seismic behaviour of geotechnical structures

8/12/2019 Seismic Behaviour of Geotechnical Structures

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ANNALS OF GEOPHYSICS, VOL. 45, N. 6, December 2002

799

Seismic behaviour of geotechnicalstructures

Stefania Sica, Filippo Santucci de Magistris and Filippo Vinale

Dipartimento di Ingegneria Geotecnica, Polo delle Scienze e delle Tecnologie,Universit degli Studi di Napoli Federico II, Napoli, Italy

AbstractThis paper deals with some fundamental considerations regarding the behaviour of geotechnical structures underseismic loading. First a complete definition of the earthquake disaster risk is provided, followed by the importanceof performing site-specific hazard analysis. Then some suggestions are provided in regard to adequate assessmentof soil parameters, a crucial point to properly analyze the seismic behaviour of geotechnical structures. The coreof the paper is centered on a critical review of the analysis methods available for studying geotechnical structuresunder seismic loadings. All of the available methods can be classified into three main classes, including thepseudo-static, pseudo-dynamic and dynamic approaches, each of which is reviewed for applicability. A moreadvanced analysis procedure, suitable for a so-called performance-based design approach, is also described inthepaper. Finally, the seismic behaviour of the El Infiernillo Dam was investigated. It was shown that coupledelastoplastic dynamic analyses disclose some of the important features of dam behaviour under seismic loading,confirmed by comparing analytical computation and experimental measurements on the dam body during andafter a past earthquake.

1. Introduction

On December 3rd and 4th 2001, the EarthSciences and Natural Disaster Prevention. AJapan-Italy joint meeting in year 2001 was heldin Kyoto and Kobe.

Session III of the meeting was devoted toCivil Engineering Aspects of Seismic andVolcanic Risk Prevention. This paper sum-marizes the contribution from the Department

Mailing address: Dr. Filippo Santucci de Magistris,Dipartimento di Ingegneria Geotecnica, Polo delle Scienze edelle Tecnologie, Universit degli Studi di Napoli Federico II,Via Claudio 21, 80125 Napoli, Italy; e-mail: [email protected]

Key words case histories dams f.e.m. seismic

design soil dynamicsof Geotechnical Engineering, University ofNaples (Italy), at this session of the confer-ence.

After an introduction to the problem ofseismic risk evaluation, the paper focuses on afew considerations of the geotechnical sitecharacterization, including some notes on soilbehaviour under cyclic loading and measu-rement of soil parameters. Then, some analysismethods that are currently available in literatureto study the seismic performance of earthstructures will be assessed. Finally the dynamicbehaviour of an earth dam will be presentedas a typical, though complex, case history.Since the Seismic Behaviour of GeotechnicalStructures theme is extremely broad, onlysome of the previously mentioned topics willbe extensively treated in the next pages. Moreextensive details can be found in the referencesand in the technical literature for the specifictopics.


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2. Risk analysis

For over forty years, since the devastating1964 Alaska (U.S.) and Niigata (Japan) earth-quakes occurred, considerable progress has beenmade in the field of soil dynamics and geo-technical earthquake engineering. Significantdevelopment has been achieved in forecastingthe strong ground motion after appropriateseismic hazard analysis, in understanding themechanical behaviour of geomaterials, inevaluating the ground response during anearthquake and in modeling structures response

under seismic loading. These studies provide animportant contribution to the general field ofseismic risk analysis.

Seismic risk studies are conventionally basedon the analysis of a single component of risk,often directed at a particular region. More com-plete analyses require the definition of all factorson which an areas earthquake disaster risk de-pends. Furthermore, the risk level in a particularregion should be periodically updated.

In general, disaster could be considered notonly a function of the expected physical impactof future earthquakes, but also of the capacity ofthe affected area to sustain that impact, as wellas the implications on local economic and socialaffairs (Davidson, 1997). As a matter of fact,while people may not be able to stop the oc-currence of earthquakes, they might be able toregulate some of the other contributing factors(e.g., resources available for emergency responseand recovery, vulnerability of the infrastructure),

thereby reducing the frequency and severity ofearthquake-induced damage. It should beconsidered also that worldwide earthquakedisaster risk has grown significantly over the pastdecades due to exploding populations in seismicregions, unimpeded urbanization, and theincreasingly interconnected and internally com-plex urban plan of most existing cities.

