Paper liquefaction

Acta Geod. Geoph. Hung., Vol. 46(3), pp. 347–369 (2011)

DOI: 10.1556/AGeod.46.2011.3.6

LIQUEFACTION AND POST-LIQUEFACTIONSETTLEMENT ASSESSMENT — A PROBABILISTIC

APPROACH

E Gyori1, L Toth1, Z Graczer1, T Katona2

1Seismological Department, Geodetic and Geophysical Research Instituteof the Hungarian Academy of Sciences, Meredek u. 18, H-1118 Budapest, Hungary,

e-mail: [email protected] Nuclear Power Plant, Hungary

[Manuscript received June 22, 2011; accepted July 28, 2011]

Low velocity surface layers can significantly increase ground accelerations duringearthquakes. When saturated sandy sediments are present, because of pore pres-sure increase, decrease of soil strength or even liquefaction can occur. Some volumechange follows the dissipation of excess pore pressure after the earthquake resultingsurface settlements. To determine the liquefaction probability and post-liquefactionsettlement is very important for critical facilities e.g. for the site of Paks NuclearPower Plant, Hungary. Pore pressure increase and so the liquefaction and surfacesettlements depend on the characteristics of seismic loading and soil parameters. Toquantify the extent of these phenomena is rather difficult. Uncertainties arise bothfrom the probabilistic nature of the earthquake loading and from the simplifications ofsoil models as well. In the paper, the most important semi-empirical and dynamicaleffective stress methods for liquefaction and post-liquefaction settlement assessmentare summarized. Most significant contributors to the uncertainties are highlighted,and particular examples through the investigation of Paks NPP site are given. Fi-nally, a probabilistic procedure is proposed where the uncertainties will be taken intoaccount by applying a logic tree methodology. At the same time, the uncertaintiesare reduced by the use of site-specific UHRS and stress reduction factors.

Keywords: liquefaction; logic tree methodology; Paks NPP; site amplification;surface settlement; uncertainties

1. Introduction

Low velocity surface layers can significantly increase ground accelerations duringearthquakes. Besides strong shaking, soil failures can also occur causing damagesto built environment. When cohesionless loose granular soils can be found in theupper strata, in dry conditions, shaking can induce compaction and settlement ofthe ground; this phenomenon is called seismic settlement. Dry or nearly dry sandsdensify very quickly; settlement of such deposits is usually complete by the end ofthe earthquake. When saturated sandy deposits are subjected to shaking duringan earthquake, pore water pressure builds up leading to loss of strength or evenliquefaction. Some volume change follows the dissipation of excess pore pressure

1217-8977/$ 20.00 c©2011 Akademiai Kiado, Budapest

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after the earthquake, resulting so-called post-liquefaction surface settlements. Thesettlement of a saturated soil requires more time; settlement can occur only as earth-quake induced pore pressures dissipate, accompanied by some volume change of thedeposit. The time required for this depends on the permeability and compressibilityof the soil, and the length of the drainage path. Liquefaction and surface settlementfrequently causes distress to structures supported on shallow foundations, damageto pipelines that are commonly buried at shallow depths. To determine the liq-uefaction probability and post-liquefaction settlement is particularly important forcritical facilities e.g. at the site of Paks NPP, Hungary.

Estimation of earthquake-induced settlements of sands is difficult. Errors of 25to 50% are common in static settlement predictions; even less accuracy could beexpected for the more complicated case of seismic loading. Uncertainties arise notonly from the simplifications of the soil model, but from the probabilistic nature ofthe earthquake loading.

In this paper the most important semi-empirical and dynamic effective stressmethods for liquefaction and post-liquefaction settlement assessment are summa-rized. The most significant contributors to the uncertainties are highlighted, andparticular examples through the investigation of Paks NPP site are given. Finally,a probabilistic procedure is proposed where the uncertainties will be taken into ac-count by applying a logic tree methodology. At the same time, the uncertaintiesare reduced by the use of site-specific UHRS and stress reduction factors.

2. Methods of liquefaction analysis

2.1 Simplified methods

2.11 Principles

Liquefaction susceptibility can be expressed in terms of factor of safety (FS)against the occurrence of liquefaction as (Seed and Idriss 1971):

FS =CRR

CSR(1)

where CRR (cyclic resistance ratio) is the soil resistance to liquefaction, expressedin terms of the cyclic stresses required to cause liquefaction, and CSR (cyclic stressratio) is the cyclic stress generated by the given earthquake.

CSR =τav

σ′v0

= 0.65 · σv0

σ′v0

· amax

g· rd (2)

where τav is the equivalent shear stress amplitude, amax is the peak horizontalacceleration at ground surface, g is the acceleration of gravity, σv0 and σ′

v0 are thetotal and effective vertical overburden stresses, respectively, and rd is a nonlinearstress reduction coefficient that varies with depth.

