nonlinear site response and its evaluation and
TRANSCRIPT
NONLINEAR SITE RESPONSE AND ITS EVALUATION AND PREDICTION
Nozomu YOSHIDAEngineering Research Institute, Sato Kogyo Co., Ltd., Tokyo, Japan
Susumu IAIPort and Harbour Research Institute, Ministry of Transportation, Yokosuka, Japan
ABSTRACT: Nonlinear behavior of a soft surface ground during strong earthquakes are reviewed anddiscussed. Firstly, dynamic deformation characteristics of soil are reviewed briefly. Then method of nonlinearanalysis and its accuracy is discussed. Finally, vertical arrays where strong ground motions were recorded areintroduced. Researches using these strong motion data are also reviewed to identify the occurrence of thenonlinear behavior and to explain the ground shaking. Through the review, nonlinear behavior is confirmed tooccur in these sites and importance to take nonlinear behavior into account in predicting the site response isrecognized. Equivalent linear analysis is shown to be a good approximation when maximum strain is less thanabout 0.5%, but not applicable at a liquefied site. Effective stress analysis is shown to be better than nonlineartotal stress analysis, and nonlinear analysis is better than equivalent linear analysis.
1 INTRODUCTION
Figure 1 shows a schematic figure showing the wavepropagation from a fault to a ground surface. In theengineering point of view, the earthquake wavetravels from the fault to the ground surface thoughthe seismic bedrock where earthquake motion can bedefined to be a function with respect to the distancefrom the fault, and the engineering seismic baselayer at which earthquake motion is not affected bythe existence of the surface ground, i.e., the subsoilabove the engineering seismic base layer. Theearthquake wave propagates vertically in the surfaceground because the ground becomes softer to theground surface. In addition, since the soil is soft, itmay exhibit nonlinear behavior under the largeearthquake. We focus the nonlinear behavior of thesurface ground caused by the vertically propagatingS-wave in this paper. The surface wave may alsopropagate at the site, but it is not treated here. There were two research fields to deal with theground motion in the surface ground: seismology(engineering seismology) and soil mechanics (soildynamics or earthquake geotechnical engineering).Engineers or researchers in soil mechanics knew thatsoil behaves in a nonlinear manner long ago. Theirinterests are mainly what will happen at theparticular site where they are going to makestructures. In the seismological field, on the otherhand, rather large area has been dealt with. There
were discussions where nonlinear behavior actuallyhappens in the actual earthquake. At present,importance of the nonlinear behavior of soil seemsto be recognized in this field (Aki 1993), too. In this state of arts, we discuss the nonlinearbehavior of surface ground mainly from the point ofview of earthquake geotechnical engineering. In thispoint, it is important to grasp the nonlinear behaviorof soil to recognize the behavior of the ground.Therefore, we review nonlinear characteristics ofsoil at first. Then we discuss the nonlinear behaviorof ground based on the earthquake observationobtained at the vertical array site.
2 DYNAMIC PROPERTIE S OF SOIL
Figure 2 shows strain dependent characteristics ofrock and soil. As shown in the figure, soil exhibitsnonlinear nature even at small strains. We classify
Rupture of fault
Wave propagtion
Surfacewave
Bodywave
Seismic bedrock
Engineering seismic
Surface ground
base layer
Figure 1. Schematic figure showing wavepropagation from fault to ground surface
Proc. 2nd International Symposium on the Effect of SurfaceGeology on Seismic Motion, Yokosuka, Japan, pp. 71-90, 1998
the behavior of soil subjected to cyclic loading intothe elastic modulus, dynamic deformationcharacteristics and dynamic strength in this paper.
2.1 Elastic modulusElastic modulus can be measured both in-situ and ina laboratory. Because of the disturbance in samplingand handling, however, elastic modulus obtained inthe laboratory does not coincide with in-situmodulus (Yasuda & Yamaguchi 1984) even anundisturbed sample in the ordinary degree is tested.Sample taken by in-situ freezing technique exhibitsthe elastic modulus same with in-situ (Tokimatsu1989). Downhole PS logging has been used in Japan inorder to obtain the in-situ elastic modulus from theelastic wave velocities. Recently, a suspensionmethod is also come to use in practice. A suspensionsonde that installs a source driver and two receiversis suspended in the borehole. The wave velocity iscomputed from the time lag of the arrival timebetween two receivers, therefore they are moreaccurate than those measured by the downholemethod. Kokusho (1992) compared S-wavevelocities measured by two methods as shown inFigure 3 and concluded that the downhole methodhas a tendency to give an average value and S-wavevelocity distribution by the suspension method is inconsistent with the SPT-N value distribution. Thesame characteristics have been confirmed bysubsequent observations. The effect of the differenceof the S-wave velocity evaluation on the dynamicresponse analysis will be discussed in section 4.3. Two elastic modulus, shear modulus Gmax andbulk modulus K, are computed from S-wave velocityVs and P-wave velocity Vp as
G Vmax s= ρ 2 , K V Vp S= −FHGIKJρ 2 24
3(1)
Here, it is noted that this bulk modulus is not the oneof soil skeleton, but that of mixture of soil particleand water. Therefore, it can be used for the totalstress analysis, but not for the effective stressanalysis. There is no relevant method to measure in-situ bulk modulus. In the engineering practice,Poisson's ratio between 1/4 and 1/3 are frequentlyassumed to obtain it. The effect of bulk modulus onthe earthquake response analysis under S-wavepropagation is small.
2.2 Dynamic deformation characteristicsSeed & Idriss (1970) and Hardin & Drnevich (1972)expressed nonlinear characteristics of soil subjectedto cyclic load as shear modulus G and damping ratioh as a function with respect to shear strain γ.Figure 4 schematically shows dynamic deformationcharacteristics test (DDC test hereafter) to compute
Linear elastic Elastic-plastic Shear banding
Start of clear yielding So-calledcritical state
Ultra-sonicResonant-column Special tests measuring
strains in shear bandImproved cyclic testConventional cyclic test
Seismic surveyCross-hole seismic survey
In-situ cyclic testAnalysis on earthquake recordsLinear
Equivalent linearNonlinear step by step
Hard rocksSoft rocks
GravelsSandsClays
Laboratorytests
Field tests
Method ofresponseanalysis
1. For normally consolidated soils subjected to monotonic loading2. Increases as OCR increases and with cyclic loading
10-7Average strain Local strain in shear band(in decimal)
10-6 10-5 10-4 10-3 10-2 10-1 100 101 102
Residual
1 2
Figure 2. Strain dependent soil properties,measurement, and analysis (modified from Ishihara1982 and Tatsuoka & Shibuya 1991)
0
20
40
60
80
100
Vs (m/s)
LoamFine sand
ClayFine sand
SiltFine sand
GravelFine sandSilty sandFine sandSilty sandFine sand
Silty sand
SPT-N value
Dep
th (m
)
0 100 200 300 500 700
Suspensionmethod
Downholemethod
Figure 3. Comparison of S-wave velocitiesmeasured by down hole and suspension methods
τ
10-6 10-5 10-4 10-3 10-2 10-1 100
Shear strain, γ
Shea
r mod
ulus
, G
Dam
ping
ratio
, h
t
τ γ
1G
h= 14π
τ
γ
σ'o σ'o σ'o
σ'oσ'd τd
Figure 4. Schematic figure showing the dataprocessing in dynamic deformation characteristicstest.
them by triaxial and torsional shear test apparatus.Usually, hysteresis loop at the 10th cycle of loadingis used to compute them (JGE 1996). Becausebehavior at small strains was difficult to measure atthe beginning, another tests such as a resonancecolumn test were used to measure the property atsmall strains. Improvement of the loading systemand the measurement (e.g., Kokusho 1980; Goto etal. 1991) enabled it to use from very small strains tolarge strains up to failure. Triaxial test has beenwidely used, but recently, torsional shear test alsocomes to be used especially in the research fieldbecause change of effective mean stress is notassociated with shear stress loading (it may occurdue to dilatancy). Since the expression as G-γ and h-γ relationshipsfit the equivalent linear analysis very much, it hasbeen used widely. They are reviewed by, forexample, Richart (1977), Ishihara (1982), Kokusho(1987), Woods (1991), and Tatsuoka & Shibuya(1991). Many empirical formulae have also beenproposed, but are not shown here because of thepage limitation. The G-γ and h-γ relationships obtained in DDCtest are generally recognized to express the sheardeformation characteristics of soil. They are,however, affected by the drainage condition.Figure 5, for example, shows stress-strain curvesunder drained and undrained conditions. They arequite different to each other. This is caused becauseof the dilatancy of soil, i.e., volume changeassociated with shear deformation. The sample inthe drained test becomes dense under the cyclicloading, which results in the hardening behavior instress-stress curve. On the other hand, since effectivemean stress decreases under the undrained condition,degrading behavior appears. In spite of the clear difference of the behavior,this difference is not strongly recognized in thedynamic deformation characteristics. In the pastresearches, both conditions have been employed. Atpresent, a test under undrained condition is popular,but drained test is also conducted (JGE Committee1988). Difference of the behavior under drained andundrained condition is small at stains smaller thanabout 10-3. After that, the effect of dilatancy appearsresulting in the difference between them.Degradation of stress-strain curve is also confirmedto occur for clay (Hyodo et al. 1988), but the effectis small in the earthquake response analysis. Maximum strain in the existing G-γ and h-γrelationships obtained by DDC test is about 10-2 atmaximum. There is no test data exceeding this strain.Of course, liquefaction strength test, shown in nextsub-section, treats strains of the order of severalpercent, but stress-strain relationship is hardlyoutput.
