m

Ks011×10e3kPa/m

Table 2 Definition of uncertain parameters

Parameter Meanvalue (μ)

Standarddeviation (σ)

Probabilitydistribution

Residual shearstrength alonginterfaces(degrees)

11 2 Normal

Water level(metres over sea)

71.7 m 1.25 m Normal

Shear modulus(Gmax) ofcolluvium (kPa)

6,200 1,600 Normal

Slope angle,θ (degrees)

4.57 1 Lognormal

0.0000

0.0001

0.0010

0.0100

0.1000

1.0000

0.01 0.1 1

PGA, g

Exci

danc

e fr

eque

ncy

1/ye

ar

Fig. 7 Site hazard curve

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Landslides 10 & (2013)732

types of damping are considered in FLAC and Quake/Wanalysis, therefore the comparison of results won’t bestraightforward.

Results of analysisDuring the application of proposed methodology, numerousanalysis and different variants were observed. The most sig-nificant outcomes of this study are presented below.

Preliminary analysis of the above presented slope hasbeen conducted using code Flac/Slope 5.0. The deterministicmean values of the input parameters listed in Table 2 havebeen used. For assessment of the seismic behaviour of theslope, horizontal force of 0.05 g (obtained as 0.5 of the 0.1 g)for a return period of T0100 years, the most critical slidingmechanism for horizontal force is the lifting of the roadembankment presented in Fig. 10. This “failure mode” wasthe lowest safety factor obtained (around 0.9), wherefore thepresented sliding mechanism was to be followed in furtheranalysis. The probabilistic factor of safety analysis involvedthe distribution of input values from Table 3 and also theconstant seismic force of 0.05 g for seismic analysis, same as

in the preliminary analysis. Static and pseudo-static seismicanalysis has been conducted using slope/W. Stability factoranalysis proposed by Krahn (2004) was done for the assess-ment of the static slope stability. For seismic (pseudostatic)is employed the GLEM formulation developed by Fredlund etal. (1981) that encompasses the key elements of all the other meth-ods. It is based on two factors of safety equations and allows for arange of interslice shear–normal force conditions. The model ispresented in Fig. 11. Sampling each slice for shear strength of a slidingsurface is employed while cohesion is zero for all slices. Theresults of the probabilistic analysis are presented in Table 4.The mean value of the seismic factor of safety for 2,000simulations of 1.05 suggests that the available slope shearstrength is near equilibrium with shear forces so that seismic

0 0.5 1 1.5 20

1

2

3

4

5

Period (s)

Res

pons

e Sp

ectr

a (m

/s2 )

Fig. 8 All 20 selected records

Fig. 9 Average value of 20. selectedrecords

Table 3 Input values for Tornado diagrams

Uncertainvariables:

Upperbound90 %percentile

Bestestimation50 %percentile

Lowerbound10 %percentile

Residual shearstrength value(degrees)

8.5 11 13.5

Water level ofSava river(meters over sea)

73.3 71.7 70.1

Slope angle(degrees)

5.9 4.57 3.4

Gmax—colluviumshear modulus(kPa)

3,600 6,200 8,300

Ground motionrecord

Recordno. 3

Recordno. 10

Recordno. 17

Peak groundaccelerationT0100 years

0.13 g 0.064 g 0.04 g

Landslides 10 & (2013) 733

instabilities are possible. The obtained value of the probabilityof failure value that is actually a percent of simulations thatgives a factor of safety of less than 1.0 is 0.08.

Permanent seismic displacement sensitivity analysis Having inmind that the accent of the study was on the step-by-stepprocedure and the relative importance of input variables,some important issues about modelling, especially about thecontinuum mechanic approach, are not motioned. Most ofthem can be found in literature, namely Chugh and Stark(2006), Itasca Consulting Group (2000) for the continuummodelling approach and Krahn (2004) for the sliding blockprocedure. The soil was modelled using the linear elasticperfectly plastic constitutive law, with the Mohr–Coulombyield criterion and the non-associated flow rule. The geotech-nical model was built step-by-step, starting from a simplemodel and gradually increasing the degree of complexity afterconsistent and stable results were obtained for the previousphase of the analysis. The following damping parameters werechosen: 0.01 % Rayleigh damping centred at 1 Hz, plus thehysteretic damping option included in FLAC. It is importantto be noted that, in the FLAC analysis, 14 points were fol-lowed. The results for two characteristic points are presentedhere. The first one (M1 centre of the mass of the slope) inorder to be compared with the Newmark sliding block method andanother (M2 middle of the motorway) valuable for assessment ofpossible damage on the designed road structure above (Fig. 13).

The range of displacements obtained by use of the FLAC analysis(1–15.5 cm) is less scattered beside the fact that it is more accuratethan the one determined by the slide block analysis (0–60 cm). Thesummary of the results is given in Table 5. The best estimate valuesagree very well with the results from Chugh and Stark (2006) givingapproximately two times larger displacement by the sliding block

method. By comparing the upper bound values, the differenceincreases—the displacements obtained with the Newmark methodare four times larger.