The potential for liquefaction is assessed with the aid of liquefaction charts,which are based on observations of whether liquefaction did or did not occur at

Acta Geod. Geoph. Hung. 46, 2011

LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 349

Fig. 1. CRR curves determined from SPT data for sands with various fines content(Youd et al. 2001)

specific sites during numerous past earthquakes. These charts can be used to de-termine what combinations of shaking intensity and soil resistance are likely toresult in liquefaction. Cyclic resistance ratio (CRR) curves represent limiting con-ditions that determine whether liquefaction will occur (Fig. 1). In the simplifiedprocedure, soil resistance to liquefaction is evaluated using in situ tests, includingthe standard penetration test (SPT), the cone penetration test (CPT), shear wavevelocity measurements (Vs), and the Becker penetration test (BPT).

The classical method for determining CRR curves is based on SPT measure-ments, which is still the most widely used procedure. As discussed by the NCEERWorking Group (Youd and Idriss 1997, Youd et al. 2001), one of the most widelyaccepted and widely used SPT-based correlations is the “deterministic” relationshipproposed by Seed et al. 1984, 1985). This familiar relationship is based on com-parison between SPT N-values, corrected for both effective overburden stress andenergy, equipment and procedural factors affecting SPT testing (to N1,60-values)versus intensity of cyclic loading, corresponding to an earthquake of magnitude7.5. (CSR7.5). The relationship between corrected N1,60-values and the intensity ofcyclic loading required to trigger liquefaction is also a function of fines content (Fig.1). This correlation has no formal probabilistic basis, and so provides no insight


350 E GYORI et al.

regarding either uncertainty or probability of liquefaction. Efforts at developmentof similar, but formally probabilistic correlations have been published by a numberof researchers, including Liao et al. 1988, Liao and Lum 1998, Youd and Noble 1997,Toprak et al. 1999) and more recently (Cetin et al. 2004).

In addition to SPT, three other in situ index tests are now sufficiently advancedas to represent suitable bases for correlation with soil liquefaction triggering poten-tial, and these are the cone penetration test, in situ shear wave velocity measure-ment, and the Becker penetration test. As it was discussed in EERC report in 2003(Seed et al. 2003) up to that point in time, the SPT-based correlations had beenbetter defined, and had provided lesser levels of uncertainty, than the other threemethods. CPT, however, is approaching the same level, and newly developed CPT-based correlations (Robertson and Wride 1998, Idriss and Boulanger 2004, Juanget al. 2006, Moss et al. 2006, Robertson 2009) now represent nearly co-equal statuswith regard to accuracy and reliability. SPT-based correlations are currently aheadof CPT based correlations, due in large part to enhanced databases and better dataprocessing and correlation development. The new SPT-based correlations are moreaccurate and reliable, and provide much lower levels of uncertainty or variance. TheCPT offers advantages with regard to cost, efficiency (since no borehole is required)and consistency. However, the most important aspect is the continuity of data overdepth. SPT can only be performed at vertical spacing of about 75 cm or more, soit can completely miss thin (but potentially important) liquefiable strata; SPT canfail to suitably characterize strata less than about 90 to 120 cm in thickness. CPT,in contrast, is fully continuous and so “misses” nothing. Therefore, the authors ofthe EERC report recommend the use of SPT and CPT based methods together, aseach offers significant advantages not available with the other.

Liquefaction triggering correlations based on measurements of in situ shear wavevelocity (VS-based correlations) have the advantage that VS can be measured incoarse soils (gravelly soils and coarser) in which SPT and CPT can be obstructedby interference with coarse soils particles (Andrus and Stokoe 1997). But thiscorrelation is less well defined (more approximate), than either SPT- or CPT-basedcorrelations. Therefore, use of it cannot be recommended at critical structures.

Simplified methods have become widely used in routine engineering practice.Procedures for carrying out a liquefaction assessment using empirical methods arediscussed and recommended by NCEER Workshop by Youd et al. (2001) and byEERC Report No. 2003-6 (Seed et al. 2003). In these studies, the authors havemade recommendations for the use of the procedures considered the most reliable.

The methods described here are based on empirical correlations between the insitu measurement of the soil strength and liquefaction occurring in shallow depths aswell as on laboratory measurements of soil behaviour during cyclic loading. There-fore these methods may be used reliably only for about the upper 15 meters depth.

The CRR curves in the SPT, CPT, and VS charts correspond to an earthquakeof magnitude 7.5. Seed and Idriss (1982) suggested the use of magnitude scalingfactors (MSF) for earthquakes of magnitude other than 7.5. MSF takes into accountthe longer duration i.e. the more equivalent loading cycles of larger earthquakes.Similarly, the shorter duration of smaller quakes is corrected in MSF. These factors



are used to shift the CRR base curve vertically according to:

CRR = CRR7.5 · MSF (3)

2.12 Input parameters and uncertainties

To compute CSR according to Eq. (2) the following soil parameters have to beknown:

— thicknesses of the subsurface layers,

— densities of soil layers,

— ground water level,

— PGA at the ground surface (amax),

— stress reduction factor (rd).

The maximum ground surface acceleration (PGA) comes from site effect evalu-ation (without considering pore pressure increase) succeeding PSHA (ProbabilisticSeismic Hazard Assessment) analysis. It has considerable uncertainty.