Kiku & Yoshida (1998) conducted DDC test atlarge strains and pointed out that conventional DDCtest is not applicable at large strains becausehysteresis loop does not stabilize but strain increasesrapidly. They employ the hysteresis loop at the thirdcycle and showed that damping ratio decreases asstrain because of dilatancy effect. There is nostandard to express the nonlinear behavior of sand atlarge strains. Yoshida (1995b) presented questions that G-γand h-γ relationships may be a good index of thenonlinear behavior, but may not appropriate toconsider it the stress-strain curve for the earthquakeresponse analysis. His points are as follows.1. G-γ and h-γ relationships at each cycle changes
significantly at the beginning and becomes stableafter several cycles of loading. In the earthquakeresponse analysis, on the other hand, peakresponse frequently occurs at virgin loading.Therefore what important is the behavior at thefirst cycle, but is not the stabilized behavior.
2. Stress-strain curve may not be the same even if
-0.01 0 0.01Shear strain, γ
Shea
r stre
ss, τ
(kPa
)
12
3
-0.05 0 0.05Shear strain, γ
Shea
r stre
ss, τ
(kPa
)
0.1-0.1
Toyoura sande=0.801
σ'm=147kPa σ'm=294kPa
Toyoura sande=0.809
-100
0
100
-100
0
100
(a) Drained (b) UndrainedFigure 5. Stress-strain relationships obtained bycyclic simple shear test under different drainagecondition (Modified from Towhata 1989)
10-6 10-5 10-4 10-3 10-2Shea
r mod
ulus
, G (k
gf/c
m2 )
Dam
ping
ratio
(%)
200
0
400
600
800
1000
5
0
10
15
20
25
Ko=1.0Ko=0.5
Ishikari undisturbed sand
Single amplitude shear strain, γ
σmo=1.84kgf/cm2'
(a) G-γ and h-γ relationships (Yamashita & Toki1994)
-0.1 0.0 0.1-100
-50
0
50
100Sh
ear s
tress
, τ (k
Pa)
-0.1 0.0 0.1 0.2-100
-50
0
50
100
Shea
r stre
ss, τ
(kPa
)Shear strain, γ (%) Shear strain, γ (%)
Ko=1.0 Ko=0.5
(b) Stress-strain relationshipFigure 6. Dynamic deformation characteristicsunder isotropic and anisotropic initial stresses.
G-γ and h-γ relationships are identical.Figure 6(a), for example, shows G-γ and h-γrelationships obtained by the torsional shear testunder isotropic initial stress (coefficient of earthpressure at rest, Ko=1.0) and anisotropic initialstress (Ko=0.5), keeping the initial effective meanstress constant. Both relationships are same witheach other. When looking at the stress-straincurves shown in Figure 6(b), however, thebehavior is quite different to each other. Thisoccurs because only the shape of hysteresis loopis used in calculating G and h, but the absolutelocation of the hysteresis curve is not interested ator documented.
In the existing h-γ relationship data, dampingratio of 2 to 4 % is frequently seen even at verysmall strains, as typically seen in Figure 6(a). This iscaused by various factors such as friction in the testapparatus, phase lag between stress and strainmeasurements, bedding error, etc., therefore notactual damping that the soil has. Yoshida (1984)pointed out that this value is of the same order withthe damping caused by wave scattering. He guessedthat, in the ordinary simulation of the earthquakeobservation at small to medium earthquake, althoughthis error is not corrected, but, at the same time,damping due to scattering is not considered. Botherrors canceled out resulting in a good simulation.
2.3 Dynamic strengthLiquefaction began to be focused on by engineersand researchers after the 1964 Niigata earthquake.At the beginning, mechanism of the liquefaction wasof primary interests, then the interests have moved tothe behavior up to or after the liquefaction. Cleansoil is the easiest soil for liquefaction to occur, butrecent earthquakes showed that widespread soil fromsandy silt to gravel liquefied. Test procedure of the dynamic strength test is thesame with dynamic deformation characteristics test,except that the load is applied until the test specimenfails in each stage. Figure 7 shows an example of thebehavior of sand obtained in the dynamic strengthtest. There are two important features in recognizingthe behavior up to and after the liquefaction. At first,
effective confining stress decreases under constantshear stress amplitude loading due to negativedilatancy, resulting in increase of shear strain orsoftening behavior. After stress path crossed thephase transformation line, positive dilatancy alsooccurs, resulting in hardening behavior when shearstrain increases. Therefore hysteresis loop becomesinverse-S shape. Under the cyclic loading, effectivestress gradually decreases and shear strain increasesreaching liquefaction. This phenomenon is calledcyclic mobility. The details of the dynamic strengthtest and liquefaction is not described here.
3 METHOD OF NONLINE AR ANALYSIS
First earthquake response analysis computer code inpractical use was SHAKE (Schnabel et al. 1972). Ithas been used widely, and name is now used as if itwere a common noun. This code based on themultiple reflection theory, and nonlinearity of soil isconsidered by the equivalent linear method. Unlikethe name of "equivalent", this is an approximatemethod. In order to solve the equation of motion inthe frequency domain, stress-strain relationship mustbe linear. Shear modulus and damping ratio to beused in the analysis is computed from the effectivestress γeff that is computed asγ α γeff max= (2)where γmax is a maximum shear strain. Thenonlinearity can be controlled by the coefficient α,but the value of 0.65 is frequently used as if it were aconstant. The hysteresis damping is taken intoaccount by employing the complex modulus. There are several advantages in SHAKE in thepractical use. Source list is open, which enable touse any computer and to modify depending on usersrequest. Data preparation is easy. It requires G-γ andh-γ relationships for soil data, therefore noengineering judgement is required. The mostimportant one is that it can compute incident wave atarbitrary depth from the earthquake data at theground surface or any other depth. Effective stress analysis then came to use (Finnet al. 1977; Ishihara & Towhata 1980). The sourcelist of these codes was also open. Nonlinear totalstress analysis (nonlinear analysis hereafter) wasalso possible by these computer codes. After thatmany computer codes have been developed, butcomputer code based on only total stress was hardlydeveloped. The difference between the total and effectivestress analyses comes from the consideration ofdilatancy. Both analyses evaluate mechanicalproperty of soil based on the effective stress. Ifdilatancy does not take place or is neglected,effective mean normal stress will fluctuate duringearthquake, but average value will keep nearly
-4 -2 0 2 4-30-20-10
0102030
Shea
r stre
ss (k
Pa)
Sheaer strain (%)-6
Effective confining stress (kPa)
Failure line
line
20 40 60 80 100
Phase transform
Figure 7. Stress-strain curve and stress path ofToyoura sand under cyclic loading
constant. Under this assumption, use of materialproperty evaluated from the initial stress state maybe justified. Total stress analysis employs thisapproximation. If dilatancy occurs, on the other hand,average effective mean normal stress changesmonotonically. In such a situation, material propertymust be evaluated at each time following the changeof the effective stress. This kind of analysis is calledeffective stress analysis. The governing equation for the effective stressanalysis was first proposed by Biot for theconsolidation problem (Biot 1941). This equation,frequently called Biot's equation, has been improvedand modified by many researchers for the dynamicanalysis as well as consolidation analysis. The mostexact formulation is described by usingdisplacement of soil skeleton u, displacement ofwater U (or displacement relative to soil skeleton w= n(U-u), where n is porosity) and pore waterpressure p as unknowns, and is called u-U-p (or u-w-p) formulation, but there is no computer code basedon this formulation. Several assumptions ormodifications were made partly in order to reducethe number of unknowns and partly in order to applyin particular cases. They are summarized inFigure 8. Many computer codes have been developedbased on Biot's equation, each of which employsdifferent constitutive models. They are not reviewedhere because of page limitation. Accuracy of the computer codes have beenconfirmed through the simulation of the shakingtable tests and the earthquake observations, some ofwhich are shown later. The blind test orsimultaneous analysis for constitutive model (Saada& Bianchini 1987) or dynamic response(Midorikawa 1992; Ishihara et al. 1989; Iai et al.1993; Arulanandan & Scott 1993) shows that thereexists significant scattering between computer codes,and there is no computer code that worked well inall situations. Comparisons between the equivalent linear andnonlinear analyses were also made by severalresearchers. When compared with earthquakeobservation, the nonlinear analysis is shown to agreewith the observed record better than the equivalentlinear analysis as shown later. Generally, equivalentlinear analysis has a tendency to give larger peakacceleration and shear stress under large earthquakes,and lower amplification in high frequency range. The reason of the latter phenomena is clear;damping ratio evaluated from the effective strain γeffis too large for small amplitude (high cycle)vibration. This effect becomes predominant underthe small to medium earthquake, resulting in smalleracceleration. The use of smaller α value in Eq. (2)can improve it. On the other hand, there are two opinions on the
reason of the former phenomena. Finn et al. (1978)compared dynamic response of a model ground bythree computer codes SHAKE, DESRA andCHARSOIL. DESRA uses hyperbolic model, andCHARSOIL uses Ramberg-Osgood mode. Resultsby two nonlinear analyses are almost the same as
u-p formulat ion
el iminate pKw ≠ 0
w = 0 (u = U)
neglect timederivative termCoupled
Uncoupled
)(0 Uuw ==•• •• ••
0=u••
Undrained condit ionKw ≠ ∞
Seepage
Static
u-U-p formulat ion
u-w-p formulat ion
u-U formulat ion
u-w formulat ion
Sandhu type(PWP at node)
Chr ist ian type(PWP in element)
Undrained condit ionKw=∞ possible
Consolidation
ε = 0•
p = 0Kw
nmT ε −• •
0)( =− dVpKn
w
Tεm⌠⌡elem.
