1. The document summarizes methods for assessing liquefaction and post-liquefaction settlement, including simplified and effective stress methods. 2. Simplified methods use empirical correlations between in-situ tests like SPT and CPT to determine liquefaction potential, while effective stress methods directly model pore pressure buildup using constitutive soil models. 3. Both methods have uncertainties from earthquake loading, soil properties, and testing, though effective stress modeling is more accurate but relies on precise soil parameters. The document proposes a probabilistic approach using logic trees to account for uncertainties.

1. Acta Geod. Geoph. Hung., Vol. 46(3), pp. 347–369 (2011)
DOI: 10.1556/AGeod.46.2011.3.6
LIQUEFACTION AND POST-LIQUEFACTION
SETTLEMENT ASSESSMENT — A PROBABILISTIC
APPROACH
E Gy˝ori1
, L T´oth1
, Z Gr´aczer1
, T Katona2
1Seismological Department, Geodetic and Geophysical Research Institute
of the Hungarian Academy of Sciences, Meredek u. 18, H-1118 Budapest, Hungary,
e-mail: gyori@seismology.hu
2Paks Nuclear Power Plant, Hungary
[Manuscript received June 22, 2011; accepted July 28, 2011]
Low velocity surface layers can significantly increase ground accelerations during
earthquakes. When saturated sandy sediments are present, because of pore pres-
sure increase, decrease of soil strength or even liquefaction can occur. Some volume
change follows the dissipation of excess pore pressure after the earthquake resulting
surface settlements. To determine the liquefaction probability and post-liquefaction
settlement is very important for critical facilities e.g. for the site of Paks Nuclear
Power Plant, Hungary. Pore pressure increase and so the liquefaction and surface
settlements depend on the characteristics of seismic loading and soil parameters. To
quantify the extent of these phenomena is rather difficult. Uncertainties arise both
from the probabilistic nature of the earthquake loading and from the simplifications of
soil models as well. In the paper, the most important semi-empirical and dynamical
effective stress methods for liquefaction and post-liquefaction settlement assessment
are 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 into
account by applying a logic tree methodology. At the same time, the uncertainties
are 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 during
earthquakes. Besides strong shaking, soil failures can also occur causing damages
to built environment. When cohesionless loose granular soils can be found in the
upper strata, in dry conditions, shaking can induce compaction and settlement of
the ground; this phenomenon is called seismic settlement. Dry or nearly dry sands
densify very quickly; settlement of such deposits is usually complete by the end of
the earthquake. When saturated sandy deposits are subjected to shaking during
an earthquake, pore water pressure builds up leading to loss of strength or even
liquefaction. Some volume change follows the dissipation of excess pore pressure
1217-8977/$ 20.00 c 2011 Akad´emiai Kiad´o, Budapest

2. 348 E GY ¨ORI et al.
after the earthquake, resulting so-called post-liquefaction surface settlements. The
settlement of a saturated soil requires more time; settlement can occur only as earth-
quake induced pore pressures dissipate, accompanied by some volume change of the
deposit. The time required for this depends on the permeability and compressibility
of the soil, and the length of the drainage path. Liquefaction and surface settlement
frequently causes distress to structures supported on shallow foundations, damage
to pipelines that are commonly buried at shallow depths. To determine the liq-
uefaction probability and post-liquefaction settlement is particularly important for
critical facilities e.g. at the site of Paks NPP, Hungary.
Estimation of earthquake-induced settlements of sands is difficult. Errors of 25
to 50% are common in static settlement predictions; even less accuracy could be
expected for the more complicated case of seismic loading. Uncertainties arise not
only from the simplifications of the soil model, but from the probabilistic nature of
the earthquake loading.
In this paper the most important semi-empirical and dynamic effective stress
methods for liquefaction and post-liquefaction settlement assessment are summa-
rized. The most significant contributors to the uncertainties are highlighted, and
particular 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 uncertainties
are 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, expressed
in terms of the cyclic stresses required to cause liquefaction, and CSR (cyclic stress
ratio) is the cyclic stress generated by the given earthquake.
CSR =
τav
σv0
= 0.65 ·
σv0
σv0
·
amax
g
· rd (2)
where τav is the equivalent shear stress amplitude, amax is the peak horizontal
acceleration at ground surface, g is the acceleration of gravity, σv0 and σv0 are the
total and effective vertical overburden stresses, respectively, and rd is a nonlinear
stress 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