Besides amax the main source of uncertainty in CSR is the stress reduction factor,rd. Its usual functional forms were developed by averaging stress distribution withdepth from numerous site effect analyses. In the literature, several authors haveproposed formulas that are sometimes significantly different from each other. Thisuncertainty can be reduced using site specific CSR, that can be determined directlyfrom site effect studies. In this case equivalent linear or nonlinear total stressmethods have to be applied in computations where the pore pressure increase is nottaken into account.

Liquefaction can occur only in saturated granular soil, practically below groundwater table. Raise of ground water level increases the probability of liquefaction.The higher the groundwater level the less is the effective pressure at a given depth.In this case, lower excess porewater pressure is enough to reduce the effective stressto zero. Ground water level shows a seasonal variation, which also cause uncertain-ties in computations.

As it was mentioned in the previous section, CRR curves in the SPT, CPT, andVS charts correspond to earthquakes of magnitude 7.5. The MSF, which is usedto correct the duration of earthquakes of magnitude different from 7.5, has beendeveloped by a variety of different approaches (using cyclic laboratory testing and/orfield case history data) by a number of investigators. Figure 2 shows a number ofrecommendations and the recommendations (shaded zone) of the NCEER WorkingGroup (Youd and Noble 1997). Recently Idriss (1999) and Cetin et al. (2004)provided equations for MSF.

Relative contribution to liquefaction hazard from earthquakes with various mag-nitudes and distances from the site can be determined from deaggregation of PSHA.Deaggregation provides information useful for review of the PSHA and insight into


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0

1

2

3

4

MSF

5 6 7 8 9Mw

Andrus and Stokoe (1997)

Seed and Idriss (1982)

Idriss (NCEER)

Youd and Noble (1997) PL <50%



Ambraseys (1988)

Arango(1996)

Cetin (2004)

Idriss (1999)

Fig. 2. Recommendations for magnitude-correlated duration weighting factor with recommenda-tions of EERC Report (Seed et al. 2003)

the seismic sources that have the most impact to the hazard at a particular site.It can also be used to determine the controlling earthquakes (i.e., magnitudes anddistances), which can be used to perform dynamic site response analyses and todetermine liquefaction potential. MSF has to be determined in accordance with themagnitude of controlling earthquakes.

2.2 Effective stress method

2.21 Principles

In the analytical effective stress method, a constitutive model of soil is incorpo-rated into the non-linear step by step analysis to evaluate directly the build-up ofpore pressure and the dynamic ground response. The model takes into account theimportant factors that affect the dynamic response of a sandy layer, such as tran-sient pore pressure increase, soil damping, hardening, variation of shear moduluswith shear strain and changes in effective mean normal stress. Volumetric strainand post-liquefaction settlement can be calculated by analysing the pore pressuredissipation after the cessation of earthquake.

In most cases, the effective stress analysis is carried out because it can simulatetime dependent changes in pore pressure and their effects on changes in the proper-ties of soil. In this sophisticated analysis, the liquefaction potential can be directlyassessed according to chosen seismic input motions in terms of pressure build-up ordevelopment of strain. However, the results may be quite variable owing to differentinput motions, constitutive models and other parameters, and the final assessment



should be made in consideration of the extent of variability. The advantage of themethod besides the accurate modelling of the soil behaviour that in principle thereis no depth limit in the applicability unlike the simplified methods.

2.22 Input parameters and uncertainties

Analytical methods rely on accurate measurements of constitutive soil proper-ties. The input parameters necessary to the computations are listed below:

— the thicknesses of the subsurface layers,

— densities of the soil types, wet and saturated unit weights,

— shear modulus or shear wave velocities with depth,

— shear modulus degradation (G/Gmax) and damping ratio versus shear straincurves,

— undrained cyclic strength,

— ground water level,

— grain size distribution,

— relative density,

— permeability,

— appropriately scaled input earthquake acceleration time history.

The shear modulus affects both the liquefaction susceptibility and indirectly theseismic excitation. The sediments characterized by lower shear modulus, wherethe transverse wave velocity is smaller, are looser. On the other hand, because ofthe lower velocity the resulting shear stress will be higher. These factors togetherfavour the development of soil liquefaction. Shear modulus degradation and damp-ing ratio curves characterize the nonlinear stress-strain behaviour of soils. Theirrole is not so straightforward as the effects of the other parameters. Usually thecyclic strength of strongly nonlinear materials are lower, but because of the largerinternal damping lower cyclic stress can develop in them. Relative densities influ-ence the developments of volumetric strains and so the liquefaction susceptibilityand surface settlement. The susceptibility of liquefaction is very sensitive to chang-ing these values (Gyori 2004). Permeability is also a very important parameter ofliquefaction; liquefaction can occur if the permeability of surrounding strata is lowenough to prevent drainage. As it was mentioned earlier, high ground water levelsfavour the development of liquefaction.

