Simplified method for generating slope seismic deformation hazard curve

Soil Dynamics and Earthquake Engineering 69 (2015) 138–147

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Simplified method for generating slope seismic deformation hazard curve Zeljko Zugic a,n, Vlatko Sesov b, Mihail Garevski b, Mirjana Vukićević c, Sanja Jockovic c a

Geotechnics Department, The Highway Institute, Belgrade, Serbia Ss. Cyril and Methodius University, Skopje, Macedonian c University of Belgrade, Faculty of Civil Engineering, Serbia b

art ic l e i nf o

a b s t r a c t

Article history: Received 26 May 2013 Received in revised form 11 June 2014 Accepted 8 October 2014

A simplified method for generating slope deformation hazard curve that takes into account the variations of input parameters is presented in this paper. The main assumption in the new approach is that the occurrence of peak slope deformation is Poisson's process. The procedure is based on logic tree analysis, commercial software and routines programmed by the authors for generating sets of input files, and forming slope performance curve. The methodology was applied to a real landslide in order to demonstrate the advantages and limitations of the proposed approach. The results of the analysis showed the influence of the certain input factors on sliding displacement as well as the advantages of employing continuum mechanics approach. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Seismic slope stability Probabilistic approach Displacement hazard curve

1. Introduction Most of the existing methods for seismic slope deformation assessment are based on a deterministic or pseudo-probabilistic approach, in which the variabilities in the expected ground motion, soil properties, water level and geometry are either ignored or treated rigorously. Existing procedures for generating a sliding displacement curve have mainly been developed, adopted and verified in the cases of significant seismic data and require a large number of simulations [3,4,19]. They are mostly based on the sliding block (Newmark [15]) or some other simplified procedures. The concept of actual hazard (i.e., the annual probability of exceedance) associated with the computed displacement has so far not been developed in cases of low to moderate seismic excitation when usually there is no valuable seismic data apart from the design codes. There are two different types of complexity while trying to assess the seismic slope deformation in a probabilistic manner. One is related to the slope deformation technique and the other on the level of advancement of the probabilistic computation. Theoretically, it is possible to implement any of the probabilistic methods in any deformation assessment technique. The combining of the most advanced techniques for both stages will make the analysis extremely time consuming. n

Corresponding author. Tel.: þ 38163 314040; fax: þ 381 11 2466 866. E-mail address: [email protected] (Z. Zugic).

http://dx.doi.org/10.1016/j.soildyn.2014.10.005 0267-7261/& 2014 Elsevier Ltd. All rights reserved.

The challenge is to develop a procedure that will be complex enough to take into account the uncertainties associated with the main input parameters and simple enough to provide results within a reasonable time, without complex probabilistic computation, being applicable in the case of having an average amount and quality of seismic and geological data.

2. Scope of research The objective of this study is definition and application of a new simplified procedure for generating a sliding displacement hazard curve to two different slope cases in order to present all the advantages and limitations of the new procedure. The proposed simplified probabilistic framework allows the possibility to take into account the uncertainties in the prediction of earthquake ground shaking, soil properties, water level and slope geometry. The proposed procedure is applicable to any deformation assessment technique. The framework is implemented to two slope cases. The “Duboko” slope of the huge “Umka– Duboko” landslide on a real and hypothetical location was considered as an example. The procedure is based on logic tree analysis and different methods for slope deformation analysis; therefore the influence of selecting different number of branches has been observed. For numerical implementation, commercial software (Geostudio 2004 and Flac 5.0) has been used. The simulations have been performed using logic tree analysis and routines programmed by

Z. Zugic et al. / Soil Dynamics and Earthquake Engineering 69 (2015) 138–147

the authors [24] - PROBIN for generating sets of input files and PROBOUT for generating hazard curves.

