literature on lquefaction
TRANSCRIPT
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13th World Conference on Earthquake EngineeringVancouver, B.C., Canada
August 1- 6, 2004Paper No. 2973
LIQUEFACTION RISK ASSESSMENT AND DESIGN OF PILE
FOUNDATIONS FOR HIGHWAY BRIDGE
Nikolaos KLIMIS 1, Anastasios ANASTASIADIS1, George GAZETAS2and Marios APOSTOLOU2
SUMMARY
A major 1 km long bridge over Nestos river, currently under construction, is founded on fluvial deposits
containing potentially liquefiable clean sand and silty sand in a medium-dense to loose state, for a total
thickness of about 12 m. Geotechnical reconnaissance involved a considerable number of geotechnical
boreholes, CPT, SPT, Crosshole, and laboratory tests. The total thickness of soil deposits is about 50 m
and is underlain by good quality gneiss. Three different design profiles are assigned but only one of
them is used in this paper for 1D equivalentlinear and nonlinear seismic response analyses. Nine actual
accelerograms, significantly varying in frequency content define the base-rock input motion. Then, current
state of practice of semi-empirical methodologies based on SPT, CPT and VS profiles, are applied to
access the safety factor against liquefaction, and are compared with results of theoretical 1D nonlinear
effective stress analyses. The consequences of liquefaction on foundation piles are determined by
adopting a methodology inspired by the recent Japanese experience, which calls for three distinct andsuccessive stages: before, during, and after liquefaction, including lateral spreading, in a simplified
way. Kinematic soil-pile interaction and inertia soil-pile-structure interaction are considered. Specific
countermeasures are proposed, such as construction of jet-grouted piles suitably arranged between the
piles of some of the bridge piers.
INTRODUCTION
The examined case study refers to a major highway bridge of almost 1 km long, located at the
Northeastern part of Greece. The region where the examined bridge is located is almost flat with a light
bilateral inclination ranging from 0.5% to 1.5% towards Nestos riverbed. The above highway bridgeconsists of two independent branches. The total length of each branch is of 952 m and it consists of
1 Institute of Engineering Seismology & Earthquake Engineering (ITSAK), 46, Georgikis Scholis str.,
P.O. Box 53, GR-55102, Finikas, Thessaloniki, GREECE ([email protected], [email protected])2 National Technical University of Athens (NTUA), 9, Heroon Polytechniou Str., Zografou GR-15780,
GREECE; [email protected] .
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twenty spans, with the central spans being 65 m, 120 m, and 65 m long. A section of the central part of the
bridge over the riverbed is sketched in Figure 1.
The subsoil consists of clean and silty sands, of loose to medium density, with thin layers or interlayers of
sand-gravel mixture or siltysandy clays, overlaying a good quality gneissic bedrock. It is prone to
liquefaction under strong seismic motion. An integrated liquefaction risk analysis based on semi-empirical
methodologies (CPT, SPT, and VS), and also on theoretical results from 1D equivalent linear and non
linear effective stress analyses in an attempt to account for seismic site response. A cautious combination
of theoretical and semi-empirical results allows the assignment of a well determined liquefiable zone with
a high degree of confidence.
As for the consequences of the liquefied zone on foundation piles, according to the current state of art and
practice, it is widely accepted that a universal accurate solution, referring to seismic motion of a complex
system, such as: soil pile group pier bridge under conditions of liquefaction and lateral spreading, is
rather unlikely to exist. However, due to Kobe earthquake (1995) experience, simplified methods of
analyses have been proposed in the framework of recent Japanese Earthquake Resistant Design Codes [1].
A characteristic feature of the above simplified analyses is dissociation of pre- and post liquefaction
stages.
Figure 1. A section of the bridge including the 120 m long, central span over the riverbed.
SITE CHARACTERIZATION AND LIQUEFACTION SUSCEPTIBILITY
The general geology of the broad area consists of Pleistocenic sediments (gravel, coarse sand and
moraine) and semi-consolidated pleistocenic sediments (cemented gravel and sands).