3. 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 to
result in liquefaction. Cyclic resistance ratio (CRR) curves represent limiting con-
ditions that determine whether liquefaction will occur (Fig. 1). In the simplified
procedure, soil resistance to liquefaction is evaluated using in situ tests, including
the standard penetration test (SPT), the cone penetration test (CPT), shear wave
velocity 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 NCEER
Working Group (Youd and Idriss 1997, Youd et al. 2001), one of the most widely
accepted and widely used SPT-based correlations is the “deterministic” relationship
proposed by Seed et al. 1984, 1985). This familiar relationship is based on com-
parison between SPT N-values, corrected for both effective overburden stress and
energy, equipment and procedural factors affecting SPT testing (to N1,60-values)
versus intensity of cyclic loading, corresponding to an earthquake of magnitude
7.5. (CSR7.5). The relationship between corrected N1,60-values and the intensity of
cyclic 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
Acta Geod. Geoph. Hung. 46, 2011

4. 350 E GY ¨ORI et al.
regarding either uncertainty or probability of liquefaction. Efforts at development
of similar, but formally probabilistic correlations have been published by a number
of 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 advanced
as 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 been
better defined, and had provided lesser levels of uncertainty, than the other three
methods. CPT, however, is approaching the same level, and newly developed CPT-
based correlations (Robertson and Wride 1998, Idriss and Boulanger 2004, Juang
et al. 2006, Moss et al. 2006, Robertson 2009) now represent nearly co-equal status
with regard to accuracy and reliability. SPT-based correlations are currently ahead
of CPT based correlations, due in large part to enhanced databases and better data
processing and correlation development. The new SPT-based correlations are more
accurate and reliable, and provide much lower levels of uncertainty or variance. The
CPT offers advantages with regard to cost, efficiency (since no borehole is required)
and consistency. However, the most important aspect is the continuity of data over
depth. SPT can only be performed at vertical spacing of about 75 cm or more, so
it can completely miss thin (but potentially important) liquefiable strata; SPT can
fail 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 of
the EERC report recommend the use of SPT and CPT based methods together, as
each offers significant advantages not available with the other.
Liquefaction triggering correlations based on measurements of in situ shear wave
velocity (VS-based correlations) have the advantage that VS can be measured in
coarse soils (gravelly soils and coarser) in which SPT and CPT can be obstructed
by interference with coarse soils particles (Andrus and Stokoe 1997). But this
correlation is less well defined (more approximate), than either SPT- or CPT-based
correlations. 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 are
discussed and recommended by NCEER Workshop by Youd et al. (2001) and by
EERC Report No. 2003-6 (Seed et al. 2003). In these studies, the authors have
made recommendations for the use of the procedures considered the most reliable.
The methods described here are based on empirical correlations between the in
situ measurement of the soil strength and liquefaction occurring in shallow depths as
well 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 earthquake
of magnitude 7.5. Seed and Idriss (1982) suggested the use of magnitude scaling
factors (MSF) for earthquakes of magnitude other than 7.5. MSF takes into account
the 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
Acta Geod. Geoph. Hung. 46, 2011

5. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 351
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 be
known:
— 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 (Probabilistic
Seismic 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 with
depth from numerous site effect analyses. In the literature, several authors have
proposed formulas that are sometimes significantly different from each other. This
uncertainty can be reduced using site specific CSR, that can be determined directly
from site effect studies. In this case equivalent linear or nonlinear total stress
methods have to be applied in computations where the pore pressure increase is not
taken into account.
Liquefaction can occur only in saturated granular soil, practically below ground
water 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 stress
to 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, and
VS charts correspond to earthquakes of magnitude 7.5. The MSF, which is used
to correct the duration of earthquakes of magnitude different from 7.5, has been
developed by a variety of different approaches (using cyclic laboratory testing and/or
field case history data) by a number of investigators. Figure 2 shows a number of
recommendations and the recommendations (shaded zone) of the NCEER Working
Group (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
Acta Geod. Geoph. Hung. 46, 2011

6. 352 E GY ¨ORI et al.
0
1
2
3
4
MSF
5 6 7 8 9
Mw
Andrus and Stokoe (1997)
Seed and Idriss (1982)
Idriss (NCEER)
Youd and Noble (1997) PL <50%
Youd and Noble (1997) PL <32%
Youd and Noble (1997) PL <20%
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 and
distances), which can be used to perform dynamic site response analyses and to
determine liquefaction potential. MSF has to be determined in accordance with the
magnitude 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 of
pore pressure and the dynamic ground response. The model takes into account the
important factors that affect the dynamic response of a sandy layer, such as tran-
sient pore pressure increase, soil damping, hardening, variation of shear modulus
with shear strain and changes in effective mean normal stress. Volumetric strain
and post-liquefaction settlement can be calculated by analysing the pore pressure
dissipation after the cessation of earthquake.
In most cases, the effective stress analysis is carried out because it can simulate
time 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 directly
assessed according to chosen seismic input motions in terms of pressure build-up or
development of strain. However, the results may be quite variable owing to different
input motions, constitutive models and other parameters, and the final assessment
Acta Geod. Geoph. Hung. 46, 2011

7. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 353
should be made in consideration of the extent of variability. The advantage of the
method besides the accurate modelling of the soil behaviour that in principle there
is 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 strain
curves,
— 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 the
seismic excitation. The sediments characterized by lower shear modulus, where
the transverse wave velocity is smaller, are looser. On the other hand, because of
the lower velocity the resulting shear stress will be higher. These factors together
favour the development of soil liquefaction. Shear modulus degradation and damp-
ing ratio curves characterize the nonlinear stress-strain behaviour of soils. Their
role is not so straightforward as the effects of the other parameters. Usually the
cyclic strength of strongly nonlinear materials are lower, but because of the larger
internal damping lower cyclic stress can develop in them. Relative densities influ-
ence the developments of volumetric strains and so the liquefaction susceptibility
and surface settlement. The susceptibility of liquefaction is very sensitive to chang-
ing these values (Gy˝ori 2004). Permeability is also a very important parameter of
liquefaction; liquefaction can occur if the permeability of surrounding strata is low
enough to prevent drainage. As it was mentioned earlier, high ground water levels
favour 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 usually
known as ranges of values rather than as discrete values. Besides, these parameters
Acta Geod. Geoph. Hung. 46, 2011