3. Proposed methodology 3.1. Main assumptions The common assumption is that an earthquake is generated through a random process and it is independent of its last occurrence [12]. This assumption is the basis for considering earthquake occurrences a Poisson process in PSHA. Similarly, ground motions are also characterized by Poisson's process. Another assumption by Saygili [20] is that the annual rate of occurrence (or exceedance) for an event (i.e., T ¼1 year) is numerically equal to its annual probability of occurrence (or exceedance): P(E)¼ λ. As a result, a conversion is not necessary between rates of occurrence/exceedance and probabilities of occurrence/exceedance, and in the following sections the terms rate and probability are used interchangeably. This approximation is used for rare events (such as earthquakes) where λ is small and is often called the “rare event assumption” proposed by Bazzuro and Cornell [2]. Finally, the main assumption of the new simplified procedure is that the occurrence of peak slope permanent displacements in time can be treated as (generalized) Poisson's process. It is a widely accepted assumption that strong (characteristic) earthquakes as well as peak ground motions from these earthquakes occur as generalized Poisson's process. The slope seismic deformation in this approach is treated as a “peak ground motion” for a certain earthquake (Fig. 1). Every occurrence of peak slope displacement in time is a product of specific combination of seismic, soil and water level conditions (Fig. 2). The idea for this approximation came from Kramer [12] who stated that if earthquake events are assumed to be the Poisson process, then the failure events caused by earthquakes also become Poisson, thus simplifying the computation. Let D be a random variable representing, for an earthquake that has ruptured the soil surface, the absolute value of the displacement across the sliding surface at the ground surface, and Dslope be the same type of displacement at the site, which may or may not have been affected by the earthquake, and let p(d,t) be the probability that Dslope exceeds level d during the exposure period pðd; tÞ ¼ PfDslope 4 djtgÞ Being a direct consequence of an earthquake occurrence, the probabilistic model for this event (exceedance of a certain level of displacement) has been determined by the probabilistic model of earthquake occurrence. In [21] are presented the models for Poissonian earthquakes and (smaller earthquakes and zero displacement) for earthquakes occurring at a time dependent rate (bigger earthquake displacement), related to permanent displacement across seismic faults.

occurrence of values of a phenomenon which are less than the referent value, where the phenomenon may be time or space dependent. The observed phenomenon is seismic deformation of slope therefore, it is time dependent. In order to obtain the performance curve, a lot of simulations should be done and the performance curve will be defined by interpolation between the calculated simulations. Firstly, the deterministic analysis should be done with median values of input parameters. For time dependent events, 50% of exceedance during the exposure time should be used and also mean values of space dependent variables. All the branches of the logic tree are generated around this median event wherefore the hazard curve is later centered on this point. The work flow of the proposed methodology is presented in Fig. 3. Numerous of simulations are observed in order to mix the different ground motions, soil properties, water level and geometry scenarios (Fig. 4). The general idea and main difference in comparison with earlier probabilistic studies are performing the limited number of “wisely” selected simulations. From this reason,

Fig. 2. Occurrence of peak slope displacement as Poisson's process.

Fig. 3. Flow chart of a proposed methodology.

3.2. Description of methodology

of

The goal has been to perform cumulative frequency (frequency non-exceedance) analysis—analysis of the frequency of

Fig. 1. Analogy between seismic slope displacement and seismic fault displacement.

139

Fig. 4. Logic tree generation.

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the logic tree approach has been used instead of Monte-Carlo simulations. Therefore, beside the reliable input data and computation software the engineering judgment is necessary. Five steps are proposed: Step 1. Defining the possible scenarios, construction of a logic tree, assigning branch's weights. For generating sets of inputs for numerical simulations, a logic tree approach has been used. In a logic tree, often a normal distribution is assumed for each node, but if there are reliable data some other probability distribution can be employed. For this application, the three point approximation method is proposed by Keefer and Bodily [8] as well as method of Saygili [20] that include five branches. This modification uses the area under the standard normal probability density function so that 2σ,  1σ, 0σ, þ1σ, and þ2σ are associated with weights (w) of 0.05, 0.25, 0.4, 0.25, and 0.05, respectively. The three branches can be well represented using the 5th, 50th, and 95th percentiles with weights (w) of 0.2, 0.6 and 0.2, respectively. In this case, the alternatives represent values of each parameter equal to  1.6  times the standard deviation (σ), the mean, and þ 1.6σ. In case data are not available, standard deviations of geotechnical properties are used from the literature [13]. Step 2. Calculation of seismic displacement for every branch of the logic tree. Slope deformation analysis can be performed by using any of the available methods rigid block, or the continuum mechanics approach. Important property of the above mentioned PROBIN routine should be mentioned here in case of calculating the sliding displacement for same hazard level for different soil property branches. It starts running for the upper to lower values of soil strength. Therefore, in case of obtaining displacement less than “zero” displacement, (will be explained in step 4) the procedure starts analyses for another seismic event branch, and considers all other soil branches to be “zero”. It improves analysis to run faster especially in cases when there are many “zero” events. Step 3. Assigning weight to calculated displacements, representing each calculated displacement against its total weight, obtaining the cumulative fractal curve. The procedure for obtaining fractile hazard curves involves a relationship between annual probability and cumulative weights at each sliding displacement level. As shown in the left part of Fig. 5, to develop a cumulative weight curve, the weights of the displacements are summed from lower D to higher D for a given value of D. The probability for each D value is derived from the cumulative weight curve. This procedure corresponds with findings of [1] that argued that the uncertainty is better represented by fractile hazard curves.