At the study area where the bridge is scheduled to be founded, soil materials are distinguished as follows:
M5 M6 M7
RDg
ALsALs
ALs
gngn
LIQUEFIABLE
ZONE
riverbed deposits
0 100 m
M5M5 M6M6 M7M7
RDg
ALsALs
ALs
gngn
LIQUEFIABLE
ZONE
riverbed deposits
0 100 m0 100 m
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River deposits (RD) of river Nestos consisting of sands, silty and clayey silty sands, gravels and
occasionally pebbles of gneiss or marble.
Alluvial deposits (AD) essentially of sandy nature, with fluctuating percentage of clays, silts and
gravels. Occasionally, thin layers of gravels and clays / silts are encountered. According to
geotechnical investigation programs carried out for this area, alluvial deposits are of considerable
thickness ranging from 12 to almost 55m. Those layers are relatively loose and considerably
uneven, and in some cases an increased percentage of organics has been detected.
The bedrock consists mainly of biotitic gneiss (gn) locally interpolated by amphibolites and marbles of
gray green colour. Sedimentary layers become thicker and more cohesive or dense with depth. Free
ground water level is normally located at a depth ranging from 1.5 to 6.0m below ground surface and the
pore water pressure is hydrostatic from this level.
Based on geotechnical investigation the under study area, of almost 1 Km length, can be divided into three
major regions, if physical, mechanical and dynamic characteristics of different soil layers are carefully
combined. In the present work the most representative profile I, in terms of liquefaction susceptibility,
corresponding to the central spans of the bridge is used for seismic analysis purposes and is presented in
Figure 2.
55
50
45
40
35
30
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15
10
5
0
0 400 800 1200
VS(m/s)
55
50
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40
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30
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10
5
0
18 20 22 24 26
Unit Weight (KN/m3)
55
50
45
40
35
30
25
20
15
10
5
0-3.0
GPSP
SP
SM
SP
WZ
WR
Loose to mediumdense, poorly graded
sandy gravels andmedium grained
poorly graded Sand
Loose-mediumdense
fine-grainedpoorly graded SAND
Medium densesilty sand
with gravels (~15%)
Medium dense todense medium grained
poorly gradedSAND
(silty sand &gravels, locally)
Weathered zone
of gneiss
Weathered Gneiss
Dr(%)
50
45
60
40
65
85
Uc(d60/d10)
20.0
12.113.3
3.0
5.7
3.3
3.3
50
K(m/s)
10-7
10-7
10-7
10-7
10-8
10-9
10-8
( )
33
36
33
35
35
38
'co/'
1.5
1.1
2.0
1.0
4.0
4.0
c(kPa)
0
0
0
0
0
0
el hys mob
1E-08 1E-04 1E-01
1E-08 1E-04 1E-01
1E-08 1E-04 1E-01
1E-08 1E-04 1E-01
1E-08 1E-05 1E-01
1E-08 1E-03 1E-01
Figure 2. Representative soil profile of the central area (soil profile ) and dynamic properties used
in effective stress seismic analyses.
A critical step to start with, is the assignment of soil layers liquefaction susceptibility, by implementation
of compositional criteria relevant to soil texture, sieve analysis, grain size and physical characteristics.
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Criteria described as above result from laboratory tests and observations on liquefied soils. Limits of
sandy soils prone to liquefy according to uniformity coefficient (UC), are proposed in Technical Standards
for Port and Harbour facilities in Japan [2]. In case of increased percentage of gravels or fines,
implementation of additional criteria referring to plasticity and water content are applied in order to
quantify liquefaction susceptibility according to Wang [3], Finn [4] and Andrews [5].
SITE RESPONSE AND LIQUEFACTION RISK ASSESSMENT
Nine accelerograms have been considered in this project to describe the excitation at rock outcrop. Based
on seismic hazard analysis for the area under consideration, the peak ground horizontal acceleration at
outcropping bedrock conditions was at 0.26g.
Site response analyses were performed using total and effective stress analyses. Total stress analyses were
performed with SHAKE [6]. In this paper site response analyses are restricted only to the central area of
the project, as being the most representative and appropriate for liquefaction risk assessment. Shear
modulus ratio, G/Gmax, and damping ratio, DS, curves as function of shear strain, were obtain from the
literature [7], [8], [9,10], [11], [12]), as shown in Figure 3. Non-Linear analyses [13], and effective stress
analyses using elastoplastic multimechanism model [14], [15], [16,17] and the reduced-order bounding
hypoplasticity model [18, 19] were also performed.