• •
neglect timederivative term
Static
Dynamic analysis
Figure 8. Flow of Biot's formulation depending ondegree of approximation.
0.1 0.3 1 30.00
0.25
0.50
0.75
1.00
1.25
2
El Centro(αmax=0.1g)CHARSOILSHAKEDESRA
Period (sec.)
Pseu
do a
ccel
erat
ion
(g)
0 1 2 3 4 5 615
10
5
0
Dep
th (m
)
Maximum shear stress (tf/m2)
El Centro 1940, N-SBase input motion(αmax=0.1g)
SHAKE
DESRA
CHARSOIL
Figure 9. Comparison of three computer codes
τ
γ
A B
C
γmaxγeff
τ1
τ2
OFigure 10. Schematic figure showing the reason whySHAKE exhibits larger shear strain than specified.
shown in Figure 9, but SHAKE gives larger shearstress. He explained that large amplification comesfrom the resonance because equivalent linearanalysis is a linear analysis. Similar opinion ispresented by, for example, Iwasaki et al. (1980) andKokusho (1982). Yoshida (1994) showed another opinion. Letsolid line in Figure 10 is a stress-strain curvespecified for the analysis and γmax is a maximumstrain, then linear relation used in the equivalentlinear analysis is a line OAC. Therefore peak shearstress is not τ2 at point B that lies on the specifiedstress-strain curve, but τ1. In the same manner, whenspecified stress-strain curve is a solid line inFigure 10, then the peak stress-peak strainrelationship is expressed to be a dashed line; theshear stress is always overestimated. This is thereason why equivalent linear analysis gives largershear stress than the nonlinear analysis. If the formeropinion is true, SHAKE always gives largeracceleration regardless of the magnitude of theground motion. If the latter opinion is true, largeracceleration begin to appear as nonlinear behaviorbecomes predominant. Equivalent linear analysis has a deconvolutionfunction that is important in the engineering practice.It becomes possible when multiple reflection theoryin frequency domain is used. Deconvolution in time
domain is also proposed (Sakai et al. 1997), but itsapplicability is limited and is not in practical use atpresent. Because of the deconvolution function,equivalent linear analysis based on the multiplereflection theory is necessary even if nonlinearanalysis will be predominant and equivalent linearanalysis is less accurate. In this sense, it is importantto improve the accuracy of the equivalent linearmethod. Sugito et al. (1994) improved the latterdisadvantage of the equivalent linear analysis bytaking frequency dependent characteristics intoaccount. They put effective strain in each frequencycomponent as
γ α γeffmax
maxF fF
= ( ) (3)
where F(f) denotes Fourier amplitude of shear strainemphasizing it a function with respect to frequency f,and Fmax denotes maximum value of F(f). Figure 11is an example how it improves the response in highfrequency region. Although physical meaning of Eq.(3) is not clear, this modification sometimesimproves equivalent linear analysis significantly asshown in section 4.4. This method is called FDEL.Suetomi & Yoshida (1996) pointed that thisimprovement comes from the frequency dependencyof shear modulus but not from the that of dampingratio.
4 VERTICAL ARRAY AN D IDENTIFICATIONOF NONLINEAR BEHAVIOR
Examination of the vertical array record is one of thebest methods to identify the nonlinear behavior ofground and to evaluate the accuracy of the analyticalmethod. In this section, we review the vertical arrayswhere strong ground motion were recorded, andresearches based on these records.
0.1 0.10.1 0.1
1 1
10 10
1 110 10
ObservedComputed
ObservedComputed
Frequency (Hz) Frequency (Hz)
Ampl
ifica
tion
ratio
Ampl
ifica
tion
ratio
(a) SHAKE (b) FDELFigure 11. Amplification ratios by SHAKE andFDEL.
0.2 0.4 0.6 2 4 6 8 0.04 0.08
Peak Acceleration(cm/s2)
G/Go Damping ratio(%)
Peak strain(%)
100 200 300Soil type
Loam
Sandy clay
Fine sand
Fine sand
Depth(m)
Unitweight(tf/m3)
Vs(m/s)
140
320
420
420
1.15
1.95
2.00
2.0040
15
10
5
0
24
3201.50
Observed
0.8
SHAKER-O model
20 40
SPT-N valueReferencestrain(%)
0.30
0.05
0.08
0.30
0.08
Figure 12. Soil profiles and peak response at IIS Chiba Experiment Station
4.1 IIS Chiba Experiment Station Chiba Experiment Station, Institute of IndustrialScience, University of Tokyo is located about 30 kmeast of Tokyo, Japan (Katayama et al. 1990). Thereis a large dense array station including horizontaland vertical arrays with 44 three-directionalaccelerometers installed in 1982. Soil profiles basedon the borehole data of the main vertical array areshown in Figure 12. Accelerometers were installedat depths GL-1, 5, 10 and 40 meters in the mainvertical array. During the 1987 Chibaken-toho-oki earthquake,earthquake, acceleration with peak value of about400 cm/s2, were recorded. Acceleration time historyof the observed record is shown in Figure 13. Katayama et al. (1990) and Yamazaki (1994)conducted both equivalent linear analysis (SHAKE)and nonlinear analysis in which Ramberg-Osgood
model is used. The damping ratio h is given ash h G G ho o= − +max ( / )1 (4)In the nonlinear analysis, the first term correspondsto the hysteresis damping. The second term,minimum damping ratio ho, is given through theRayleigh damping so that h=2% at frequency f=2.3and 5.7Hz. The maximum damping ratio hmax is set0.25. The reference strains are shown in Figure 12.Peak responses of h and shear modulus ratio G/Goare shown in Figure 12, and acceleration timehistory at GL-1m is shown in Figure 14. Both resultsagree with the observed record. They concluded that,this good agreement comes because maximum shearstrain is less than 0.1%, i.e., nonlinearity is notpredominant. Although waveforms in Figure 14 are similar toeach other, peak acceleration by SHAKE is fairlylarger than observed. Yoshida (1996a) pointed thereason shown in chapter 3 and 0.80 for α in Eq.(2)instead of conventional value of 0.65 improves theresult so that peak acceleration agrees without largechange of other response.
4.2 Shin-Fuji Electric Substation siteAt the eastern part of Shizuoka Prefecture, Japan,Tokyo Electric Power Company installed verticalarray in 1977. Site conditions are shown inFigure 15. The accelerometers were set up at GL andGL-28m. Sato et al. (1997) evaluated nonlinear behaviorof soil by analyzing 9 earthquake motions observedbetween 1982 and 1991. S-wave velocities anddamping factors were evaluated by using the systemidentification technique. SHAKE was modified inorder to evaluate the theoretical spectral ratio so thatfrequency dependent damping ratio (Sato et al.1995)h h fo= −α (5)can be taken into account. Obtained dynamic deformation characteristicswere compared with the laboratory test result, whichis shown in Figure 16. They reported that shearmodulus ratio decreases as shear strain, but straindependency of the frequency dependent dampingratio is not clearly observed, both of which agreeswith laboratory test. Yoshida et al. (1995d) analyzed the biggestrecords, the earthquake of August 8, 1983, byvarious dynamic analysis methods. The magnitudeof the earthquake was 6.0, but the station is locatedonly 12 km from the epicenter. They used twoequivalent linear analyses (SHAKE and FDEL), andnonlinear analyses with hyperbolic model, Ramberg-Osgood model and Yoshida-Ishihara model. TheYoshida-Ishihara model is a nonlinear stress-strainmodel that satisfies given G-γ and h-γ relationships
-1000
100
20151050Time (sec.)
GL-40m-100
0100 GL-20m
-1000
100 GL-5m-300
0
300 GL-1m
-1000
100 GL-10m
Acce
lera
tion
(cm
/s2 )
Figure 13. Acceleration time histories (NScomponent)
400
7 11 158 12 169 13 1710 14
0
-400400
0
-400
Acce
lera
tion
(cm
/s)2
SHAKE
R-O model
AnalysisObserved
Peak acc. (cm/s )Observed 327.1SHAKE 362.9R-O 321.6
2
Time (sec.)