The presented results from the Newmark sliding blockanalysis (Fig. 12) can be considered as a good reference fromtwo reasons, namely (a) the repair solution does not includeany pile or shaft along the slide mass. In that case, a complexsoil structure phenomenon should include (b) a well-definedsliding surface along the material discontinuity can make thesliding block assumption reliable enough. The necessity forusing the continuum mechanics approach arises from the factthat there is a road structure above. The displacement of themiddle of the road (point M2, d03.4 cm) is a little bit smallerthan the one obtained for the centre of the mass (point M1,d03.1 cm). For the upper bound, the difference is againaround 10% (15.5–17.3 cm). These values from FLAC analysis includeboth x and y components, same as results from Table 5.

Fig. 11 Landslide “Duboko” Slope/W model

Table 4 Summary of results of probabilistic static and seismic analysis (2,000 trials)

Result Static analysisstability factor(FEM)

Seismic(T0475 years)factor of safety(GLEM)

Mean value (μ) 1.71 1.05

Standard deviation (σ) 0.09 0.104

Reliability indexβ0 (μ−1)/σ

7.914 0.568

Probability of failure 0 0.08

Fig. 10 Critical sliding mechanismdetected by preliminary analysis

Table 5 Summary of the results

Method Best estimationD (cm)

Maximal expectedD (cm)

Continuum approach(point M1)

3.1 15.5

Newmark sliding block 6 60

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Obtained result represents a very good basis for damage assess-ment of the road structure due to seismic movement. The results oftime history analyses have shown that the amount of final displace-ment can be very different for different accelerograms, despite thefact that they are scaled to the same PGA. Therefore, any designprocedure relying only on a PGA-derived parameter will impreciselypredict the actual behaviour of the slope. This emphasizes the im-portance of proper selection of seismic intensity measure for perfor-mance-based design of slopes. The actual approaches developingduration depending parameters give very good results (Rathje andSaygili 2009). It was confirmed in the finding of Bray and Rathje(1998) that tje Newmark method can be reliable if the fundamentalperiod of the slope is sufficiently low (i.e. shallow soil deposits withT<0.2 s). Observed slope is quite shallow, therefore, the obtaineddifference in the results (two to four times larger displacementobtained by Newmark method) was expected. Having in mind thefrequency content of the employed seismic records (Fig. 9) and thatnatural period of the slope is around 0.2 s, one can expect thatNewmark sliding block will underestimate the seismic deformation,but it did not happen, probably due to small yield acceleration of theactive landslide analysed with residual soil parameters. Comparisonof the results in Figs. 12 and 13 (left) show that resultsobtained by Newmark method can be unconservative in casesof very low seismic excitation (lower bound values); but inthat case, the difference in the results is insignificant from theengineering viewpoint. A relatively big result sensitivity on theshear modulus of the sliding mass has been detected, but thestiffness parameters, by their definition, should influence theslope deformation in cases of either static or dynamic loadingmore than the strength parameters. The using of simplified

methods for slope stability analyses is the reason why thisaspect was not researched intensively. The results proved that,for the low level of seismic excitation, the variability of soilproperties can have a significant effect on the slope displace-ment performance that corresponds with the results obtainedby Kim (2001).ConclusionsThe obtained values of displacement according to the CaliforniaGeological Survey classifications (Table 6) fall into the class of lowlandslide hazards (5 cm<D<15 cm); therefore, the road project isfeasible from the viewpoint of seismic performance. Designing ofstructures over active or potential landslides definitely requiresusing advanced procedures and consideration of the uncertaintiesrelated to input parameters. Permanent seismic deformation is avaluable parameter; in most cases, directly correlated with damageto the observed structure and can be evaluated by the two pre-sented methods. In this study, the Newmark method basicallyprovided the larger estimates of displacements. Those results wereexpected having in mind that observed slope is shallow and thenatural period of sliding mass is small. The reliability of Newmarkmethod results is commented in terms of other factors like level ofseismic loading, frequency content of the input motion, yield accel-eration, and sliding surface precision. It was shown that the differ-ence between the results obtained by these two methods depends onthe particular set of input data (best estimate values, upper or lowerbound). This fact emphasises the significance of performing thesensitivity analysis. Performing sensitivity analysis for a continuummodelling approach requires a lot of time but the benefits are verybig; therefore, it should be done for important projects.

Table 6 Landslide hazard criteria used by CGS

Landslide hazard Sliding displacement

Very low D<5 cm

Low 5 cm<D<15 cm

Moderate 15 cm<D<30 cm

High D>30 cm

Fig. 13 Tornado diagrams for permanent displacement obtained from continuum approach

Fig. 12 Tornado diagram—Newmark method

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M. Garevski : Z. Zugic ()) : V. SesovInstitute of Earthquake Engineering and Engineering Seismology, IZIIS,University “Ss. Cyril and Methodius”,73, Salvador Aljende Str. P.O. Box 101, 1000 Skopje, Macedoniae-mail: zzugic@gmail.com

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