0.0001 0.001 0.01 0.1 1 10
Shear Strain, (%)
0.0
0.2
0.4
0.6
0.8
1.0
G/G
max
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
G/G
max
1. Ishibashi & Zhang (1993) ' = 50 kPa2. Ishibashi & Zhang (1993) ' = 100 kPa3. Ishibashi & Zhang (1993) ' = 200 kPa4. Ishibashi & Zhang (1993) ' = 300 kPa5. Ishibashi & Zhang (1993) ' = 400 kPa6. Ishibashi & Zhang (1993) ' = 500 kPa7. Anastasiadis (1994) Stiff sandy Clay with gravels8. Hatanaka et al. (1995) Sandgravels9. Vucetic & Dobry (1991) Clay PI=010. Vucetic & Dobry (1991) Clay PI=1511. Pitilakis et al. (1998) Sand (SP, SM)12. Pitilakis et al. (1998) Weathered Rock13. Idriss (1972) Rock
0.0001 0.001 0.01 0.1 1 10
Shear St rain, (%)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
DS
(%)
1. Ishibashi & Zhang (1993) ' = 50 kPa2. Ishibashi & Zhang (1993) ' = 100 kPa3. Ishibashi & Zhang (1993) ' = 200 kPa4. Ishibashi & Zhang (1993) ' = 300 kPa5. Ishibashi & Zhang (1993) ' = 400 kPa6. Ishibashi & Zhang (1993) ' = 500 kPa7. Anastasiadis (1994) Stiff sandy Clay with gravels8. Hatanaka et al. (1995) Sandgravels9. V ucetic & Dobry (1991) Clay PI=010. Vucetic & Dobry (1991) Clay PI=1511. Pitilakis et al. (1998) Sand (SP, SM)12. Pitilakis et al. (1998) Weathered Rock13. Idriss (1972) Rock
Figure 3. Variation of shear modulus (G/Gmax) and damping ratio (DS) with shear strain (%):
curves from literature used in seismic response analyses (equivalent linear).
Comparison of peak acceleration, shear strain and stress values obtained from total and effective stress
analyses is portrayed in Figure 4. For the majority of input motion accelerograms, shear strains calculated
with equivalentlinear methodology appear to be rather unrealistically high. On the other hand, some ofthe inelastic methods of analysis may be somewhat unsafe in leading to reduced amplitudes of
acceleration. It is believed that reality lies somewhere in between.
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55
50
45
40
35
30
25
20
15
10
5
00.1 0.2 0.3 0.4 0.5 0.6
max Acceleration (g's)
55
50
45
40
35
30
25
20
15
10
5
0
0 0.2 0.4 0.6 0.8 1
max Shear Strain (%)
55
50
45
40
35
30
25
20
15
10
5
0-3.0
GPSP
SP
SM
SP
WZ
WR
0 50 100 150 200 250
Shear Stress (kPa)
55
50
45
40
35
30
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0
55
50
45
40
35
30
25
20
15
10
5
0
KAL-DecAigrockPacoima-NSShinkobe-NS
Non-Linearanalyses
EquivalentLinear analyses
Figure 4. Soil Profile I - Peak accelerations, shear strains and stresses : confrontation of results
from non-linear (solid lines) and equivalent linear (dashed lines) analyses with 4 input motions.
Highly non-linear behavior of loose clean-sandy layers is depicted in calculated excess pore water pressure
ratio time histories (Figure 5a) indicating high liquefaction risk. Maximum pore water pressure variation
with depth is shown in Figure 5b. It is easily shown that the zone of high pore water pressure in excess of
80% extends from 5 to 16m below free ground surface and also another zone is delimited between 22 and
32m. It is then theoretically concluded that liquefaction risk is very high at the aforementioned depths.
Despite theoretical results for the deeper zone, we cannot convincingly argue that liquefaction will occur
for depths exceeding 25 m to 30 m since almost no evidence of liquefaction at such depths exists.