Step 4. Treating the small displacement events. It is expected that some of the branches will give zero or very small displacement. As outlined by Travasarou and Bray [22], permanent displacements can be modeled as a mixed random variable, which has a certain probability mass at zero displacement and a probability density for finite displacement values. It can be argued that displacements smaller than the proposed value D are not of engineering significance and can, for all practical purposes, be considered as “negligible” or “zero”. The probability of zero events is obtained simply by reading from the fractile curve. The rest of the values can be interpolated in order to generate a displacement hazard curve. Step 5. Transforming the fractile axis into rate of occurrence— obtaining the sliding displacement hazard curve. The procedure for getting probability of exceedance for certain D from the fractile curve is described. It is based on the above described assumption about the occurrence of a peak slope permanent displacement in time as Poisson's process (Fig. 1) and it is performed with PROBOUT [24] routine. The following procedure is to be followed in order to determine the sliding displacement hazard-curve. According to basic probabilistic equations, the return period of a certain level of displacement will be t(d)¼ Texposer/  ln(NEP)¼Texposer/ln(fractile(d)), where NEP is a non-exceedance probability. The probability of exeedance of certain level of displacement will equal pexcidance(d)¼1/t(d). On the basis of the above explained assumption we have that: probability of excidance (d)¼ annual rate (d); annual rate (d) ¼ ln(percentile(d)/Texposer ¼  ln(fractile(d))/Texposer. Finally we have a final equation for determining the annual rate of a certain level of slope displacement: annual rate ðd o dmin Þ ¼ ∑d0min lnðf ractileðdÞÞ

4. Application of methodology and results 4.1. Observed case study According to both general and preliminary designs of the motorway running from Belgrade to the South Adriatic, i.e. E-763, at the exit from Belgrade – the capital of Serbia, the road facility corridor is located on the right bank of the Sava river, at the meandering apex (Fig. 6). Along a length of 3 km, it crosses “Umka– Duboko”, a large active landslide of the depth of 10–26 m, with a dominant presence of marly clays, covering an area of 1.8 sqkm. Based on analyses and a series of iterative procedures [14], it has been decided to widen-up the Sava river channel on the left bank, build a parallel protective-retaining structure made of crushed stone on the right bank, and set the motorway road base on a high

Fractile curve for certain T Annual rate of exceedance 0.9 0.8

Performance curve

0.5

0.1 0.0

permanent displacement Fig. 5. Transformation of the fractile curve into a performance curve.

Permanent displacement

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141

Fig. 6. Location map of study area (Jelisavac et al. [14]).

static and seismic performance of such repair solution using advanced methods became obvious. The landslide is located in a seismically active area and the impact of possible seismic movements of the landslide on the structure of the future motorway is a very important issue of this project.