Figure 14. Comparison of time histories at GL-1 mdepth
completely (Yoshida et al. 1990). Peak responsevalues are shown in Figure 15, comparisons ofacceleration time histories are shown in Figure 17,and stress-strain curves are shown in Figure 18, inwhich damping caused by complex rigidity is alsoconsidered in the hysteresis curve. The agreementsof the acceleration time histories are generally well.Equivalent linear analysis, however, shows largerpeak acceleration. Overestimation is the largest inFDEL because it makes acceleration in highfrequency range large. Hyperbolic modelunderestimates acceleration because of theunderestimation of the shear stress as seen inFigure 18. Both Ramberg-Osgood model andYoshida-Ishihara model shows better agreementthan others. By comparing stress-strain curves inFigure 18, it is recognized that better agreementcomes from the better agreement of the skeletoncurve in stress-strain relationships. The maximum shear strains in the analyses arebetween 0.2 and 0.4%. Referring to Figure 2, thesestrains are boundary of the applicable range of the
2 4 6 1 2 2 4 6 0.2 0.4Upperscoriaw/lome
Andosol
Upperlome
w/scoria
Upperlome
w/scoria
Upperscoria
SPTN-value
20 40αmax (m/s2) δmax (cm) τmax (tf/m
2) γmax (%)Depth(m)
-25
-20
-15
-10
-5
Vs(m/s)
γt(tf/m3)
1.46
1.48
1.68
1.69
1.95
125
130
252
425
780
Soiltype
Eq. linearEq. linear (freq. depend)Hyperbolic modelRamberg-Osgood modelYoshida-Ishihara method
Observed
Figure 15. Site conditions and peak responses
10-6 10-5 10-4 10-3 10-2
Effective shear strain, γ
1.0
0.5
0
Shea
r mod
ulus
ratio
, G/G
o
0.3
0.2
0.1
0 Dam
ping
ratio
h a
t f=3
.1 H
zIdentified LaboratoryG/Go h Test 1st layer (GL 0~-5m) 2nd layer (GL-5~7m) 3rd layer (GL-7~12.2m)
EW
Figure 16. G-γ and h-γ relationships (γ is effectivestrain)
-500
0
500 Observed Hyperbolic model
-1000
100
8765432Time (sec.)
GL-28m, observed
-500
0
500 Observed R-O model
-500
0
500 Observed Yoshida-Ishihara model
-500
0
500 Observed FDEL
-500
0
500 Observed SHAKE
Acce
lera
tion
(cm
/s2 )
Figure 17. Comparison between time histories(EW components)
-30-20-10
0102030
Shea
r stra
in (k
Pa)
-0.4 -0.2 0 0.2 0.4Shear strain (%)
Y-I Skeleton
-30-20-10
0102030
Shea
r stra
in (k
Pa) Hyperbolic
Skeleton
-30-20-10
0102030
Shea
r stra
in (k
Pa) SHAKE
Skeleton FDEL Skeleton
-0.4 -0.2 0 0.2 0.4Shear strain (%)
R-O Skeleton
Figure 18. Stress-strain curves
equivalent linear analysis. It is noted that this record was not used by Satoet al. (1997), therefore strains corresponding to thisrecords are not shown in Figure 16.
4.3 Technical Research Center, Kansai ElectricPower Co.
This site is located in Amagasaki City, east ofHyogo Prefecture, Japan. The accelerometers were
set up at GL, GL-24.9, and GL-97m. During the1995 Hyogoken-nambu earthquake, accelerationwith peak value of about 500 cm/s2 was recorded. Aborehole investigation was conducted before theearthquake, which is shown in Figure 19. Here, PSlogging was made by downhole method.
Gravel
SurfacesoilFill
Finesand
Finesand
Finesand
Finesand
Finesand
Gravel
Gravel
Gravel
Gravel
Clay
Clay
Clay
Silt
Silt
Silt
5
10
15
20
25
30
0 10 20 30 40 50 60Soil type SPT-N valueDepth
(m)Vs
(km/s)0.0980.098
0.098
0.117
0.1170.117
0.117
0.149
0.149
0.342
0.342
0.154
0.222
0.400
0.400
γ't(tf/m3)
1.41.4
1.4
1.7
1.71.6
1.7
1.7
1.6
2.0
2.0
2.0
2.0
2.0
2.0
Accelerometer (GL, GL-24.7m)
10 20 30 40 50
Vs(km/s)
0.110
0.130
0.140
0.130
0.180
0.140
0.270
0.180
0.480
0.270
0.220
0.400
γ't(tf/m3)
2.00
2.00
1.95
2.00
2.05
1.80
2.10
1.65
2.00
2.00
1.75
2.20
5
10
15
20
25
30
Before Eq. (Downhole method) After Eq. (suspension method)
Surfacesoil
Finesand
Gravel
Clay
Finesand
Clay
Gravel
Clay
Clay
Gravel
Clay
Finesand
SPT-N valueSoil typeDepth(m)
Figure 19. Soil profiles based on borehole investigations before and after the earthquake (data below GL-30mis not shown here)
200 400 1 2
NS(1D)NS(2D)EW(1D)EW(2D)
Peak Acceleration(m/sec2)
Max. Strain(%)
25
20
15
10
5
0 200 400 1 2
Peak Acceleration(m/sec2)
Max. Strain(%)
NewOld
Dep
th (m
)
EW component1-D analysis
Observed
(a) 1D vs. 2D (b) Borehole new vs. oldFigure 20. Peak response
-500
0
500
Acce
lera
tion
(cm
/s2 )
20151050Time (sec.)
Observed Computed
(a) borehole data before the earthquake
-500
0
500
Acce
lera
tion
(cm
/s2 )
20151050Time (sec.)
Observed Computed
(b) borehole data after the earthquake
-200
0
200
Acce
lera
tion
(cm
/s2 )
20151050Time (sec.)
(c) Observed record at GL-24.9m depthFigure 21. Comparison of time histories at theground surface (EW component)
In analyze this site, Yoshida et al. (1995c)pointed out 2 questions on this data. The first one isthat water table is too deep compared with the watertable nearby. The second one is on the S-wavevelocities between GL-3.6 and 7m; fine sand, gravel,and silt layers have the same S-wave velocity of 117m/s. Their point is that S-wave velocity in gravellayer should be larger and that in silt layer should besmaller than described based on the commonknowledge there. They corrected the former, butcould not correct the latter. Both 1-directional and 2-directional analysis were conducted by theequivalent linear analysis code DYNEQ (Yoshida &Suetomi 1996b). They pointed out, as shown inFigure 20(a) that two directional effect is small inthe predominant direction of shaking, but may besignificant in the minor direction. Computed surfaceacceleration is much smaller than observed as seenin Figure 21(a) because of the nonlinear behavior inthe gravel layer. As pointed above, S-wave velocityin gravel layer is too small, resulting in earlynonlinear occurrence. After the earthquake, Soeda et al. (1996)
conducted borehole investigation again, which isalso shown in Figure 19. Here, PS logging wasconducted by the suspension method. This seems togive a more reasonable S-wave velocities. Theymade earthquake response analysis by SHAKE andconcluded that the agreement between computed andobserved is well. Since only comparison withacceleration time histories are shown in their paper,the author calculate the same problem by usingrelevant dynamic deformation characteristics (DDCtest were conducted (Soeda et al. 1996), but not openat present). The result is shown in Figure 20 andFigure 21, too. The acceleration time history at theground surface is nearly the same with Soeda et al.(1996). The agreement improved very muchcompared with the result of the analysis based on theborehole data conduced before the earthquake, i.e.,S-wave velocity by downhole method. This exampleshows the importance to use accurate in situ elasticmodulus. In treating this data, it is noted that the sign ofthe NS component at the ground surface is opposite,and the accelerometer for NS component at GL-97m record was directed N46E.
4.4 Lotung Experiment siteEPRI and TRA installed surface and vertical arraysat Lotung, Taiwan. Instrumentation is shown inFigure 22, and site conditions are shown inFigure 23. Chang et al. (1991) back computed
1/4-scale model
3.2m 45.7m
4.57m10.52m
6m11m17m
ElevationView
DHB6DHB11DHB17
DHB47
6m
30m
6m5m
47m
N
N30.48m
6.10m6.10m3.05m1.50m
Arm 3
Arm1
Arm 2FA3-5 FA3-4
FA1-4
Plan View FA1-5
DHB
DHB
: Triaxial accelerometers
DHA DHB
(a) Downhole array (b) Surface arrayFigure 22. Instrumentation of Lotung experimentsite
3002001000
Vs
10
Shear wave velocity (m/sec)
0
20
30
40
50
Dep
th (m
)
SPT-N value
Sandy-Siltand
Clayey-Silt
3020100
SPT-N value
-60 m
~400 m
Backfill
Silty-Sand and
Sandy-Siltwith gravel
Bedrock
Figure 23. Site conditions at Lotung site
1.0
0
11-17 m Depth
0.0001 0.001 0.01 0.1 1Effective Shear Strain (%)
Shea
r mod
ulus
ratio
, G/G
o 0.5
1.0
0
0.5
1.0
0
0.5
6-11 m Depth
0-6 m Depth
E-WN-SE-WN-S
} LSST06
} LSST07
RadialTransvRadialTransv
} LSST09
} LSST10
E-WN-SRadialTransvE-WN-S
} LSST11
} LSST12
} LSST16
Figure 24. Variation of shear modulus ratio witheffective shear strain back-calculated fromdownhole ground motions
downhole records with a peak ground motionranging from 30 to 210 cm/s2 for seismic eventshaving Magnitudes 4.5 - 7.0 rage using Fourierspectral ratio technique. Major results are shown inFigure 24. Comparison of these results with thelaboratory test results, shown in Figure 25, suggeststhe following.- The back-computed shear moduli for low levels of
shaking (i.e. peak ground surface accelerations lessthan 30 cm/s2) were only slightly smaller than S-wave velocities determined by laboratory tests,confirming the adequacy of the laboratory tests forsmall strain levels.