Response spectra resulting from total and effective stress analyses are presented in Figure 6 and exhibit
relatively high values at periods between 0.2 and 0.8 sec and to some extent up to 1.2 sec.
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0
0.2
0.4
0.6
0.8
1
u/'v0
-25.5 m-16.0-14.0-22.5
-20.0-12.0
0 5 10 15 20 25 30Time (sec)
-3-2
-10123
acc.
(m/s2)
Input Motion: KAL86-dec. 0.26g
3 6.0 4 8.0 5 10.0 6 12.0 7 14.0 8 16.0 9 18.0 10 20.0 11 22.5 12 25.5 13 29.0
Soil MeanLayer Depth(m)
55
50
45
40
35
30
25
20
15
10
5
0
0 200 400 600 800
Pore-Pressure (Over) (kPa)
55
50
45
40
35
30
25
20
15
10
5
0-3.0
GPSP
SP
SM
SP
WZ
WR
'VO
1 sec4 sec6 sec10 sec
KAL-D
Figure 5. Soil Profile I - Effective stress analysis: (a) Calculated excess pore water pressure ratio
time histories at various depths and (b) maximum pore water pressure variation with depth.
Elastic Acceleration Response Spectra at free Surface Soil Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
T : sec
Sa
:g
Aigio-DKalam-D
Kozani-TArgost83-1LKEDE-DShinkobe-NSTemplorPacoima-EWPacoima-NSKAL-H NLAIGIO-H NLShink-H-NLPaco-NS-H-NLKozani-TArgost83-1L
Elastic Acceleration Response Spectra at free Surface Soil Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
T : sec
Sa
:g
Aigio-DKalam-D
Kozani-TArgost83-1LKEDE-DShinkobe-NSTemplorPacoima-EWPacoima-NSKAL-H NLAIGIO-H NLShink-H-NLPaco-NS-H-NLKozani-TArgost83-1LKEDE-DTemplorPacoima-EWAver.Aver.+1SDAver.-1SDPROPOSED
Figure 6. Elastic acceleration response spectra at free ground surface (Soil Profile I): synthesis of
total and effective stress analyses results.
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Mean elastic acceleration response spectrum one standard deviation (m +) is also included in Figure 6.
The design peak ground horizontal acceleration adopted for this case study is 0.36g, mainly based on
theoretical results of non-linear and effective stress analyses.
Evaluation of liquefaction risk was based on results of theoretical analyses and selected semi-empirical
methodologies, with emphasis on stressbased procedures. More specifically, the amplitude of
earthquake-induced demand (quantified by cyclic stress ratio parameter CSR) was determined using
simplified relation-ships and peak ground horizontal design acceleration values, and also from results of
theoretical analyses. The soil strength against liquefaction (quantified as a function of the cyclic resistance
ratio CRR) was determined by empirical relationships provided in EC8 [12], NCEER 97 13] based on
field data such as: SPT, CPT and Vs. Figures 7 and 8, based on a characteristic borehole and static
penetrometer borehole, show synthetical results of semi-empirical methodologies applied to assess factors
of safety against liquefaction (FSL) and an accurate, as possible, description and evaluation of liquefaction
risk.
30
25
20
15
10
5
0
3.9
3.9
3.9
3.9
4.1
4.1
4.1
4.1
29.2
29.2
29.2
29.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
Log 0 10 20 30 40 50
N-(S.P.T.) (N1)60CS
30
25
20
15
10
5
0
14
19
22
19
13
19
31
34
30
0 0.2 0.4 0.6 0.8
Cyclic Resistance RatioCRR7.5
30
25
20
15
10
5
0
0 0.2 0.4 0.6 0.8
Cyclic Stress RatioCSR
30
25
20
15
10
5
0
0 1 2 3 4
Factor of SafetyFSL - =7
30
25
20
15
10
5
0
30
25
20
15
10
5
0
-4.20
EC-8NCEER 98
E.L.A.-max
E.L.A.-rd,=0.379g
EC-8 -=0.260gNCEER 98-=0.260g
E.L.A.-max
E.L.A.-r d ,=0.379g
EC-8 -=0.260gNCEER 98-=0.260g
GPSP
SP
Liquefaction
Risk
SM
SPSM
Liquefaction"Susceptibility"
based onCompositional
criteria
Figure 7. Implementation of various methodologies for estimating cyclic resistance ratio (CSR) and
safety of factor against liquefaction (FSL) from SPT tests.