The normal variability in soil and rock materials is such that many input pa-rameters, such as soil types, layer thicknesses, and soil strengths, etc. are usuallyknown as ranges of values rather than as discrete values. Besides, these parameters


354 E GYORI et al.

are determined from different types of measurements, which also contribute to thisvariability.

The liquefaction potential for a given location is determined by earthquake mag-nitude, duration, and the epicentral distance. Based on sensitivity calculations(Gyori et al. 2002a, 2002b, Gyori 2004) it can also be concluded that the effectof the excitation, namely the applied input acceleration time histories are at leastas important as the parameters discussed so far that mainly influence susceptibil-ity. The reason is that besides the same PGA the spectra of earthquakes differsignificantly from each other even if we select earthquakes with similar magnitudeand focal mechanisms. The variability arising from the differences of earthquakespectra can be reduced by increasing the number of input time histories, using ar-tificial time histories generated compatible with the bedrock UHRS or fitting realearthquake spectra to the bedrock UHRS. Generally, the use of real, registered ac-celeration time histories are recommended in earthquake engineering practice at siteeffect (Ansal and Tonuk 2007) as well as liquefaction (Youd et al. 2001) estimations.According to Ansal studies the use of artificial accelerograms to estimate site am-plifications leads to an unknown degree of conservatism. As stated by the AmericanNCEER (National Center for Earthquake Engineering Research) the use of artifi-cial accelerograms should be avoided in case of estimating liquefaction potential.As a compromise, fitting the real earthquake spectra to the bedrock UHRS can beconsidered. For example, Hancock et al. (2006) have presented a fitting method,which preserves the long period non-stationary phasing of the original time history.

3. Methods for evaluating settlements

A number of procedures have been presented in the literature in the past 25years to study the earthquake-induced settlement problem and they can vary fromthe simplified semi-empirical methods to the complex non-linear dynamic ones. Thesemi-empirical methods are based on the simplified liquefaction analysis procedures.It is common essentially in every procedure that they estimate the consolidationsettlement from the volumetric strain.

For sites with level ground, far from any free face (e.g., riverbanks, embank-ments), it is reasonable to assume that little or no lateral displacement occurs afterthe earthquake. So the volumetric strain will be equal or close to the verticalstrain. If the vertical strain in each soil layer is integrated with depth using Eq. (4),the result should be an appropriate index of potential liquefaction-induced groundsettlement.

S =n∑

i=1

εvi∆zi (4)

where S is the calculated liquefaction-induced ground settlement; εvi is the post-liquefaction volumetric strain for the soil sublayer i; ∆zi is the thickness of thesublayer i; and n is the number of layers.



3.1 Semi-empirical methods

3.11 Review of semi-empirical methods

If the simplified procedure is used to evaluate liquefaction potential, liquefactioninduced ground settlement of saturated granular deposits can be estimated usingone of the semi-empirical methods. This type of procedures were developed byTokimatsu and Seed (1987), Ishihara and Yoshimine (1992), Shamoto et al. (1998),Zhang et al. (2002), Wu and Seed (2004) and recently Cetin et al. (2009).

Tokimatsu and Seed (1987) have developed procedures to estimate volumetricstrain and ground settlement for dry and saturated sands, too.

Seismic settlement in dry sands is a function of density of the soil, the numberof strain cycles and the magnitude of the cyclic shear strain induced by seismicshaking (Silver and Seed 1971). The effective shear strain (γeff) can be computedfrom effective cyclic shear stress (τeff) as follows:

γeff =τeff

GmaxGeffGmax

(5)

where Gmax is the small strain shear modulus, and Geff the effective shear modulusat the induced strain level. Substituting the expression of effective cyclic shearstress, the above expressions can be rewritten as:

γeffGeff

Gmax=

0.65 · amax · σv0 · rd

g · Gmax. (6)

Gmax can be determined from shear wave velocity measurements or other suit-able small-strain laboratory or field procedures. The right-hand side of Eq. (6)can be computed with depth so the product on left-hand side is also determined.The effective shear strain can be determined using graph that shows the prod-uct γeff(Geff/Gmax) a function of γeff . Then volumetric strain is estimated fromknowledge of the effective shear stress. In 1971 Silver and Seed have published arelationship between these two quantities for sands with different relative densities.

Tokimatsu and Seed (1987) have developed charts to estimate volumetric strainin saturated sands, too. The relationship that was based on cyclic triaxial and sim-ple shear tests performed on clean sands were then calibrated on field case studies.As a result, their procedure estimates the volumetric strain as a function of earth-quake induced CSR and corrected SPT blowcounts. The recommended post-cyclicvolumetric strain boundary curves are given in Fig. 3. Use of this methodologyrequires determination of overburden-, fines-, and procedure-corrected SPT blow-counts, and duration corrected CSR values. Solid lines in Fig. 3 show the volumetricstrain for liquefied soil. Dashed lines describe the case where pore pressure increasesbut the earthquake loading is not large enough to cause liquefaction. In such cases,volumetric strain also develops after dissipation of pore pressure, which, however islower than if liquefaction would have occurred. The curves for determining strainof saturated sand are related to earthquakes of magnitude 7.5 so these have to becorrected for different magnitudes.