- The back-computed shear moduli for moderatelevels of shaking (i.e. peak ground accelerationsranging from 160 to 210cm/s2) were substantiallysmaller than those obtained by laboratory tests,indicating considerable shear modulus reduction atthe Lotung site even during moderate earthquakeshaking.
Ueshima & Nakazono (1996) made equivalentlinear analyses by SHAKE and FDEL to computethe downhole responses by specifying the surface
record. The result is shown in Figure 26. Theypointed out that, as shown in the figure, FDELimproves the result very much when maximumstrain is large, but two analyses gives almost thesame results when maximum strain is not so large.The maximum strain in these analyses was about0.06%.
4.5 Wildlife siteThe acceleration and pore water pressure record wasobtained at the Wildlife site, California, USA in theSuperstition Hills earthquake of November 24, 1987,with magnitude of 6.8 (Holzer et al. 1989). Siteconditions are shown in Figure 27. The accelerationand excess porewater pressure time histories areshown in Figure 28 (Brady et al. 1989). Since the
1.0
0.5
00.0001 0.001 0.01 0.1 1
Shea
r mod
ulus
ratio
, G/G
max
Effectiv Shear Strain (%)
0-6m Depth6-17m Depth
Average computed curve
Resonant colurnn testsCyclic shear tests
Figure 25. Comparison of back calculated shearmodulus with laboratory test data
No. 16 (EW)
No. 11 (NS)
SHAKEFDEL
0 100 200 300 400Peak acceleration (cm/s2)
60
50
40
30
20
10
0
Dep
th (m
)
10-6 10-5 10-4 10-3 10-2
γ
G/G
o
0.3
0.2
0.1
h
1.0
0.5
0 0
No. 11 (NS)
No. 16 (EW)
Range of strain
Figure 26. Comparison between two equivalentlinear analyses and strain range
Silt
Siltysand
Siltyclay
Silt
P3SM2
SM1
P1P4P2P5
1.601.94
1.97
2.00
0.67990.7955
0.4253
0.4075
21.320.0
22.0
35.0
0
5
10
Dep
th (m
)
50 100 150Vs (m/s) γ't
tf/m3e φ
deg.Soiltype
CrossholeSASW
AccelerometerPiezometer
γ't: total densitye: Void ratioφ: Friction angle
Figure 27 Soil profile (Modified from Stokoe &Mazarian 1985 and Keane & Prevost 1989)
-200-100
0100200
EW
GL
-200-100
0100200
4035302520151050Time (sec.)
GL-7.5m
EW
-200-100
0100200 GL-7.5m
NS
-200-100
0100200 GL
NS
60
40
20
0P1P2
P3
P4Ex
cess
PW
P
(kP
a)Ac
cele
ratio
n (c
m/s
2 )
Figure 28. Acceleration and PWP time history
excess porewater pressure began to increase after themain portion, delay of PWP measurement wassuspected. Hushmand et al. (1992) conducted lowvelocity calibration test and reported that only P5worked normally and there may be delay of responsebecause of air bubble. On the other hand, Youd &Holzer (1994) discussed and concluded that theyworked. Brady et al (1989) reported that long periodcomponents up to 4 seconds are reliable. Zeghal & Elgamal (1994) computes averageshear stress and strain in the liquefiable layer asγ τ ρ α= − =( ) / , /d d z z1 2 1 2 (6)where d1 and d2 are displacement at GL±0 and -7.5mobtained by integrating acceleration records at SM1and SM2, z=7.5m, ρ is mass density (=2.1t/m3), andα1 is acceleration at SM1. Stress-strain curve shownin Figure 29 is the inverse-S shape that is acharacteristic shape during cyclic mobility. Many effective stress dynamic response analyseshave been conducted on this record. Analysis byKeane & Prevost (1989) is introduced here as anexample. They conducted 1-D analysis with 3directions of freedom. Figure 30 shows comparisonwith observed record. The analysis grasp the generaltendency of the record well. Other analyses alsoshowed similar results. The analysis based on theequivalent linear analysis was also conducted, butthe agreement was not so good as effective stress
analysis.
4.6 Kushiro PortIn the 1993 Kushiro-oki earthquake of magnitude7.8, earthquake motions were recorded at the groundsurface and at a depth of 77 meters in a densesaturated sand deposit at Kushiro, Japan. The sitecondition is shown in Figure 31. As shown inFigure 32 the peak horizontal acceleration was 470cm/s2 on the ground surface and 210 cm/s2 at a depthof 77 meters. The acceleration record at the groundsurface showed a distinctive ground response, whichconsisted of a cyclic motion having a period of about1.5 seconds overlain by a spike at each peak of themotion. In order to study the mechanism of this peculiarground response, Iai et al. (1995) conductedeffective stress analysis on the dense saturated sanddeposit. The model used for this study was a strainspace multiple mechanism model, which takes intoaccount the effect of dilatancy of soil. The recordedearthquake motion at a depth of 77 meters was usedas the input earthquake motion for the analysis.Sampling after in-situ freezing was done in order toevaluate the properties of the sand deposit. Theresults of the analysis were consistent with thoseobserved as shown in Figure 33. This study
Shea
r stre
ss,
(kPa
)τ
10
5
0
-5
-10-1.0 0 1.0 0 10 20 30 40
Shear strain, (%)γ Effective overburden stress' (kPa)σ m
NS component
Figure 29. Stress-strain relationships and stress pathcomputed from records
0
50
0
50
-0.50-0.25
00.250.50
0
50
RecordedComputed
Acce
lera
tion
(g)
NS component
Exce
ss P
WP
(kPa
)
P2
P4
P3
5 10 15 20 25 30 35 400Time (sec.)
Figure 30. Comparison between analysis and record
CoarseSand
FineSand
GravellySand Silt
Eleva-tion(m)
SoilType
SPTN-valus
Density (tf/m3)
0 4020 1.5 2.0+5+3.6
+1.60
-5
-10
-15
-20
-25
-30
-35
-40
Ground SurfaceSeismograph
Eleva-tion(m)
SoilType
SPTN-valus
Density (tf/m3)
0 4020 1.5 2.0-40
-45
-50
-55
-60
-65
-70
-73.4
DownholeSeismograph
Figure 31. Boring log at the recording station
concluded that the observed ground response wasdue to the effect of dilatancy of sand, which plays asignificant role in the response of the dense saturatedsand deposits during strong earthquake motions. One of the authors also conducted SHAKE, butcomputed surface acceleration was much smallerthan observed.
4.7 Port IslandDuring the 1995 Hyogoken-nambu earthquake,accelerations were recorded at the Port Island, a man
made island located in Hyogo Prefecture, Japan.Figure 34 shows soil profiles and Figure 35 showsobserved accelerations. This record has acharacteristics that horizontal accelerationdeamplified probably because of the nonlinear andliquefaction effect, but vertical accelerationamplifies. Yoshida (1995a) conducted equivalent linearanalysis, total stress nonlinear analysis, and effectivestress analysis. Comparisons between observedrecord and analysis are shown in Figure 36. Hepointed out the followings- Significant nonlinear behavior occurs in Holoceneclay layer; shear strain reaches 3 to 5%, whichmakes incident wave in the fill smooth.- Equivalent linear analysis seems to simulate thebehavior well at the ground surface, but looking atthe companion at GL-16.4m, shear modulus in claylayer is underestimated and that in fill isoverestimated.- Agreement is much better by the effective stressanalysis than the equivalent linear analysis- Occurrence of the cyclic mobility made waveformcomplicated. This record has been also analyzed by manyresearchers. Kazama et al. (1996) computed stress-straincurves from the acceleration records as shown inFigure 37, and pointed out that stiffness computed
Acce
lera
tion
(cm
/s2 )
-400-200
0200400 Base (-77m) NS
-400-200
0200400 Base (-77m) EW
-400-200
0200400 Ground surface NS
-400-200
0200400
605040302010Time (sec.)
Base (-77m) UD
-400-200
0200400 Ground surface EW
-400-200
0200400 Ground surface UD
Figure 32. Recorded acceleration time history
4000
-400
4000
-400
20
0
20
0
-20
Acce
lera
tion
(cm
/s)2
Dis
plac
emen
t (cm
)
Computed
Max. 357Recorded
Max. -468Computed
Max. -14Recorded
Max. -1310 20 30 5040 60
Time (sec.)
Figure 33. Comparison of acceleration anddisplacement between record and analysis at groundsurface.