8. 354 E GY ¨ORI et al.
are determined from different types of measurements, which also contribute to this
variability.
The liquefaction potential for a given location is determined by earthquake mag-
nitude, duration, and the epicentral distance. Based on sensitivity calculations
(Gy˝ori et al. 2002a, 2002b, Gy˝ori 2004) it can also be concluded that the effect
of the excitation, namely the applied input acceleration time histories are at least
as important as the parameters discussed so far that mainly influence susceptibil-
ity. The reason is that besides the same PGA the spectra of earthquakes differ
significantly from each other even if we select earthquakes with similar magnitude
and focal mechanisms. The variability arising from the differences of earthquake
spectra can be reduced by increasing the number of input time histories, using ar-
tificial time histories generated compatible with the bedrock UHRS or fitting real
earthquake spectra to the bedrock UHRS. Generally, the use of real, registered ac-
celeration time histories are recommended in earthquake engineering practice at site
effect (Ansal and T¨on¨uk 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 American
NCEER (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 be
considered. 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 25
years to study the earthquake-induced settlement problem and they can vary from
the simplified semi-empirical methods to the complex non-linear dynamic ones. The
semi-empirical methods are based on the simplified liquefaction analysis procedures.
It is common essentially in every procedure that they estimate the consolidation
settlement 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 after
the earthquake. So the volumetric strain will be equal or close to the vertical
strain. 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 ground
settlement.
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 the
sublayer i; and n is the number of layers.
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9. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 355
3.1 Semi-empirical methods
3.11 Review of semi-empirical methods
If the simplified procedure is used to evaluate liquefaction potential, liquefaction
induced ground settlement of saturated granular deposits can be estimated using
one of the semi-empirical methods. This type of procedures were developed by
Tokimatsu 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 volumetric
strain and ground settlement for dry and saturated sands, too.
Seismic settlement in dry sands is a function of density of the soil, the number
of strain cycles and the magnitude of the cyclic shear strain induced by seismic
shaking (Silver and Seed 1971). The effective shear strain (γeff) can be computed
from effective cyclic shear stress (τeff) as follows:
γeff =
τeff
Gmax
Geff
Gmax
(5)
where Gmax is the small strain shear modulus, and Geff the effective shear modulus
at the induced strain level. Substituting the expression of effective cyclic shear
stress, the above expressions can be rewritten as:
γeff
Geff
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 from
knowledge of the effective shear stress. In 1971 Silver and Seed have published a
relationship between these two quantities for sands with different relative densities.
Tokimatsu and Seed (1987) have developed charts to estimate volumetric strain
in 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-cyclic
volumetric strain boundary curves are given in Fig. 3. Use of this methodology
requires determination of overburden-, fines-, and procedure-corrected SPT blow-
counts, and duration corrected CSR values. Solid lines in Fig. 3 show the volumetric
strain for liquefied soil. Dashed lines describe the case where pore pressure increases
but the earthquake loading is not large enough to cause liquefaction. In such cases,
volumetric strain also develops after dissipation of pore pressure, which, however is
lower than if liquefaction would have occurred. The curves for determining strain
of saturated sand are related to earthquakes of magnitude 7.5 so these have to be
corrected for different magnitudes.
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10. 356 E GY ¨ORI et al.
Fig. 3. Volumetric strain for saturated sand with CSR and corrected SPT blow-counts (after
Tokimatsu and Seed 1987)
The Ishihara and Yoshimine (1992) procedure estimates the volumetric strain
as a function of factor of safety against liquefaction, relative density, and corrected
SPT blowcounts or normalized CPT tip resistance. Both larger post-liquefaction
and smaller volumetric strain following pore pressure increase can be determined
by 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 fact
that Japanese average SPT hammer energy was 20% higher than the standard
value of 60%.
Shamoto et al. developed their constitutive equations describing post-liquefaction
soil deformations in 1998. They were based on the results of torsional shear tests.
Similar to Tokimatsu and Seed they estimated the developing volumetric strains
as 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 method
was calibrated for the surface subsidence observed after the 1995 Hyogoken-Nanbu
earthquake. According to their experiences, the final value of ground settlements
can be estimated as 0.84 times the value of computed ones.
The procedure of Zhang et al. (2002) to determine volumetric strain of sandy and
silty soils combines a CPT-based liquefaction estimation method with the results
of laboratory tests performed on clean sands. In the first step they computes the
safety factor against liquefaction using Robertson and Wride (1998) method. Then
diagram of Ishihara and Yoshimine (1992) is used for the estimation of volumetric
strain 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
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11. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 357
and CSR were selected as capacity and demand terms, respectively. The authors
provided a chart solution for the prediction of cyclically induced reconsolidation
volumetric strain.