356 E GYORI et al.

Fig. 3. Volumetric strain for saturated sand with CSR and corrected SPT blow-counts (afterTokimatsu and Seed 1987)

The Ishihara and Yoshimine (1992) procedure estimates the volumetric strainas a function of factor of safety against liquefaction, relative density, and correctedSPT blowcounts or normalized CPT tip resistance. Both larger post-liquefactionand smaller volumetric strain following pore pressure increase can be determinedby using the method. To be consistent with the Ishihara and Yoshimine method,field SPT-N values were corrected to 72% hammer efficiency to reflect the factthat Japanese average SPT hammer energy was 20% higher than the standardvalue of 60%.

Shamoto et al. developed their constitutive equations describing post-liquefactionsoil deformations in 1998. They were based on the results of torsional shear tests.Similar to Tokimatsu and Seed they estimated the developing volumetric strainsas a function of CSR and the corrected SPT blowcounts. The charts were de-termined for both clean sands and soils with different fines content. The methodwas calibrated for the surface subsidence observed after the 1995 Hyogoken-Nanbuearthquake. According to their experiences, the final value of ground settlementscan be estimated as 0.84 times the value of computed ones.

The procedure of Zhang et al. (2002) to determine volumetric strain of sandy andsilty soils combines a CPT-based liquefaction estimation method with the resultsof laboratory tests performed on clean sands. In the first step they computes thesafety factor against liquefaction using Robertson and Wride (1998) method. Thendiagram of Ishihara and Yoshimine (1992) is used for the estimation of volumetricstrain of clean sands.

In 2004, Wu and Seed proposed a method that is based on simple shear tests per-formed on clean sand. In their study, the SPT blowcounts corrected for clean sand



and CSR were selected as capacity and demand terms, respectively. The authorsprovided a chart solution for the prediction of cyclically induced reconsolidationvolumetric strain.

In a more recent study, Cetin et al. (2009) described a semi-empirical maximumlikelihood method for the probabilistic assessment of cyclically induced reconsoli-dation settlements of saturated cohesionless soil sites. They calibrated their SPTbased model to numerous earthquake case history data. The main advantage ofthe proposed methodology is the probabilistic nature of the calibration coefficient,which enables incorporation of the model uncertainty into settlement predictions.

3.12 The uncertainties of semi-empirical methods

The semi-empirical methods of settlement computation are based on the simpli-fied liquefaction estimation methods. Therefore, the same, partly method-dependentuncertainties arise as during determination of factor of safety against liquefaction:

— Uncertainties of CSR determination coming from the surface PGA and stressreduction factor (rd). As it was mentioned earlier, these can be reduced bythe computation of site-specific CSR.

— Choose of the method for CRR estimation.

— Magnitude scaling factor (MSF) for the correction of magnitude of controllingearthquakes.

— Uncertainties of relative densities.

— Changing ground water level.

— Scattering of SPT blowcounts and CPT tip resistance.

Additionally, different results arise from the application of different methods,which have to be taken into consideration, too.

3.2 Settlement computations using effective stress method

As it was mentioned in Section 2.2, the effective stress method allows the simul-taneous computation of pore pressure increase and dynamic response of soil strata.Volumetric strain of dry furthermore saturated or partially saturated soils can bedetermined using it.

Let’s consider, for example, a sample of saturated sandy soil sample under avertical effective stress σ′

v. During a drained cyclic simple shear test, a cycle ofshear strain of amplitude (γ) causes an increment in volume strain (∆εvd) due tograin slip. During an undrained shear test starting with the same effective stress,the cycle of shear strain (γ) causes an increase in porewater pressure (∆σw). Martinet al. (1975) showed that for saturated sands (assuming water to be incompressible),

∆σw = Er∆εvd (7)


358 E GYORI et al.

where Er is the one-dimensional rebound modulus of sand at the given verticaleffective stress. It was also shown that under simple shear conditions the volumetricstrain increment per cycle is a function of the total accumulated volumetric strain(εvd) and the amplitude of shear strain. According to Byrne (1991), the functionhas the form:

∆εvd = γC1e−C2

εvdγ (8)

where C1 and C2 are constants depending on the sand type and the relative density.The expression for Er (Martin et al. 1975):

Er =(σ′

v)1−m

mK2(σ′v0)n−m

(9)

in which σ′v0 is the initial value of the effective stress and K2, m and n are exper-

imental constants for the given sand. The pore pressure increase and the rate ofvolumetric strain can then be computed during a given loading cycle using Eqs (7–9). If the saturated sand layer can drain during shaking, there will be simultaneousgeneration and dissipation of porewater pressure. Thus the rate of pore pressureincrease will be less than for completely undrained sand. If we solve these equationswith the differential equation of motion for the entire duration of the loading, thenwe get the total volumetric strain that develops in the individual layers during theearthquake.

The computations are burdened with the previously detailed uncertainties sim-ilar to computation of liquefaction.