0 10 20 3040 50SPT-N valueDepth
(m)
Fill(Masado)
Pleistoceneclay
(Ma12)
Holocenegravel
Pleistocenegravel
Pleistocenegravel
Holoceneclay
(Ma13)
Soil Type
GL-16.4
GL-32.4
GL-83.4
Accelerometer
Vs(km/s)
Vp(km/s)
0.17 0.26
0.21
0.33
0.78
1.48
0.18 1.18
0.245 1.33
0.305 1.53
0.303
0.350 1.61
1.61
0.32 2.0
0
-5
-10
-15
-20
-25
-30
-35
-45
-50
-55
-60
-65
-70
-75
-80
-40
GL
Figure 34. Soil profile at Post Island
from the stress-strain curve is in consistent with thestiffness obtained by the back analysis of the site(Kokusho et al. 1995). Liquefaction occurred atabout 5 to 7 seconds from the beginning of theearthquake. Significant decrease of shear modulus isobserved in the liquefied layer. Investigation of theaftershocks indicated that smaller shear moduluswas also observed several minutes after themainshock, which was caused because excessporewater pressure still did not dissipate. Thestiffness seemed to recover in the aftershock onemonth later, but they did not identified the time asthey used aftershock records just after theearthquake and that one month later.
4.8 Treasure IslandIn the 1989 Loma Prieta, USA, earthquake, groundmotions recorded on Treasure Island, a man-madefill in San Francisco Bay, were considerably greaterthan the motion on the adjacent Yerba Buena rockoutcrop as shown in Figure 38. Plan of the strongmotion recording sites is shown in Figure 39 withsite conditions shown in Figure 40. In order to explain the large site amplification,one-dimensional equivalent linear analysis wasperformed by Hryciw et al. (1991) using therecorded motion at the rock outcrop as the inputmotion for the analysis. As shown in Figure 41, theequivalent linear analysis was successful inreproducing the site response for E-W component.For N-S component, however, the equivalent linearanalysis failed to reproduce the large amplificationin the period rage from one to four seconds. Seed et al. (1992) compared SHAKE and
-500
0
500Ac
cele
ratio
n (c
m/s
2 )GLN-S GLE-W GLU-D
-500
0
500 GL-16.4mN-S GL-16.4mE-W GL-16.4mU-D
-500
0
500 GL-32.4mN-S GL-32.4mE-W GL-32.4mU-D
0 5 10 15 20-500
0
500
time (sec)
GL-83.4mN-S
5 10 15 20time (sec.)
GL-83.4mE-W
5 10 15 20time (sec.)
GL-83.4mU-D
Figure 35. Observed acceleration records
-400
0
400
20151050Time (sec.)
Observed Computed
GL-16.4m-400
0
400 Observed Computed
GL
Acce
lera
tion
(cm
/s2 )
(a) Equivalent linear analysis
-400
0
400
20151050Time (sec.)
Observed Computed
GL-16m-400
0
400 Observed Computed
GL
Acce
lera
tion
(cm
/s2 )
(b) Effective stress analysis (YUSAYUSA)Figure 36. Comparison between analysis and record
Figure 37. Computed stress-strain curve fromearthquake record
nonlinear analysis and showed that nonlinearanalysis can explain better than SHAKE. Finn et al.(1993) conducted effective stress analysis, resultedin a much better simulation than total stress analysis.As shown in Figure 41, there is significantimprovement in NS component by the effectivestress analysis, but large difference still exists atsome frequency range. They conducted coherenceanalysis and concluded that there is low coherencebetween the motions at Yerba Buena and TreasureIsland in several frequency range.
5 EFFECT OF NONLINEA R BEHAVIOR ONAMPLIFICATION CHARACTERISTICS OFSURFACE GROUND
The amplification of the surface ground has twocharacteristics that work in opposite way. The firstone is amplification. Since S-wave velocity becomessmaller to the ground surface, energy accumulatesresulting in amplification. Therefore as the groundbecomes softer, amplification of the wave becomeslarger. The other is deamplification. Shear strengthdecreases as the ground becomes softer, which
indicates peak acceleration becomes smaller at softerground. These two characteristics indicate that,amplification occurs under the small ground shaking,but amplification becomes small as the groundshaking becomes large. This can be seen typically inFigure 42 (Idriss 1990). This is also seen in thevertical array records shown in the previous chapter. It is best to use vertical array records indiscussing the amplification, but available data arelimited. As the second choice, it may be possible tocompare surface response of the surface ground withthe record at the bedrock nearby. Here, it is notedthat outcrop wave at the bedrock is not the samewith the incident wave at the bottom boundary of thesurface ground. For example, Kaneko (1993)pointed out that the scattering of the predicted resultin Ashigara Valley blind prediction (ESG
200
200
100
100
0
0
-100
-100
-200
-2000 5 10 15 20
Time (s)
Acc
eler
atio
n (c
m/s
)2
Yerba Buena Island
Treasure Island
Figure 38. Recorded accelerations at Treasure Islandand Yerba Buena Island (EW component)
UM5
UM10
UM12
UM1
UM3
UM6
UM11
UM9
Bedrock at85.3m depth
*
Treasire Island
N
San Fransisco-Oakland Bay Bridge
Yerba BuenaIslandStrong motion recording staion
SCPT test locationGround response based on estimated VsConfirmed bedrock
*
500 1000m0Figure 39. Treasure Island and Yerba Buena Island
UM03UM05UM06UM09UM13UM11
ANASUM03UM10
Vs = 35z0.55
0
5
10
15
20
Dep
th, z
(m)
Fill and Sand Shoal
Vs = 150+4z
Shear Wave VelocityVs (m/sec)
0 100 200 300 400 500 0
5
10
15
25
20
30Bay Mud
Shear Wave VelocityVs (m/sec)
0 100 200 300 400 500
Dep
th, z
(m)
Figure 40. Shear wave velocities
0.8
0.6
0.4
0.2
0
EW
400
0.3
0.2
0.1
1 2 3
Spec
tral A
ccel
erat
ion
(g)
Period (sec)
NS
Range of ComputedSpectra by SHAKEDESRA2
RecordRock MotionGround Motion
Figure 41. Range of computed spectral accelerationat Treasure Island
Committee 1992) by using SHAKE comes from thedifference of the assumption of the seismic baselayer, which indicates that outcrop motion on therock is not the incident wave to the surface ground.Regardless to these limitations, however, comparing
the responses at the ground surface to the rock sitenearby will be an efficient tool. Sugito et al. (1991) computed amplification ratioby comparing the ground motion on the groundsurface with the rock surface ground motion duringthe 1989 Loma Prieta earthquake. Figure 43 isdeveloped based on their data. The amplificationratio becomes unity when acceleration reaches about300 cm/s2, and velocity reaches about 30cm/s,respectively. This data is also shown in Figure 42 bydotted frame. This area is wider than that by Idriss(1990), probably because they used near fault data aswell as data in San Francisco Bay area. Suetomi & Yoshida (1998) conducted similarcomparison based on the data in the 1995Hyogoken-nambu earthquake, which is shown inFigure 44. Looking at the acceleration, the tendencythat amplification ratio decreases as acceleration atthe base increases is also seen. Deamplificationoccurs more quickly in soft soil. When looking atthe velocity, however, deamplification is not
Acceleration on rock sites (cm/s2)
Acce
lera
tion
on s
oft s
oil S
ites
(cm
/s2 )
Based on calculations
Median relationshiprecommended for usein empirical correlations
1989 Loma Prieta
1985 Mexico City
0 100 200 300 400 500 6000
100
200
300
400
500
600
700
Hyogoken-nambu/E+F /2E1989 Loma Prieta
Figure 42. Amplification in soft ground (Modifiedfrom Idriss (1990) by adding case study in LomaPrieta and Hyogoken-nambu earthquakes)
400
300
200
100
0
Peak
acc
eler
atio
n on
gro
und
surfa
ce (c
m/s
2 )
5004003002001000
Peak acceleration on rock surface (cm/s 2)
1:11:2
1:3
NS EW
60
50
40
30
20
10
0
Peak
vel
ocity
on
grou
nd s
urfa
ce (c
m/s
)
706050403020100Peak velocity on rock surface (cm/s)
1:11:2
1:3
NS EW
(a) Acceleration (b) VelocityFigure 43. Relationships between peak responses at the surface and the base during 1989 Loma Prietaearthquake
Peak acceleration at base (cm/s2)
0 500 1000
Peak
acc
eler
atio
n at
sur
face
(cm
/s2 )
0
500
1000
1:1
1:21:3
Peak velocity at base (cm/s)0 100 200
Peak
vel
ocity
at s
urfa
ce (c
m/s
)
0
100
1:1
1:21:3
200
StiffMediumSoft
StiffMediumSoft
(a) Acceleration (b) VelocityFigure 44. Relationships between peak responses at the surface and at the base during the 1995 Hyogoken-nambu earthquake
observed; amplification ratio is nearly constant to be2, which is a big difference between the result bySugito et al. (1994). They showed not only Figure 44but also several other proofs that deamplification ofvelocity do not occur. They also described thatliquefaction occurred at all the soft grounds inFigure 44. This data is overwritten in Figure 42 aswell by solid and hollow triangle indicating thatborehole data and neighboring rock data are used inthe abscissa, respectively. This data also agrees withthe region that Idriss (1990) showed. They pointedout that amplification in the liquefied site is notcurious because, as acceleration is small at the sitefar from the fault, several cycles of loading is at leastnecessary to cause liquefaction, but peakacceleration can occur during these cycles. The difference of the amplification depending onsoil type has been investigated by many researchers.Through these investigations, we can recognize thatnonlinear behavior of soil has an important role todetermine the ground motion at the surface,especially in soft ground. At the same time, we cannotice that amplification ratios scatter very much.This indicates that, data such as Figure 42 cannot beused for engineers to evaluate the site amplificationat the particular site where they are going to makestructures, although it may be convenient to graspthe general tendency of the amplification. It is alsonoted that site classification depending on soil typeused in these studies may not be identical amongresearchers even if the same terminology is used.One of the authors made an questionnaire betweenthe S-wave velocity and soil type at the time inNorth America-Japan Workshop on theGeotechnical Aspects of the Kobe, Loma Prieta andNorthridge Earthquakes, Osaka, Japan, 1966, forexample. The result is shown in Figure 45. One cansee large scattering of S-wave velocity in the sameclassification.