In a more recent study, Cetin et al. (2009) described a semi-empirical maximum
likelihood method for the probabilistic assessment of cyclically induced reconsoli-
dation settlements of saturated cohesionless soil sites. They calibrated their SPT
based model to numerous earthquake case history data. The main advantage of
the 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-dependent
uncertainties arise as during determination of factor of safety against liquefaction:
— Uncertainties of CSR determination coming from the surface PGA and stress
reduction factor (rd). As it was mentioned earlier, these can be reduced by
the computation of site-specific CSR.
— Choose of the method for CRR estimation.
— Magnitude scaling factor (MSF) for the correction of magnitude of controlling
earthquakes.
— 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 be
determined using it.
Let’s consider, for example, a sample of saturated sandy soil sample under a
vertical effective stress σv. During a drained cyclic simple shear test, a cycle of
shear strain of amplitude (γ) causes an increment in volume strain (∆εvd) due to
grain 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). Martin
et al. (1975) showed that for saturated sands (assuming water to be incompressible),
∆σw = Er∆εvd (7)
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12. 358 E GY ¨ORI et al.
where Er is the one-dimensional rebound modulus of sand at the given vertical
effective stress. It was also shown that under simple shear conditions the volumetric
strain increment per cycle is a function of the total accumulated volumetric strain
(εvd) and the amplitude of shear strain. According to Byrne (1991), the function
has the form:
∆εvd = γC1e−C2
εvd
γ (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 =
(σv)1−m
mK2(σv0)n−m
(9)
in which σv0 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 of
volumetric 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 simultaneous
generation and dissipation of porewater pressure. Thus the rate of pore pressure
increase will be less than for completely undrained sand. If we solve these equations
with the differential equation of motion for the entire duration of the loading, then
we get the total volumetric strain that develops in the individual layers during the
earthquake.
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 in
the young sedimentary Pannonian Basin characterized with moderate seismicity.
The basin is filled with sediments of different ages. At the site Quaternary deposits
˝u– 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 large
thickness. In 1996, the site seismic hazard (PSHA), site effect and liquefaction
potential was re-evaluated by Ove Arup & Partners. This study was based on
a very extensive geophysical and geotechnical investigation. The measurements
indicated that saturated sandy layers under the site between 10 and 20 m below the
ground level are susceptible to liquefaction. The site effect analysis — computing
the response of the uppermost Quaternary layers — was carried out for 10−4
annual
probability level with nonlinear method.
Ove Arup & Partners investigated the stability of the foundation to seismic
motion and found that the only risk to the structure is an earthquake ground
motion 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 of
ground 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.
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13. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 359
They evaluated liquefaction occurrence by Seed and Idriss (1971) simplified method;
seismic settlement was computed by the semi-empirical method of Tokimatsu and
Seed (1987).
Recent studies preliminary estimated liquefaction to be more probable, and the
magnitude of surface settlement to be significantly larger. Factor of safety against
liquefaction 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’s
method 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 computations
resulted 23.8 cm for the post liquefaction settlement when Tokimatsu and Seed
method was applied. The seismic settlement under dry conditions was assessed as
1.11 cm using Tokimatsu and Seed (1984) method.
The results could not be used for the safety assessment since the variation of
the results obtained by different methods are very large, and do not allow proper
conclusions even if the conservative case would be accepted.
Differences between the results of the earlier and the present computations arise
from the use of different input parameters (best estimate or conservative side) and
from different approaches of the same type of computation procedures. In the
present section we review the sources of uncertainties arising during liquefaction
and post-liquefaction settlement assessment at Paks NPP site.
During site investigation, the soil properties were determined from numerous
different type measurements. In most cases, they have given different values for the
same parameter, therefore best estimate and lower and upper bound profiles were
also 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 & Partners
1995) near the reactor building. For CPT penetration resistance the best estimate
profile with the lower and upper bounds were estimated at the main and the reactor
sites, too (Fig. 4 b). As the figures show, significant variability can be observed in
the parameters, which have to be taken into account in computations.
The small strain shear modulus (Gmax) or shear wave velocity is one of the most
important input parameter of site effect analysis (both in case of total and effective
stress methods too). Its function versus depth for the representative soil profile can
be seen in Fig. 5 a. It was determined from a number of different tests, namely
cross-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 and
upper bound Gmax profiles was derived for use in site response analysis. Sensitivity
studies Gy˝ori (2004) showed that surface accelerations and liquefaction potential
are very sensitive to changing the shear modulus profile (use of best estimate, lower
and 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
Acta Geod. Geoph. Hung. 46, 2011