Fig. 7. The most critical slope “Duboko” of Umka–Duboko landslide (Jelisavac et al. [14]).

embankment (made of dredged sand) behind the mentioned structure (Fig. 7). In addition, it has been envisioned to carry out works for drainage, leveling and aforestation of the unstable terrains. Considering that a motorway of such an importance is planned to be built above the presented landslide, the necessity for assessing the

4.1.1. Geotechnical parameters Before the application of the above described procedure, previous geotechnical analyses and selection of design parameters were considered. For the established landslide models, along 15 geotechnical profiles, the natural stability of the slope intercepted by the landslip has been analyzed in [14] in a recurrent mode, for the design conditions of equilibrium Fs¼ 1, a tentative angle has been

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looked for, at an average water of the Sava river and a maximum water-saturation of the slope. The laboratory residual resistance and tentative angles for the design conditions of equilibrium are correlative. It has been recommended for the purpose of checkingup the effect of repair to utilize the design residual parameters for the Duboko landslide which are φr ¼111 and cr¼ 0 kPa. In the past, analysis was performed on all the defined profiles. It was detected that the cross section 12–12 of the “Duboko” slope located at 9 þ611 m (Fig. 7) gives the lowest factor of safety wherefore the proposed methodology was applied on this particular slope. The slope “Duboko” is of a frontal type, with a length of 1.45 km along the river, whereas along the slope it is 300 m long, thus amounting approximately to 40 ha (Fig. 8). The volume of the landslide is 6,000,000 m3 with an average depth of 15 m. So far, observations have been made at the installed 19 inclinometers, 15 piezometers and three exploratory shafts. In accordance with the morphology and the sliding mechanism, three blocks have been singled out: D, E and F. The length of the blocks along the river is 350–550 m, whereas the maximum depths of sliding 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 were focused on the cross section presented in Fig. 9. The soil properties evaluated from the geological investigations, designed repair strength of materials and iterative calculations are presented in Table 1. More information can be found in Ref. [14]. The uncertainties of soil properties are defined by probability distribution functions (Table 2). The standard deviations and types of probability distributions are defined according to the detected scatter of the data and recommendations presented by other authors [13]. The influence of the geometry and water level uncertainties has not been used in the logic tree analysis in order to decrease the number of simulations, but generally it can be included as it has been mentioned in the methodology description. 4.1.2. Observed slope models The displacement analysis has been proposed to be done using two different methods: Newmark's sliding block (GEOSTUDIO 2004 (Slope/W, Quake/W) and the continuum modeling approach (FLAC 5.0). Due to the lack of space some important issues about slopes modeling are not mentioned here. The work of Chugh and Stark [5] is a good reference for assessing the seismic slope

deformation using different techniques. Both models are presented in Figs. 10 and 11. The modeling issues can be found in Refs. [9,23].

4.1.3. Definition of seismic input On the basis of the available seismic data from the seismic hazard maps, the location of Umka–Duboko is within the zone of maximum intensity of VII MSK PGA ¼0.1 g T ¼475 years. Fig. 12 shows the hazard curve approximated according to seismic maps and historical data. More details about seismic hazard assessment for this region can be found in [14]. Considering there is no valuable data, a set of spectrum-compatible accelerograms for dynamic analyses has been defined. That means that the average response spectrum computed from all the accelerograms should match a target spectrum prescribed by a seismic code Eurocode 8, (see [6]) within a certain tolerance, over a specified range of periods. Spectral-compatibility is not simply achieved when recorded accelerograms are used; however, it is an important requirement in order to avoid using records that are inconsistent with code prescriptions. For defining seismic records for logic tree analysis, all the records have been scaled to the best estimated PGA value of 0.064 g (median value Table 3). The median value (11th largest displacement) was used as a best estimation(Figs. 13-16). Having 20 records and 20 calculated displacements simply by sorting in a decreasing array (Table 4) we have defined 2/20 value as a 5% percentile and 20/20 as 95% value. The same procedure has been used for all the other branches in order to achieve a certain percentile for the 5 branch analysis. The inputs are summarized in Table 5. For most of the cases the real site location was observed, the spectral shape of Eurocode 8 type 2 (as used (M o5.5), considering ground type A (rock site Vs30Z 800 m/s) has been used [6]. Just for one case, curve B, the slope is considered to be located at hypothetical site with PGA ¼0.18 g for a return period of 475 years (Table 5); therefore the records compatible to type 1 Table 1 Soil strength and stiffness parameters. Soil

Name

Colluvium

Fig. 8. Slope “Duboko” (Jelisavac et al. [14]).

Density [kg/m3]

c0 ø0 [kPa] [deg.]