4. Paks Nuclear Power Plant — a case study

Paks Nuclear Power Plant (NPP) is situated in the central part of Hungary inthe young sedimentary Pannonian Basin characterized with moderate seismicity.The basin is filled with sediments of different ages. At the site Quaternary depositsu– fluvio-aeolian strata, fluvial sand and gravel –u can be found on the top 27 m;under it Pannonian age (upper Miocene) very dense and very silty sand is in largethickness. In 1996, the site seismic hazard (PSHA), site effect and liquefactionpotential was re-evaluated by Ove Arup & Partners. This study was based ona very extensive geophysical and geotechnical investigation. The measurementsindicated that saturated sandy layers under the site between 10 and 20 m below theground level are susceptible to liquefaction. The site effect analysis — computingthe response of the uppermost Quaternary layers — was carried out for 10−4 annualprobability level with nonlinear method.

Ove Arup & Partners investigated the stability of the foundation to seismicmotion and found that the only risk to the structure is an earthquake groundmotion that is sufficiently extreme to cause liquefaction. Liquefaction induced set-tlement of up to 60 mm within the underlying sand material may occur. In case ofground motion corresponding to a return period of 10 000 years (PGA = 0.25 g)liquefaction does not happen and about 12 mm settlement is likely to take place.



They evaluated liquefaction occurrence by Seed and Idriss (1971) simplified method;seismic settlement was computed by the semi-empirical method of Tokimatsu andSeed (1987).

Recent studies preliminary estimated liquefaction to be more probable, and themagnitude of surface settlement to be significantly larger. Factor of safety againstliquefaction was estimated also by simplified method of Seed and Idriss. For deter-mination of post liquefaction settlement, procedures of Tokimatsu and Seed (1987)moreover Ishihara and Yoshimine (1992) were used. Using Ishihara and Yoshimine’smethod the settlement of ground surface was estimated to 11 and 9.9 cm at the east-ern and western side of the main reactor building, respectively. The computationsresulted 23.8 cm for the post liquefaction settlement when Tokimatsu and Seedmethod was applied. The seismic settlement under dry conditions was assessed as1.11 cm using Tokimatsu and Seed (1984) method.

The results could not be used for the safety assessment since the variation ofthe results obtained by different methods are very large, and do not allow properconclusions even if the conservative case would be accepted.

Differences between the results of the earlier and the present computations arisefrom the use of different input parameters (best estimate or conservative side) andfrom different approaches of the same type of computation procedures. In thepresent section we review the sources of uncertainties arising during liquefactionand post-liquefaction settlement assessment at Paks NPP site.

During site investigation, the soil properties were determined from numerousdifferent type measurements. In most cases, they have given different values for thesame parameter, therefore best estimate and lower and upper bound profiles werealso determined.

SPT and CPT measurements can be used to determine CRR at simplified liq-uefaction assessment methods. Numerous tests were carried out during site inves-tigations therefore best estimate, lower and upper bound SPT blow-count profiles(Fig. 4 a) could be determined at the main exploration site (Ove Arup & Partners1995) near the reactor building. For CPT penetration resistance the best estimateprofile with the lower and upper bounds were estimated at the main and the reactorsites, too (Fig. 4 b). As the figures show, significant variability can be observed inthe parameters, which have to be taken into account in computations.

The small strain shear modulus (Gmax) or shear wave velocity is one of the mostimportant input parameter of site effect analysis (both in case of total and effectivestress methods too). Its function versus depth for the representative soil profile canbe seen in Fig. 5 a. It was determined from a number of different tests, namelycross-hole and down-hole seismic tests, seismic cone tests, SPT and CPT results.By comparing the profiles derived from each of the tests, best estimate, lower andupper bound Gmax profiles was derived for use in site response analysis. Sensitivitystudies Gyori (2004) showed that surface accelerations and liquefaction potentialare very sensitive to changing the shear modulus profile (use of best estimate, lowerand upper bound profiles).

Relative densities are input parameters of both semi-empirical settlement esti-mation and effective stress methods. Their values were determined from SPT, CPT


360 E GYORI et al.

Fig. 4. SPT blow-counts with depth at the main exploration site (a); CPT cone penetrationresistance with depth at the main and reactor site (b) of the Paks NPP (after Ove Arup &

Partners 1995)

Fig. 5. Small strain shear modulus (after Ove Arup & Partners 1995) (a) and relative densities(b) with depth

moreover from laboratory measurements and are characterized by high variability.Best estimate, lower and upper bound profiles can be seen in Fig. 5 b.

Degradation of shear modulus (G/Gmax) with shear strain for Quaternary stratawas obtained from the results of cyclic triaxial and resonant column tests. Best



Fig. 6. Shear modulus degradation (a) and damping ratio (b) curves with shear strain (after OveArup & Partners 1995)

estimate, lower and upper bound curves of the variation of G/Gmax with cyclic shearstrain (Fig. 6 a) have been derived from these results (Ove Arup & Partners 1995).The hysteretic damping ratio (Fig. 6 b) was derived directly from the G/Gmax curvesdue to the assumption that the soil behaviour is described by Masing principles.Sensitivity studies performed by effective stress method showed that using lower orupper bound curves instead of best estimate one in the computations, the resultsare less sensitive than changing the Gmax profile.