14. 360 E GY ¨ORI et al.
Fig. 4. SPT blow-counts with depth at the main exploration site (a); CPT cone penetration
resistance 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 strata
was obtained from the results of cyclic triaxial and resonant column tests. Best
Acta Geod. Geoph. Hung. 46, 2011

15. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 361
Fig. 6. Shear modulus degradation (a) and damping ratio (b) curves with shear strain (after Ove
Arup & Partners 1995)
estimate, lower and upper bound curves of the variation of G/Gmax with cyclic shear
strain (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 curves
due to the assumption that the soil behaviour is described by Masing principles.
Sensitivity studies performed by effective stress method showed that using lower or
upper bound curves instead of best estimate one in the computations, the results
are less sensitive than changing the Gmax profile.
The power plant site is located near the Danube. The site ground water level is
in hydraulic continuity with the river but the environmental wells show a much more
consistent ground water level than the Danube. For design purposes a ground water
level of 89 mBD, equivalent to a depth of 8 m was used. This value was used by
Ove Arup & Partners (1996) for liquefaction analysis. The ongoing studies assumed
the ground water level more conservatively at 91 mBD i.e. 6 m below ground
level. Sensitivity computations showed that factor of safety against liquefaction
decreased with increasing ground water level. But the results were less sensitive to
the reasonable modification of ground water level than to the changing the other
input parameters (Gy˝ori 2004). It was probably because the liquefaction could
occur at relatively large depths, between 10 and 20 m below ground level. The
same 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. The
bedrock PGA computed for 10 000 years return period event was 0.178 g, 0.23 g and
Acta Geod. Geoph. Hung. 46, 2011

16. 362 E GY ¨ORI et al.
0.299 g at 15%, 50% and 85% confidence levels, respectively (Gy˝ori 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 which
is affected by the magnitude of the earthquake. In case of Paks NPP, earthquakes
occurring about 15 km from the site have the greatest relative contribution to the
liquefaction hazard. There is also a small input from about 200 km as a result of
the high earthquake activity in the Sava-Zagreb seismic source zone (Ove Arup &
Partners 1996). Studying their magnitude, it was showed that the hazard is seen
largely as a result of earthquakes with magnitudes between 5.5 and 6.5. Therefore
three controlling earthquakes were chosen; these earthquakes had magnitudes of
5.7, 6.2 and 7.2 at distances of 11, 18 and 200 km from the site, respectively. In
simplified analysis duration can be taken into account by MSF. So it has to be
chosen in accordance with the magnitude of controlling earthquakes. According to
the NCEER recommendation MSF is about 2.2, 1.8 and 1.1 for an earthquake with
magnitude of 5.7, 6.2 and 7.2 respectively. This implies such a differences in the
factor of safety. Using effective stress analysis, acceleration time histories have to
be 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 function
of maximum shear stress with depth was predicted by nonlinear method. They
estimated CSR by averaging shear stress versus depth curves using five earthquake
time histories as input in the computations. In contrast, later studies used averaged
rd function with depth, which could cause also differences in the results.
In 2008, a sensitivity study was performed (T´oth et al. 2008) about the effect
of different input parameters to the liquefaction potential assessment. It was found
that 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 in
earthquake 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
(Gy˝ori 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 taken
into account (because of the high acceleration levels) during determination of ground
accelerations. Therefore nonlinear effective stress analysis has been applied. Three
real earthquake accelerograms were used as input motion in the computations. Tak-
ing into account the uncertainties in bedrock motion, in the soil parameters and the
variation 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 bedrock
acceleration 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 was
chosen as input time history for the analysis (Fig. 8 a). We used the best estimate
curves for the soil profile parameters and the average value of 8 m for the ground
Acta Geod. Geoph. Hung. 46, 2011

17. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 363
· ··· ··
PGA ON THE
BEDROCK
EARTHQUAKE
TIME HISTORY
SHEAR
MODULUS
G/GMAX RELATIVE
DENSITY
5% percentile
50% percentile
95% percentile
0,185
0,63
0,185
time history 1
time history 2
time history 3
0,33
0,33
0,33
mean
mean+1,6*sigma
mean-1,6*sigma
0,2
0,6
0,2
mean+1,6*sigma
mean-1,6*sigma mean-1,6*sigma mean-1,6*sigma
mean+1,6*sigmamean+1,6*sigma
meanmeanmean
0,20,20,2
0,20,20,2
0,60,60,6
GROUND-
WATER
LEVEL
Fig. 7. Logic tree applied to compute site effect and liquefaction potential by effective stress
method
water depth. The analysis was carried out assuming horizontally layered soil model
using computer program DESRA-2C developed by Lee and Finn (1997). The second
and 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, where
previous 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 it
can be seen from the figure a small increase in pore pressure and volumetric strain
can be expected assuming such an earthquake loading. However the extent of this
volume strain is very small, about 0.05% in the selected layer. If the volume strain
for 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 the
developed volumetric strain and surface settlement was different.
The studies conducted in case of Paks NPP showed that the different methods
sometimes provided significantly different results even if the input parameters were
the same. Therefore, efforts should be made to use the best available and reliable
methods, 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 the
analytical 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 surface
settlement have been presented. The most significant contributors to the uncertain-
ties were highlighted, and particular examples through the investigation of Paks
NPP site were given. In the present section, a probabilistic procedure is proposed
for accounting these uncertainties.
Our method is based on the logic tree methodology, which is widely used in
hazard 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
Acta Geod. Geoph. Hung. 46, 2011

18. 364 E GY ¨ORI et al.
Fig. 8. The acceleration time history of Parkfield earthquake (M = 5.6) scaled to 0.25 g bedrock
PGA (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 with
time (g) in 16.5 m depth
Acta Geod. Geoph. Hung. 46, 2011

19. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 365
the bedrock surface. The procedure focuses on uncertainties arising in computation
of site amplification, liquefaction and surface settlement, utilizes the geotechnical
nature of the strata and the results of sensitivity computations. The effects of
epistemic 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. The
method can be applied for arbitrary probability level however the weights of the
branches must be changed at different probability levels. For example, it is recom-
mended to choose the weights for the parameters (MSF, input time histories) of
controlling earthquakes proportionally with their contribution to the hazard. The
magnitude 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. 9
treats all arising uncertainties. According to the sensitivity studies, the number of
branches can be reduced continuing the computations with the best estimation or
with the conservative boundary curve.
Both types of computation methods (the effective stress and semi-empirical
methods) will be applied to estimate the liquefaction and the settlement. By us-
ing both methods, the benefits can be exploited and the disadvantages of them
reduced. Therefore, the proposed logic tree bifurcates first according to the type of
used 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 degradation
and damping ratio curves are accounted. Here the non-linear total stress analysis
would be applied. The use of real earthquake acceleration histories as input bedrock
motion is preferred. To reduce the number of applied time histories, matching their
response spectra to the bedrock UHRS is proposed. Even in this case, minimum
3 earthquake time histories have to be used as input for the computations. The
magnitudes, distances, and the tectonic environments of the chosen earthquakes
have to be in accordance with parameters of the controlling earthquakes coming
from the deaggregation of PSHA.
Hereinafter the safety factor against liquefaction and the surface settlements
would be computed solely with the values of 15, 50 and 85% percentiles of the
PGA and CSR. This reduces the number of logic tree branches, but substantially
does not affect the results. If both SPT and CPT measurements were carried out
on the site then the computation of CRR should be carried out also by SPT- and
CPT-based method according to the recommendations of EERC. Selection of the
specific methods within them is made from the best available and reliable ones.
The correction of magnitude dependent duration (MSF) has to be made by the
magnitude values and weights coming from deaggregation of PSHA. Of course, these
magnitude values and weights have to be equal with the applied ones during the
site effect computation. We propose the use at least two methods to estimate the
Acta Geod. Geoph. Hung. 46, 2011