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The calculated factors of safety against liquefaction, based on SPT values, specify zones presenting a high
risk to liquefy. For the above borehole the high risk zone for liquefaction to occur ranges from 11 to 25 m
of depth. The estimated risk is slightly reduced between 17 and 20 m. The bullets of red, yellow and black
color are indicative of liquefaction susceptibility (Red color: high susceptibility, yellow color: medium
susceptibility, green color: small susceptibility and black color: refers to soil sample not prone to
liquefy).
The CPT based factors of safety against liquefaction delimit a more extended zone of medium high to
high risk of liquefaction from 7 to 25 m. They differ slightly from the SPT based factor. Those differences
are deemed justified, since SPT measurements are relatively sparsed (every 2 to 2.5m), compared to CPT
values registered every 0.2m, as shown in Figure 8.
30
25
20
15
10
5
0LOG
7
5878
9
8
9
5
9898
9
89
8
9
8
9
0 20 40
qC(MPa)
30
25
20
15
10
5
00 0.2 0.4 0.6 0.8
CRR7.5
0 0.2 0.4 0.6 0.8
CSR
NLIQ
NLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQNLIQ
NLIQNLIQNLIQ
NLIQ
0 1 2 3 4 5
Factor of SafetyFSL - =7
30
25
20
15
10
5
0
30
25
20
15
10
5
0
-4.
E.L.A.- maxE.L.A.-r d ,=0.379g
EC-8 - =0.260gNCEER 98- =0.260g
0 2 4 6
fr (%)
0 1 2 3 4
IC
0 40 80
FC (%)
0 200 400
qc1,cs
1 Sensitive fine grained2 Organic material3 Clay4 Silty clay to clay5 Clayey silt to silty clay6 Sandy silt to clayey silt
7 Silty sand to silty clay8 Sand to silty sand9 Sand10 Gravelly sand to sand11 Very stiff grained (OC or Cem.)12 Sand to clayey sand (OC or Cem.)
SieveAnalysis
Liquefaction
Risk
Ic=2.6
E.L.A.-max
E.L.A.-rd,=0.379g
EC-8 -=0.260gNCEER 96-=0.260g NCEER 98- CPT& E.L.A.-
max
EC-8Seed et al.(1986)Ishihara (1985)Rob.&Camp.(1985)NCEER-98- Vs NCEER-98- CPT
-4.20
Robertson,1
986 EC-8
Seed et al.(1986) NCEER-98- CPT
Figure 8. Implementation of various methodologies for estimating cyclic resistance ratio (CSR) and
factor of safety against liquefaction (FSL) from CPT and Cross-Hole tests.
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The kinematic response of the soil-pile system after excess pore water pressures arise is subdivided into
two distinct stages of response:
Stage A, when considerable pore water pressures have developed ( vou > 50.0 ) but no
widespread liquefaction has yet occurred. At this stage, the soil reaction to pile is drastically
reduced, but it still preserves a non-zero shear stiffness so that seismic waves can propagate
through and affect the pile. Thus, the nature of pile response is still predominantly dynamic but is
also significantly different from a linear or moderately nonlinear behavior.
Stage B, which takes place after the earthquake loading has ended. Now, lateral spreading of the
liquefied soil may take place under certain conditions, such as an inclination of the soil layers or
the surface resulting in a quasi-static, gravity-induced loading to the pile. Static analysis can be
performed to estimate the pile response by imposing a displacement loading along the supports of
springs connecting soil and pile; no inertial loading from the superstructure applies.
The analysis of the soil-pile system in the realm of a limited pore water pressure build-up (stage A) is
based on the procedure adopted by the conventional soil-pile interaction analysis. However, in this casequite softer Winkler soil springs along the pile account for the soil nonlinearities arising in the vicinity
of the pile. In the Nestos Bridge case, the calibrated distributed springs are portrayed in Figure 9.