Class

Marly clay Rock Marlstone Mini dam Crushed stone Embankment Refueled sand Slip surface Marly clay

Material strength

Stiffness parameters Gmax/damping curve (shear and normal stiffness for interface)

1790.0

30

23.0

6200 kPa [25]

1890.0 2600.0

290 0

25.2 45.0

1.2 GPa—constant 13,000 kPa [10]

1700.0

0

25.0

8400 kPa [10]

1790.0

0

11

Kn ¼ 3  10e5 kPa/m Ks¼ 11  10e3 kPa/m

Fig. 9. Parameters obtained by investigation works and previous analysis.

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Table 2 Definition of soil uncertain parameters Parameter

Unit

μ Mean value

σ Standard deviation

Probability distribution

Residual shear strength along interfaces Shear modulus (Gmax) of sliding mass-colluviums

degrees kPa

11 6200

2 1600

Normal Normal

Table 4 Observed seismic records ranking for curves A, C, D, and E.

Fig. 10. Slope “Duboko” Slope/W model.

Excidance frequency 1/year

Fig. 11. Slope “Duboko” FLAC model.

1.0000 0.1000 0.0100 0.0010 0.0001 0.0000 0.01

0.1 PGA, g

1

Fig. 12. Site hazard curve.

Table 3 Observed values of peak ground acceleration Fractile

Return period (years)

PGA (site 1)

PGA (site 2)

50% in 100 years 20% in 100 years 80% in 100 years 95% in 100 years 75% in 100 years 25% in 100 years 5% in 100 years

144.3 448.1 62.1 33.4 72.1 347.6 1949.6

0.064 0.095 0.048 0.038 0.050 0.087 0.158

0.15 0.315 0.077 0.05 0.09 0.22 0.38

(M 45.5) have been used. This was done in order to verify the procedure in cases of relative bigger levels of seismic excitation.

5. Results During the application of the proposed procedure on the real slope, numerous different analyses were performed. Only the main results are presented in order to demonstrate the method applicability and the authors' way of thinking while analyzing this particular slope case. Five different cases were observed therefore five classes of curves were obtained (Table 5). In the presented curves the gray lines represent the results from the real simulations while the black ones are the results of interpolation of considering the exponential shape of sliding displacement curve, that coincide with the Poisson distribution assumption. These

Record

Newmark displacement(cm)

Percentile

Rank

Rec. no. 12 Rec. no. 13 Rec. no. 20 Rec. no. 7 Rec. no. 16 Rec. no. 17 Rec. no. 2 Rec. no. 10 Rec. no. 5 Rec. no. 18 Rec. no. 19 Rec. no. 15 Rec. no. 6 Rec. no. 8 Rec. no. 4 Rec. no. 9 Rec. no. 11 Rec. no. 1 Rec. no. 3 Rec. no. 14

0 0 0 0 0.00184 0.094 3.33 4.43 5.95 6.404 12.01 20.22 39.48 39.6 58.8 89.11 91.97 109.5 129.33 181.2

95

20th 19th 18th 17th 16th 15th 14th 13th 12th 11th 10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

80 25

50

25 20

5

interpolations were made for the purpose of detecting the trends between different curves more easily. For all curves as “zero event” are treated displacements less than 1 cm; therefore all the simulations that give the displacement less than that threshold are grouped into the “zero event” set. The Newmark sliding block method was used for all curves except for Curve D where the continuum modeling approach was applied for the purpose of comparing the results. Figs. 17 and 18 represent the slope performance assessment in cases of real (0.1 g in 475 years) and hypothetical sites (0.18 g in 475 years). The impact of considering uncertainties of soil properties (in this case the residual shearing strength of sliding surface) are considered for both cases. One can see that, at a lower level of displacement (Fig. 17), the soil properties have a bigger influence on the annual rate of occurrence, while at the bigger level this influence is almost negligible, which is consistent with results presented by Kim and Sitar [11]. In Fig. 17 one can notice (on the interpolated curve) the bigger probability at a lower level of displacement hazard in the curve where soil uncertainty is neglected. This is rather a product of interpolation and big concentration of zero events in cases of low seismicity. In cases of higher seismicity (Fig. 18) this phenomenon does not occur. This outcome stresses the importance of treating the soil uncertainties in cases of lower seismic excitation and agrees with findings of [11,16–18] that stated that neglecting the soil uncertainties may lead to unconservative results. Fig. 19 presents influence of using a different number of branches in the logic tree analysis on the obtained sliding displacement curve. For preliminary analysis, three branch analyses are sufficient to ensure an insight into the slope seismic deformation but it is quite unconservative, especially at higher levels of sliding displacement hazard. A further analysis is continued using 5 branches, but the effort is made on decreasing the number of parameters, considering that performing 125 simulations while obtaining curve C was time