6 CONCLUDING REMAR KS
In this state of art paper, we reviewed dynamicdeformation characteristics of soil, and evaluationand prediction of the nonlinear behavior of thesurface ground through the vertical array earthquakeobservations and researches using them. Thenonlinear behaviors were confirmed to occur duringthe earthquake, and dynamic deformationcharacteristics of soil is shown to play an importantrole in determining the ground shaking at the surface.Other discussions are as follows:
1. Back calculated nonlinear characteristics of soilare in consistent with the nonlinear characteristicsobtained in the laboratory.
2. Ground shaking can be evaluated in reasonabledegree of accuracy when relevant earthquakeresponse analysis method is employed andmaterial property is well modeled.
3. Effective stress analysis is more accurate thantotal stress nonlinear analysis, and nonlinearanalysis is more accurate than equivalent linearanalysis. Equivalent linear analysis may beapplicable at strains less than about 0.5%, and itis not applicable at the liquefied site.Applicability of the equivalent linear method atlarge strains without liquefaction was notconfirmed because of the lack of the earthquakeobservation data.
4. Amplification of the acceleration occurs wheninput motion is small. Deamplification begins tooccur as input motion increases. On the otherhand, amplification of velocity by nonlinearbehavior of soil is not confirmed; there were twodata indicating opposite tendency.
Through the review, at the same time, followingresearch is found to be required for accurateprediction of the ground motion in practical use.
1. The index or standard test method to grasp thebehavior of soil at strains larger than about 1%, inwhich soil shows degradation behavior, isrequired. There is nearly no test data in this strainrange except dynamic strength test result at whichstress-strain relationships are less interested.
2. Earthquake observation data is still not sufficient.Especially, data with both acceleration andporewater pressure is very short. Dense verticalarray data, which is necessary to recognize whathappens in the ground in detail, is also short.Coetaneous efforts on making observation sitesare encouraged.
3. Relevant index of ground motion is necessary toevaluate the relationships between ground motionand structural damage due to earthquake. Peak
Hard Rock Soft Rock Stiff soil Soft Soil
US
Japa
n2000 1500 700 500 300 200 150
Vs (m/s)
Figure 45. Variation of S-wave velocity in each soilclassification by researchers.
acceleration has been used widely as the index. Itis, however, obvious that peak acceleration is notperfect. Iwata et al., for example, reported that,among the peak acceleration, peak velocity,maximum displacement, and Spectral Intensity,correlation between earthquake damage and peakvelocity and SI is higher than others through theinvestigations of the past earthquake damage. Itmay depend on structural type.
4. Research is not sufficient for surface wave andvertical wave.
5 Both incident wave and amplification in thesurface layer is important to predict accuratesurface response. The effort on predicting theaccurate incident wave to the surface ground isencouraged, because it seems less accurate thanthe evaluation of amplification in surface ground.
REFERENCES
Aki, K. 1993. Local site effects on weak and strongground motion, Tectonophysics, 218: 93-111
Arulanandan, K. & Scott, R. F. ed. 1993. Proc., Int.Conf. on the Verification of NumericalProcedures for the Analysis of Soil LiquefactionProblems, Davis, California
Biot, M. A. 1941． General Theory of Three-dimensional Consolidation, Jour. Applied Physics,12: 155-164
Brady, A. G., Mork, P. N., Seekens, L. C., &Switzer, J. C. 1989. Processed Strong-motionRecords from the Imperial Wildlife LiquefactionArray, Imperial County, California, Recordedduring the Superstition Hills Earthquakes,November 24, 1987, Open File Report 89-87, USGeology Survey
Chang, C.-Y., C. M. Mok, M. S. Power, Y. K. Tang,H. T. Tang & J. C. Stepp 1991. Development ofshear modulus reduction curves based on Lotungdownhole ground motion data, Proc. 2nd Int.Conf. on Recent Advances in GeotechnicalEarthquake Engineering and Soil Dynamics: 111-118
ESG committee 1992. Proc. Int. Symp. on the effectsof surface geology on seismic motion, Odawara,Japan.
Finn, W. D. L., Lee, K. W., & Martin, G. R. 1977.An effective stress model for liquefaction, GED,ASCE, 103 (GT6): 517-533
Finn, W. D. L. et al. 1978. Comparison of dynamicanalysis of saturated sand, Proc. ASCE, GTSpecial Conference: 472-491
Finn, W. D. L., Carlos, E. V. & Guoxi, W. 1993.Analysis of ground motions at Treasure Islandsite during the 1989 Loma Prieta earthquake, SoilDynamics and earthquake Engineering, 12: 383-390
Goto, S., Tatsuoka, F., Shibuya, S., Kim, Y. S. &Sato, T. 1991. A simple gauge for local smallstrain measurements in the laboratory, Soils andFoundations, 31 (1): 169-180.
Hardin, B. O. & Drnevich, V. P. 1972. Shearmodulus and damping in soils: design equationsand curves, J. SMFD, Proc., ASCE, 98 (SM7):667-692
Holder, T. L., Youd T. L. & Hanks, T. C. 1989.Dynamics of liquefaction during the 1987Superstition Hills, California, Earthquake,Science, 244: 56-59
Hryciw, R. D., K. M. Rollins, M. Homolka, S. E.Shewbridge, & M. McHood 1991. SoilAmplification at Treasure Island during the LomaPrieta earthquake, Proc. 2nd Int. Conf. on RecentAdvances in Geotechnical EarthquakeEngineering and Soil Dynamics: 1679-1685
Hushmand, B., Scott, F. & Crones, C. B. 1992. In-place calibration of USGS pore pressuretransducers at Wildlife Liquefaction Site,California, USA, Proc., 10WCEE: 1263-1268
Hyodo, M., Yasuhara, K., Murata, H. & Hirao, K.1988. Prediction of pore pressure anddeformation in soft clay, Jour. of GeotechnicalEngineering, Proc. of JSCE, No. 400/III-10, pp.151-159 (in Japanese)
Iai, S et al. 1993. Simultaneous analyses onliquefaction, Proc, Symposium on remedialmeasures against liquefaction, JSSMFE: 770-190(in Japanese)
Iai, S., T. Morita, T. Kameoka, Y. Matsunaga, &K. Abiko 1995. Response of a dense sand depositduring 1993 Kushiro-oki earthquake, Soils andFoundations, 35 (1): 115-131
Idriss, I. M. 1990. Response of Soft Soil Sites duringEarthquakes, Proc., H. Bolton Seed MemorialSymp., Berkeley, California
Ishihara, K. & Towhata, I. 1980. One-dimensionalsoil response analysis during earthquake based oneffective stress method, Jour. of the Faculty ofEngineering, XXXV(4), The University ofTokyo: 656-700
Ishihara, K. 1982. Evaluation of soil properties foruse in earthquake response analysis, Proc., Int.Symp. on Numerical Models in Geomechanics,Zurich: 237-259
Ishihara, K. et al. 1989. Effective stress analyses ofground and soil structures, Proc., Symposium onBehavior of Ground and Soil Structures duringEarthquake, JSSMFE: 50-136 (in Japanese)
Iwata, T. et al. 1991. Practical evaluation of seismicintensity for earthquake control sensor, Proc. 21stJSCE Earthquake Engineering Symposium: 613-616 (in Japanese)
Iwasaki, T., Kawashima, K. & Tatsuoka, F. 1980.Effect of soil nonlinearity on earthquake responseof ground, Civil Engineering Journal, PWRI, 22
(12): 27-32 (in Japanese)JGS Committee 1988. A questionnaire of
simultaneous undrained triaxial test of saturatedToyoura sand, Proc. Symp. on Undrained CyclicTest of Soil, JSSMFE: 1-35 (in Japanese)
Japanese Geotechnical Society 1996. Method forcyclic triaxial test to determine deformationproperties of geomaterials, and Method for cyclictorsional shear test to determine deformationcharacteristics of soil, New standard in JGS,pp.69-146 (in Japanese with English summary).