The power plant site is located near the Danube. The site ground water level isin hydraulic continuity with the river but the environmental wells show a much moreconsistent ground water level than the Danube. For design purposes a ground waterlevel of 89 mBD, equivalent to a depth of 8 m was used. This value was used byOve Arup & Partners (1996) for liquefaction analysis. The ongoing studies assumedthe ground water level more conservatively at 91 mBD i.e. 6 m below groundlevel. Sensitivity computations showed that factor of safety against liquefactiondecreased with increasing ground water level. But the results were less sensitive tothe reasonable modification of ground water level than to the changing the otherinput parameters (Gyori 2004). It was probably because the liquefaction couldoccur at relatively large depths, between 10 and 20 m below ground level. Thesame conclusions can be drawn from the computations by effective stress method.

Liquefaction can occur during strong earthquake shaking in sediments suscepti-ble to liquefaction. Susceptibility is determined by the above mentioned soil prop-erties. Intensity of earthquake shaking is defined by the maximum acceleration(PGA), duration of strong shaking and the stress distribution inside the near sur-face sediments. These quantities are burdened also by considerable uncertainties.

Simplified liquefaction estimation methods need the knowledge of surface PGA;the input for effective stress analysis is the bedrock acceleration time history. Thebedrock PGA computed for 10 000 years return period event was 0.178 g, 0.23 g and


362 E GYORI et al.

0.299 g at 15%, 50% and 85% confidence levels, respectively (Gyori et al. 2002b).Computation of site effect adds even more uncertainties to the estimation process.

Other very important parameter is the duration of earthquake shaking whichis affected by the magnitude of the earthquake. In case of Paks NPP, earthquakesoccurring about 15 km from the site have the greatest relative contribution to theliquefaction hazard. There is also a small input from about 200 km as a result ofthe high earthquake activity in the Sava-Zagreb seismic source zone (Ove Arup &Partners 1996). Studying their magnitude, it was showed that the hazard is seenlargely as a result of earthquakes with magnitudes between 5.5 and 6.5. Thereforethree controlling earthquakes were chosen; these earthquakes had magnitudes of5.7, 6.2 and 7.2 at distances of 11, 18 and 200 km from the site, respectively. Insimplified analysis duration can be taken into account by MSF. So it has to bechosen in accordance with the magnitude of controlling earthquakes. According tothe NCEER recommendation MSF is about 2.2, 1.8 and 1.1 for an earthquake withmagnitude of 5.7, 6.2 and 7.2 respectively. This implies such a differences in thefactor of safety. Using effective stress analysis, acceleration time histories have tobe chosen from the records of earthquakes of similar magnitude.

In case of liquefaction analysis carried out by Ove Arup & Partners at Paks NPP,stress reduction with depth was determined from site effect evaluation. The functionof maximum shear stress with depth was predicted by nonlinear method. Theyestimated CSR by averaging shear stress versus depth curves using five earthquaketime histories as input in the computations. In contrast, later studies used averagedrd function with depth, which could cause also differences in the results.

In 2008, a sensitivity study was performed (Toth et al. 2008) about the effectof different input parameters to the liquefaction potential assessment. It was foundthat the results are very sensitive to changing amax, the magnitude of the earthquake(MSF) and the stress reduction factor (rd).

The use of logic tree formalism for accounting the uncertainties is common inearthquake engineering practice. For example, the site effect and liquefaction as-sessments were performed along branches of logic tree shown in Fig. 7 during seis-mic PSA (Probabilistic Safety Assessment) study of Paks NPP completed in 2000(Gyori et al. 2002a). The computations were performed at very low probability lev-els (10−4–10−6/years) therefore the effect of pore pressure increase had to be takeninto account (because of the high acceleration levels) during determination of groundaccelerations. Therefore nonlinear effective stress analysis has been applied. Threereal earthquake accelerograms were used as input motion in the computations. Tak-ing into account the uncertainties in bedrock motion, in the soil parameters and thevariation of ground water level, moreover the effect of different input accelerograms,logic tree with 6 nodes has been used for every examined probability level.

Figure 8 shows an example of the computations, which was made in order to es-timate the amplification of Quaternary layers. The maximum of the input bedrockacceleration time history was scaled to 0.25 g, which correspond to 10−4/year prob-ability level. An acceleration record of the 5.6 magnitude Parkfield earthquake waschosen as input time history for the analysis (Fig. 8 a). We used the best estimatecurves for the soil profile parameters and the average value of 8 m for the ground



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water depth. The analysis was carried out assuming horizontally layered soil modelusing computer program DESRA-2C developed by Lee and Finn (1997). The secondand third curves show the surface accelerations computed by nonlinear total stress(without taking into account pore pressure increase) and effective stress method,respectively (Fig. 8 b, c). In addition, a layer (at 16.5 m depth) was selected, whereprevious studies have shown that the sands found there are susceptible to lique-faction, and the shear strain (Fig. 8 d), shear stress (Fig. 8 e), volumetric strain(Fig. 8 f) and excess pore pressure (Fig. 8 g) we computed over the time. As itcan be seen from the figure a small increase in pore pressure and volumetric straincan be expected assuming such an earthquake loading. However the extent of thisvolume strain is very small, about 0.05% in the selected layer. If the volume strainfor every layer was computed and summed up weighting with the layer thicknesses,a 9 mm surface settlement can be obtained. Using other time histories as input thedeveloped volumetric strain and surface settlement was different.