Therefore, if in a conventional perspective,any risk, including seismic risk, is a convolutionof exposure, hazard, and vulnerability, a moreextended definition might also include otherfactors such as external context (political and

economic) and emergency response and recoverycapability. Figure 1 summarizes a proposeddefinition of earthquake disaster risk afterDavidson (1997). In this figure, hazard representsthe geological phenomena that act as initiatingevents of an earthquake disaster. Earthquakehazards include not only ground shaking but alsocollateral damage such as liquefaction, land-slides, tsunamis, ground rupture and subsidence.Exposure includes list of everything that issubject to the physical demands imposed by thehazard. Vulnerability describes how easily andhow severely physical infrastructures, popu-lation, economy, and social-political system canbe affected by an earthquake. External contextdescribes how damage to a city affects peopleand activities outside the city. It incorporates thereality that, depending on a citys prominencewith respect to economics, transportation,politics, and culture, damage to certain cities mayhave more far-reaching effects than damage to

Fig. 1. Factors contributing to the definition of earthquake disaster risk (after Davidson, 1997).


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Seismic behaviour of geotechnical structures

others. Emergency response and recoverycapability describe how effectively and ef-ficiently a community can recover from short-and long-term impact through formal, organizedactivities.

While we have little control over seismichazard, full awareness of structural and envi-ronmental seismic vulnerability, will help seismicengineers concentrate their efforts on reducingstructural and environmental weaknesses. Tohelp reach this objective, the seismic behaviourof structures, including geotechnical structures,should be fully understood.

3. The role of geotechnical engineers

From the previous paragraph it clearlyemerges that seismic risk analysis is a typicalmultidisciplinary study. While the obvious roleof a seismic geotechnical engineer is that ofdetecting and examining the performance ofgeotechnical structures under dynamic loading,his cultural responsibility in the evaluation offree-field ground response (*) is essential too.Here, it is worth remembering that groundresponse analyses are used to predict groundsurface motion for the development of designresponse spectra, to evaluate liquefaction hazardsor landslide occurrences and to determine theearthquake-induced forces on civil structures.Thus, an essential responsibility of an earthquakegeotechnical engineer consists of detectingground surface motion that is strongly influencedby the soil strata that might lie above the bedrock.This influence, as well as the general behaviourof earth structures, cannot be fully understoodwithout: 1) proper knowledge of the subsoilstratigraphy; 2) mechanical behaviour of anysubsoil strata and of the materials constitutingthe earth structure, including a proper knowledgeof experimental techniques, and 3) proper use ofnumerical models able to simulate the subsoil

response, the geotechnical structure response, aswell as their interaction.

Points (2) and (3) have some peculiarities thatwill be briefly emphasized in the followingparagraphs. Point (3) will be developed with theaim of detecting the seismic behaviour of geo-technical structures.

4. Soil behaviour under cyclic loading

The effect of earthquake loads on a soilelement can be represented by a complex shear

stress time history (t), acting after a previousloading history. Depending on the level of theconsidered earthquake motion and the dynamicproperties of the soil-structure system, the soilshear strain level induced by the seismic eventcan vary. Consequently, the soil should be char-acterized by models of different complexity.Typi-cal gross distinctions can be made between soilbehaviour at pre-failure and at failure conditions.In the first case, further distinctions are madeamong the so-called small-strain region, themedium strain region and the large strainregion. Distinction can be easily understoodby considering the schematic soil behaviourasreported in fig. 2, which shows typical rela-tionships existing between shear stiffness ordamping ratio and the shear strain level. At smallstrains, soil stiffness and damping ratio attainedtheir maximum and minimum values, respec-tively. Soil response can be adequately repre-sented by a linear model.

At medium strains, soil shows a clear non-linear behaviour but the response under cyclicloading is stable (i.e. no plastic volumetric strainsor pore water pressure is detected). In this strainrange soil behaviour can be represented bylinearly equivalent models.

Finally, at large strains shear-volumetriccoupling is apparent and the effect of the numberof cyclic loadings cannot be neglected. In thiscase, elastoplastic effective stress models couldbe opportunely used to simulate soil behaviour.Several parameters affect both initial shear strainand damping ratio and their strain dependency.Readers can refer to, for instance, DOnofrio andSilvestri (2001) for some information of thistopic.