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Table 5 Inputs for the event tree Curve

Curve A

Nubmer of branches

27 branches 27 branches (9 without soil) (9 without soil) Serbia PGA ¼ 0.1 g for Hypotetical site PGA ¼0.18 g 475 years for 475 years Mo 5.5 M 45.5 Type 2 EC8 Type 1 EC8

Sesimic information Target response spectrum Seismic PGA data

Seismic record

Geotenical data

Friction angle

Shear Modulus

Curve B

þ1.6σ Mean Mean  1.6σ

0.13 g 0.064 g 0.04 g

0.315 g 0.15 g 0.077 g

þ1.6σ Mean

Rec. no. 16

Rec. no. 16

Mean  1.6σ

Rec. no. 18 Rec. no. 4

Rec. no. 5 Rec. no. 11

þ1.6σ

8.51

Mean  1.6σ

111 13.51

Response Spectra (m/s 2 )

4

3 2

1

0

0

0.5

1 Period (s)

1.5

2

Fig. 13. All 20 selected records.

consuming. The next analysis for generating curve D was performed with only median seismic record (Record no. 18) and slightly different results were obtained (Fig. 20). Employing only the median record detected by performing the 20 simulations (Table 4) gave satisfactory results while calculating the displacement hazard curve using the above described procedure. Another important parameter presented in Table 5 classified as geotechnical but very much correlated with seismic response of slope is shear modulus of sliding mass. Decoupled sliding block analysis is performed using QUAKE/W for dynamic site response analysis and SLOPE/W for displacement calculation. In this type of analysis shear modulus of sliding mass affects only the seismic site response; therefore in Gmax they indirectly affect the calculated sliding displacement. A bigger influence should be expected while applying the continuum mechanics approach. This kind of analysis was not done here having in mind the time necessary to perform

Curve E

125 branches

25 branches

125 branches

 2σ  1σ Mean þ1σ þ2σ  2σ

0.126 g 0.064 g 0.044 g 0.0335 g Rec. no. 12

 1 σ Rec. no. 7 Mean Rec. no. 18 þ1σ Rec. no. 9 5/20 þ2σ Rec. no. 3 2/20  2σ 7.881

 1σ Mean þ1σ þ2σ

5

Curve D

Serbia PGA ¼0.1 g for Serbia PGA ¼ 0.1 g for Serbia PGA ¼ 0.1 g for 475 years 475 years 475 years M o 5.5 M o 5.5 Mo 5.5 Type 2 EC8 Type 2 EC8 Type 2 EC8 0.215 g