Figure 9. Shear wave velocity and winkler springs distribution with depth for the soil-pile
interaction analysis. The Vsprofile at low strains is applied for the equivalent non-linear case where
no liquefaction is accounted for.
The numerical analysis of the pile response under earthquake motion is performed through the semi-
analytic algorithm SPIAB (Soil-Pile Interaction analysis for bridge piers, Mylonakis and Gazetas,
Gerolymos et al 1999). At this stage, inertia loading to pile is negligible due to strongly reduced
acceleration levels, thus a kinematic interaction analysis is adequate to predict the total system response.
0
5
10
15
2025
30
35
40
0 200 400 600 800 1000
Vs [m/s]
z
[m]
Vs design profile withliquefaction
Vs profile at low strains
0
5
10
15
20
25
30
35
40
1 10 100 1000
kH[MPa/m]
z[m]
(a) shear wave velocity (b) Winkler soil springs
SOILPILE STRUCTURE INTERACTION IN LIQUEFIABLE SOIL
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The time history of the Pacoima dam recorded in the Northridge 1994 earthquake is used as excitation at
outcropping bedrock, after scaling down to 0.26 g to be compatible to the Greek code provisions (see
Figure 10).
Figure 10. The acceleration time-history and response spectrum at 5% damping ratio of the scaled
Pacoima dam record.
The results are plotted in Figure 11 for a 40 m long pile in terms of bending moment and shear force
distributions. The results of the moderately nonlinear case which does not account for any pore-pressure
built-up are also plotted in this figure. It is clear that the slightly liquefied soil has a strongly detrimentaleffect on the response. The magnitude of the bending moment below the pile cap (z = 0) increases to 2800
kNm, which is nearly double the no-liquefaction value. Furthermore, the shear force is even more
amplified reaching about 480 kN at the depth of 10 m. The detrimental effect of pore-pressure
development is mainly the outcome of strongly amplified free-field shear deformations due to soil
softening; this overshadows the beneficial reduction of Winkler spring stiffness.
Figure 11. Bending moments and shear forces along the pile for the case of slightly liquefiable soil in
comparison with the moderately nonlinear response without pore-pressures built up.
The lateral spreading potential of the liquefiable soil is of rather minor importance, regarding that the
liquefiable layers and ground surface extend almost horizontally. A possible exception to the general case
involves the two piers M6 and M7 of the central span (see Figure 1) where a slight increasing of ground
surface inclination is possible due to a future erosion of the riverbed deposits. For these piers, specific
countermeasures are proposed to prevent any additional loading to the piles after lateral spreading onset.
0
0.5
1
1.5
0 0.5 1 1.5 2
T : s
Sa:g
-0.4
-0.2
0.0
0.2
0.4
0 2 4 6 8 10
t [s]
a
[g]
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500
Q: kN
z:m
kh,min
kh,liq
0
5
10
15
20
25
30
35
40
45
0 500 1000 1500 2000 2500 3000
M [kNm]
z[m]
kh,min
kh,liq
no liquefaction
slightly
liquefied
no liquefaction
slightly
liquefied
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Such measures include the construction of 0.8 m diameter jet-grouted piles suitably arranged between the
piles. The configuration of ground improvement for the pier M6 case is sketched in Figure 12.
Figure 12. Configuration of the stone columns for the pier M6 case.
ACKNOWLEDGEMENTS
The work was conducted with the support of the Egnatia Odos Company.
REFERENCES
1. JSCE. Earthquake Resistant Design Codes in Japan. Japan Society of Civil Engineers, 2000.
2. Technical Standards for port & harbour facilities in Japan from Handbook and Liquefaction
Remediation of Reclaimed Land, Edited by Port & Harbour Res. Inst. Balkema, 1997.
3. Wang, W. Some findings in soil liquefaction, Water Conservancy and Hydroelectric Power
Scientific Research Institute, 1979, Beijing, China.
4. Finn, W.D.L., Ledbetter, R.H., and Wu. G. Liquefaction in Silty Soils: Design and Analysis, 1994,
Ground Failures under Seismic Conditions, Geotechnical Special Publication No.107, ASCE.
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