20. 366 E GY ¨ORI et al.
semi-empirical
methods
·
··
·
··
EARTHQUAKE
TIMEHISTORY
SHEAR
MODULUS
G/GMAX
15%percentile
50%percentile
85%percentile
wb1
wb2
wb3
MSF1
MSF2
MSF3
wa1
wa2
wa3
mean
upperbound
lowerbound
ww1
wg2
wg3
upperbound
lowerboundlowerboundminimum
maximumupperbound
meanmeanmean
wr1wn1wg1
ww3wr3wn3
ww2wr2wn2
GROUND-
WATER
LEVEL
·
BEDROCK
PGAAND
UHRS
effectivestress
method
surfacePGA,
liquefaction,
volumetric
strain
·
timehistory1
2timehistory
timehistory3
wa1
wa2
wa3
Siteeffectestimationwith
nonlineartotalstressmethod
···mean
upperbound
lowerbound
wg2
wg3
upperbound
lowerbound
mean
wn1wg1
wn3
wn2
EARTHQUAKE
TIMEHISTORY
SHEAR
MODULUS
G/GMAXCRR
wc1
SPTmethod
wc2
CPTmethod
wm2
wm1
FS
·ws1
method1
·
ws2
method2
MSF
SETTL.
COMP.
METHOD
·
lowerbound
upperbound
mean
wr1
wr3
wr2
volumetric
strain
·
timehistory1
timehistory2
timehistory3
wa1
wa2
wa3
··
minimum
maximum
mean
ww1
ww3
ww2
GROUND-
WATER
LEVEL
SurfacePGA
andsite
specificCSR
CRR
surface
settlement
surface
settlement
Coupledsiteeffectandliquefactionassessment
·
15%percentile
50%percentile
85%percentile
wd1
wd2
wd3
RELATIVE
DENSITY
RELATIVE
DENSITY
Fig.9.Proposedlogictreemethodologytoevaluateliquefactionandsurfacesettlement
Acta Geod. Geoph. Hung. 46, 2011

21. LIQUEFACTION AND POST-LIQUEFACTION SETTLEMENT 367
volumetric strain and post-liquefaction settlement after the computation of safety
factor against liquefaction. The selection of methods is made on the basis of the
relevant standards and recommendations (IAEA NS-G-3.6 2004, US NRC RG 1.98
2003) in line with the procedures used to determine the FS. The variability of the
influencing parameters (relative density, ground water level) has to be taken into
account during settlement computation. Of course, if a method does not require
the determination of CRR and FS, but only the CSR and the relative density values
are used in the calculation, then the logic tree will be somewhat simplified.
The other (lower) main branch shows the assessment of surface settlements by
the use of effective stress method. In doing so, the surface acceleration, pore water
increase and volume strain is determined simultaneously. The constructed logic tree
handles the uncertainties coming from different earthquake acceleration records,
low strain shear modulus, G/Gmax and damping ratio curves, relative densities and
the differences resulting from the variability of ground water levels. Based on the
calculations along logical tree branches a probability distribution is obtained for
the surface subsidence at every studied probability level from which the mean and
standard deviation can be computed.
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