 1σ Mean þ1σ þ2σ  2σ

Constant 6200 kPa

Curve C

9.441 111 12.561 14.131 Constant 6200 kPa

Rec. no. 18

Rec. no. 18

6200 kPa

2950 kPa 4575 kPa 6200 kPa 7825 kPa 9450 kPa

one Flac 5.0 slope simulation, but it will certainly be part of some future research. The influence of a variation of Gmax (initial shear modulus of sliding mass) on slope displacement calculated by decoupled approach is presented in Fig. 21. The influence of shear modulus of sliding mass on sliding performance of slope is bigger at a lower level of sliding displacement. Continuum mechanic approach was applied for curve D (that include 25 branches) in order to be able to generate the curve within a reasonable amount of time. Differences in results between the Newmark and continuum approach analyses for particular slope case (Fig. 22) were commented in terms of the following factors: fundamental period of the potential sliding mass, the frequency content of the input motion, yield acceleration and the maximum seismic loading. There are scenarios where the Newmark sliding block procedure is unconservative in predicting seismically induced permanent displacements. That is mainly because the computed slope displacement is influenced predominantly by low frequency average motion that amplifies and is not sensitive to high frequency motion. However, the Newmark deformation analyses results may be justified, if the fundamental period of the slope is sufficiently low (i.e., shallow soil deposits with T o0.2 s). The observed slope is quite shallow; therefore the obtained difference in the results (two to four times larger displacement obtained by the Newmark method) was expected. The results from Fig. 22 are interesting from the aspect of the frequency content of the input motion. Rigid sliding block analysis that ignores the flexibility of the earth structure is generally shown to be unconservative when the frequency content of the input motions is close to the fundamental period of the slope. Having in mind the frequency content of the employed seismic records (Figs. 13 and 14) and the fact that the natural period of the slope is around 0.2 s, one can expect that the Newmark sliding block will underestimate the

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145

Average difference absolute value= 7.99% 2.5

EC8 – spectrum reference EC8- reference Average response spectrum 2

Response Spectra (m/s 2)

spectrum

Average response spectrum

1.5

1

0.5

0

0

0.2

0.4

0.6

0.8

1 Period (s)

1.2

1.4

1.6

1.8

2

Fig. 14. Average value of 20 selected records.

0.04

Acceleration ( g )

0.02 0.00 -0.02 -0.04 -0.06 -0.08

0

20

40

60

80

Time (sec) Fig. 17. Curve A—lower seismicity zone (PGA ¼0.1 g in 475 years).

Fig. 15. Median time history record (Rec. no. 18).

0.08

Deformation

0.06

0.04

0.02

0.00 0

20

40 Time

60

80

Fig. 18. Curve B—hypothetical site (PGA ¼ 0.18 g in 475 years).

Fig. 16. Median displacement history (D¼ 6.4 cm).

6. Summary and conclusions seismic deformation, but this did not happen. The explanation for this might be quite a small value of yield acceleration for the active landslide calculated with residual soil parameters. The influence of the level of seismic loading on the accuracy of results is shown in Fig. 22. The Newmark method can be unconservative in cases of very low displacement hazard but in those cases the difference in the results is insignificant from the engineering viewpoint.

The proposed procedure represents a valuable tool for generating the hazard displacement curve and can be used for preliminary analysis as well as for a complex analysis in cases of availability of reliable seismic and geotechnical inputs. The main advantage is possibility to assess sliding displacement hazard in probabilistic manner by performing a reasonable amount of simulations. Therefore, the displacement hazard curve can be obtained in reasonable amount of time, even in case of

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Fig. 19. Influence on different number of branches (curves A and C).

employing the most advanced continuum approach deformation assessment technique. That is big advantage in comparison with the other approaches. In case of using proposed method based on logic tree analysis, one is able to obtain displacement hazard curve in case of the absence of significant seismic data, by selecting the several characteristic seismic load cases as it was done in presented case study analysis. On the basis of the presented results, it is important to accentuate that assessing of the seismic deformation of slopes in a probabilistic manner is an iterative procedure. The possibility to add a new uncertain parameter in the next iteration and upgrade the analysis is a very good property of the proposed technique. Adding one more set of branches to logic tree analysis is quite quick and simple, having in mind that all the probabilistic computation results from the previous step can be used. Performing the three branch analysis was found to be unconservative but it is useful for detecting a parameter that might be of interest. Performing of some kind of sensitivity study [7] might also be quite useful, before starting applying the proposed procedure. The main outcome for this paper is

 The verification of the new procedure for obtaining slope deformation hazard curve.

 Confirmation and quantification of the importance of treating the soil data variation.

 The impact of shear modulus of sliding mass on slope deformation is highlighted.

 The advantages of using advanced methods (continuum approach) are shown.

 Confirmation of the applicability of Newmark rigid block Fig. 20. Influence on employing different seismic records (curves C and D).

method in some specific cases. A further development of the proposed procedure can be made by adding the correlation factor between the seismic intensity and soil properties, or between the water table and the soil property. Another improvement could be a better estimation of the spatial variability of static and dynamic soil properties. References

Fig. 21. Influence of employing uncertainties of shear modulus of sliding mass (curves D and E).

Fig. 22. Influence on different sliding assessment techniques (curve D).

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