Kaneko, F. 1993. Sensitivity analysis of one-dimensional analysis, Research of the effect ofsurface geology on seismic motion, Report to theMinistry of Education, Takeuchi, Y. ed.: 78-90(in Japanese)
Katayama, T., Yamazaki, F., Nagata, S. Lu, L. &Turker, T. 1990. A strong motion database for theChiba Seismometer Array and its engineeringanalysis, Earthquake Engineering and StructuralDynamics, 19: 1089-1106
Kazama, M., Yanagisawa, E., Inatomi, T., Sugano, T.& Inagaki 1996. Stress-strain relationship in theground at Kobe Port Island during 1995 Hyogo-ken nanbu earthquake inferred from strongmotion array records, Jour. of GeotechnicalEngineering, Proc., JSCE, 547 (III-36): 171-182(in Japanese)
Keane, C. M. & Prevost, J. 1989. An Analysis ofEarthquake Data Observed in the WildlifeLiquefaction Array Site, Imperial County,California, Proc., 2nd U.S.-Japan Workshop onLiquefaction, Large Ground Deformation andTheir Effects on Lifelines, New York, TechnicalReport NCEER-89-0032, NCEER: 176-192
Kiku, H. & Yoshida, N. 1998. Dynamic deformationproperty tests of sand at large strains, Proc., The33rd Japan National Conf. on GeotechnicalEngineering: 869-870 (in Japanese)
Kokusho, T. 1980. Cyclic triaxial test of dynamicsoil properties for wide strain range, Soils andFoundations, 20 (2): 45-60
Kokusho, T. 1982. Dynamic deformationcharacteristics of soil and nonlinear response ofground, Report No. 301, Central ElectricResearch Institute: 207-240 (in Japanese)
Kokusho, T 1987. In-situ dynamic soil propertiesand their evaluation, Proc. 8th Asian RegionalConf. of SMFE, Kyoto, II: 215-240
Kokusho, T. 1992. Dynamic characteristics ofground, Lecture: Analytical method of theinteraction between ground and structure, Tsuchi-to-Kiso, 40 (4): 76-84 (in Japanese)
Kokusho, T., Sato, K. & Matsumoto, M. 1995.Nonlinear dynamic response of soil groundduring 1995 Hyogo-ken nanbu earthquake,Tsuchi-to-Kiso, 43 (9): 39-43 (in Japanese)
Midorikawa, S. 1992. A statistical analysis of
submitted predictions for the Ashigara Valleyblind prediction test, Proc., Int. Symp. On theEffect for the Surface Geology on Seismic Motion,Odawara, Japan, 2: 65-77
Richart, Jr., F. E. 1977. Dynamic stress-strainrelationships for soils, S-O-A Paper, Proc., 9thICSMFE, Tokyo, 3: 605-612.
Saada, A. & Bianchini, G. S. ed. 1987. Proc. Int.Workshop on Constitutive Equation for GranularNon-cohesive Soils, Case Western ReserveUniversity, Cleveland
Sakai, H., Sawada, S. & Toki, K. 1997. A basicstudy to identify the incident seismic wave on thebase layer in time domain, Jour. of StructuralMechanics and Earthquake Engineering, Proc.JSCE, 557/I-41: 53-64 (in Japanese)
Sato, T., Kawase, H. & Sato T. 1995. Evaluation oflocal site effects and their removal from boreholerecords observed in the Sendai region, Japan, Bull.Seismological Society of America, 85: 170-1789
Sato, T., Horike, M., Takeuchi, Y., Retake, T. &Suzuki, H. 1997. Nonlinear behavior of scoriasoil sediments evaluated from borehole records ineastern Shizuoka Prefecture, Japan, EarthquakeEngineering and Structural Dynamics, 26: 781-795
Schnabel, P. B., Lysmer, J. & Seed, H. B. 1972.SHAKE A Computer program for earthquakeresponse analysis of horizontally layered sites,Report No. EERC72-12, University of California,Berkeley
Seed, H. B. & Idriss, I. M. 1970. Soil moduli anddamping factors for dynamic response analyses,Report No. EERC70-10, EERC, Univ. ofCalifornia, Berkeley
Seed, R. B., Dickinson, S. E., & Mok, C. K. 1992.Recent lessons regarding seismic responseanalyses of soft and clay sites. Proc. Seminar onSeismic Design and Retrofit of Bridges,California Dept. of Transportation, Sacramento
Soeda, E., Kato, Y., Matsuda, G., Takezawa, S. &Maekawa, F. 1996. Example of earthquakeresponse analysis of vertical array records, Proc.,51st Annual Conf. of JS CE, I-B: 356-357 (inJapanese)
Stokoe, II, K. H. & Mazarian, S. 1985. Use ofRayleigh waves in liquefaction studies, Proc.Measurement and use of shear wave velocity forevaluating dynamic soil properties, GED, ASCE,Denver
Suetomi, I. & Yoshida, N. 1996. Effect of frequencycharacteristics of earthquake motion to thenonlinear response of ground, Proc., 51st AnnualConf. of JSCE (I-B): 352-353 (in Japanese)
Suetomi, I. & Yoshida, N. 1998. Nonlinear behaviorof surface deposit during the 1995 Hyogoken-nambu earthquake, Special Issue of Soils andFoundations, 2: 11-22
Sugito, M., A. S. Kiremidjian & H.C. Shah 1991.Nonlinear ground motion amplification factorsbased on local soil parameters, Proc. 4th Int. Conf.on Seismic Zonation, Stanford, II: 221-228
Sugito, M., Aida, N. & Masuda, T. 1994. Frequencydependent equi-linearized technique for seismicresponse analysis of multi-layered ground, Jour.of Geotechnical Engineering, Proc. of JSCE, 493:49-58 (in Japanese)
Tatsuoka, F. & Shibuya, S. 1991. Deformationcharacteristics of soils and rocks from field andlaboratory tests，Proc., 9th Asian Reg. Conf. onSMFE, Bangkok
Tokimatsu, K. 1989. Dynamic property of soil fromlaboratory test, in-situ rest and earthquakemeasurement, Proc. 2nd Symp. on DynamicInteraction between Soil and Structure: 11-16 (inJapanese)
Towhata, I. 1989. Models for cyclic loading,Mechanics of granular materials, Report ofISSMFE Technical Committee on Mechanics ofGranular materials, ISSMFE: 80-90
Ueshima, T. & Nakazono, N. 1996. Application offrequency dependent equivalent linear method onLotung site, Proc., 51st Annual Conf. of JSCE.408-409 (in Japanese)
Woods, R. D. 1991. Field and laboratory deter–mination of soil properties at low and high strains,SOA paper, Proc. 2nd Int. Conf. on RecentAdvances in Geotech. Earthquake Engineeringand Soil Dynamics, St. Louis: 1727-1741.
Yamashita, S. & Toki, S. 1994: Effect of initialstress on cyclic deformation characteristics, Proc.Symp. on Dynamic Problem of Soils and SoilStructures, JSSMFE: 163-168 (in Japanese)
Yamazaki, F. 1994. Example of analysis of verticalarray record, Array observation and database,Text, Seiken-seminor: 62-93 (in Japanese)
Yasuda, S. & Yamaguchi, I. 1984. Dynamic shearmoduli in the laboratory and the field, Proc. Symp.on Evaluation of Deformation and StrengthCharacteristics of Sandy Soils and Sand Deposits,JSSMFE, Tokyo: 115-118 (in Japanese)
Yoshida, N. 1994. Applicability of ConventionalComputer Code SHAKE to Nonlinear Problem,Proc. Symposium on Amplification of GroundShaking in Soft Ground, JSSMFE: 14-31 (inJapanese)
Yoshida, N., Tsujino, S. & Ishihara, K. 1990. Stress-strain Model for Nonlinear Analysis ofHorizontally Layered Deposit, Summaries of theTechnical Papers of Annual Meeting of AIJ, B(Structure I): 1639-1640
Yoshida, N. 1995a. Earthquake Response Analysisat Port Island during the 1995 Hyogoken-nanbuEarthquake, Tsuchi-to-Kiso, 43 (10): 49-54 (inJapanese)
Yoshida, N. 1995b. Processing of strain dependent
characteristics of soil for nonlinear analysis,Proc., 1st Int. Conf. on Earthquake GeotechnicalEngineering, Tokyo: 473-478
Yoshida, N., Nakamura, S. & Suetomi, I. 1995c.Nonlinear response of ground and its evaluationduring the 1995 Hyogoken-nanbu earthquake,Proc., The 23rd Symposium of EarthquakeGround Motion, AIJ, Tokyo, 39-52 (in Japanese)
Yoshida, N., Tazoh, T. & Suzuki, H. 1995d.Comparisons of Nonlinear Dynamic ResponseAnalysis Method, Proc., 23rd JSCE EarthquakeEngineering Symposium, JSCE: 49-52 (inJapanese)
Yoshida, N. 1996a. Dynamic property of soil and itsmodeling, An Introduction to Dynamic Soil-Structure Interaction, AIJ: 236-260, 281-288 (inJapanese)
Yoshida, N. & Suetomi, I. 1996b. DYNEQ: acomputer program for dynamic analysis of levelground based on equivalent linear method,Reports of Engineering Research Institute, SatoKogyo Co., Ltd.: 61-70 (in Japanese)
Youd, T. L. & Thomas L. H. 1994. Piezometerperformance at Wildlife liquefaction siteCalifornia, Jour. GT, ASCE, 120 (6): 975-995
Zeghal, M. & Elgamal, A. -W 1994. Analysis of siteliquefaction using earthquake records, Jour. GT,ASCE, 120 (6): 996-1017