The studies conducted in case of Paks NPP showed that the different methodssometimes provided significantly different results even if the input parameters werethe same. Therefore, efforts should be made to use the best available and reliablemethods, and to take into account the effects of uncertainties during computations.Most reliable results can be achieved by the combined use of the simplified and theanalytical methods.

5. Proposal and conclusions

In the previous sections, the most important semi-empirical and dynamical ef-fective stress methods of the assessment of liquefaction and post-liquefaction surfacesettlement have been presented. The most significant contributors to the uncertain-ties were highlighted, and particular examples through the investigation of PaksNPP site were given. In the present section, a probabilistic procedure is proposedfor accounting these uncertainties.

Our method is based on the logic tree methodology, which is widely used inhazard and risk assessments. It handles simultaneously the site effect computation,liquefaction assessment, and the estimation of surface settlement at sites where liq-uefiable sandy soils are present. It assumes the knowledge of PGA and UHRS on


364 E GYORI et al.

Fig. 8. The acceleration time history of Parkfield earthquake (M = 5.6) scaled to 0.25 g bedrockPGA (a), surface acceleration time histories computed by total (b) and effective stress analysis

(c), shear strain (d), shear stress (e), volumetric strain (f) and increase of pore pressure withtime (g) in 16.5 m depth



the bedrock surface. The procedure focuses on uncertainties arising in computationof site amplification, liquefaction and surface settlement, utilizes the geotechnicalnature of the strata and the results of sensitivity computations. The effects ofepistemic and aleatory uncertainties of seismicity, earthquake source zones, attenu-ation relationships, etc. are manifested in the probability distribution (15, 50, 85%percentiles) of PGA and UHRS.

The logic tree displayed in Fig. 9 summarizes the proposed complex probabilis-tic approach to assess liquefaction and post-liquefaction surface settlement. Themethod can be applied for arbitrary probability level however the weights of thebranches must be changed at different probability levels. For example, it is recom-mended to choose the weights for the parameters (MSF, input time histories) ofcontrolling earthquakes proportionally with their contribution to the hazard. Themagnitude and distance of these earthquakes come from deaggregation of PSHA.Their contribution to the hazard is changing at different probability levels. There-fore, the applied weights will be also different. The logic tree shown in Fig. 9treats all arising uncertainties. According to the sensitivity studies, the number ofbranches can be reduced continuing the computations with the best estimation orwith the conservative boundary curve.

Both types of computation methods (the effective stress and semi-empiricalmethods) will be applied to estimate the liquefaction and the settlement. By us-ing both methods, the benefits can be exploited and the disadvantages of themreduced. Therefore, the proposed logic tree bifurcates first according to the type ofused method.

The upper branch shows the process of computations by semi-empirical methods.In the first step, the assessment of site amplification will be made. Here the uncer-tainties arising from low strain shear modulus as well as shear modulus degradationand damping ratio curves are accounted. Here the non-linear total stress analysiswould be applied. The use of real earthquake acceleration histories as input bedrockmotion is preferred. To reduce the number of applied time histories, matching theirresponse spectra to the bedrock UHRS is proposed. Even in this case, minimum3 earthquake time histories have to be used as input for the computations. Themagnitudes, distances, and the tectonic environments of the chosen earthquakeshave to be in accordance with parameters of the controlling earthquakes comingfrom the deaggregation of PSHA.

Hereinafter the safety factor against liquefaction and the surface settlementswould be computed solely with the values of 15, 50 and 85% percentiles of thePGA and CSR. This reduces the number of logic tree branches, but substantiallydoes not affect the results. If both SPT and CPT measurements were carried outon the site then the computation of CRR should be carried out also by SPT- andCPT-based method according to the recommendations of EERC. Selection of thespecific methods within them is made from the best available and reliable ones.The correction of magnitude dependent duration (MSF) has to be made by themagnitude values and weights coming from deaggregation of PSHA. Of course, thesemagnitude values and weights have to be equal with the applied ones during thesite effect computation. We propose the use at least two methods to estimate the


366 E GYORI et al.

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volumetric strain and post-liquefaction settlement after the computation of safetyfactor against liquefaction. The selection of methods is made on the basis of therelevant standards and recommendations (IAEA NS-G-3.6 2004, US NRC RG 1.982003) in line with the procedures used to determine the FS. The variability of theinfluencing parameters (relative density, ground water level) has to be taken intoaccount during settlement computation. Of course, if a method does not requirethe determination of CRR and FS, but only the CSR and the relative density valuesare used in the calculation, then the logic tree will be somewhat simplified.

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