(*) Detailed explanations on the evaluation of groundmotion during an earthquake can be found in Kramer(1996).


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5. Measurement of soil parameters

In geotechnical engineering design practice,field and laboratory investigation have advan-tages and disadvantages. Therefore, it might beuseful to employ both in situ and laboratorymeasurement procedures to obtain a proper soilcharacterization. As shear modulus G

0and

damping ratioD0at small strain levels might be

affected by sample disturbance, less so in the caseof soil non-linearity, the strain dependence soilstiffness might be evaluated through

(5.1)

and the strain dependency of soil damping by

(5.2)

In the previous equations (G0)

fieldand (D

0)

fieldare

preferably evaluated by measurement of in situ

shear wave velocity; G()/G0

should be deter-mined by laboratory tests, as shouldD_(). Thelatter represents the measured damping ratioscaled to the relevant small strain valueD

0.

As the scope here is not to detail experimentaltechniques and procedures, a list of the mostcommon techniques is reported in table I.

Some other special apparatuses not listed intable I have been developed at some Universitiesand Research Centers (refer to, for instance, http://www.iis.u-tokyo.ac.jp/~hayanodex2.html; http://geotle.t.u-tokyo.ac.jp/; http://www.entpe.fr/Prive/index-recherche.htm). However, suchmachines are still prototypes and not widelyavailable.

In situ soil tests for earthquake geotechnicalengineering are typically geophysical, includingsurface tests such as Spectral Analysis SurfaceWaves (SASW), and borehole tests such as Down-Hole (DH) test and Cross-Hole (CH) test.

Laboratory tests can be categorized as either:1) Static tests, in which stress-strain proper-

ties derive from the direct measure of stress andstrain;or

Fig. 2. Typical variation of the soil response under cyclic loading at increasing strain level in terms of shearmodulus and damping and stress-strain loops.

G GG

G

( ) =( ) ( )

0

0

field

lab

D D D ( ) =( ) + ( )[ ]0 field lab.


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2) Dynamic tests, in which the soil propertiesare derived from a dynamic equilibrium analysisof a soil element.

Static tests usually include Cyclic Triaxialtests (CTX), Cyclic Simple Shear tests (CSS) andCyclic Torsional Shear tests (CTS). ResonantColumn tests (RC) and Bender Element tests(BE) are typically considered dynamic tests.

Choice of experimental technique for soilcharacterization is a matter of compromise be-tween technical and economic factors.

As far as in situtests are concerned, it is wellknown that the CH test is the most reliable, albeitmost expensive, system for evaluating initial soilstiffness. The multi-receiver CH test also allowsfor the measurement of field small strain dampingratioD

0. On the other hand, multistation testing

configuration for analyzing surface waves ap-pears to be a promising, although complex, insitu experimental technique that provides notonly the stiffness profile but also the dampingratio profile (Foti, 1999).

As for laboratory tests, sound laboratorypractice in itself might be able to mitigate theinfluence of sample disturbance. A suitablereconsolidation technique up to the in situstressstate (that includes appropriate anisotropicreconsolidation stress-path and ageing time) canbe, for instance, of some benefit to obtain morerealistic subsequent stress-strain behaviour ofsoils (Vinale et al., 2000). For the resonantcolumn tests, conventional interpretation criteriaare based on the assumption that soil can bemodeled as a linear visco-elastic medium, anidealization typically made in solving someboundary value problems in seismic geotechnicalengineering. It is worth noting that linear visco-elasticity is insufficient for understanding someimportant features regarding time-dependentbehaviour of geomaterials (see Tatsuoka et al.,2000), while new non-linear three-componentrheology models have been proposed (Di Bene-detto et al., 2002; Tatsuoka et al., 2002). In anycase, time-dependency in the stress-strain be-

Table I. In situand laboratory experimental techniques to obtain some relevant properties for analyzing theseismic behaviour of geotechnical structures (after International Navigation Association, 2001). In geotechnicalearthquake engineering CPT and SPT should be properly used only providing empirical correlation with relevantsoil properties.

VS=shear wave velocity;V

R=Rayleigh wave velocity; f

r=resonant frequency;H.p. = half-power method;

R.f. = resonance factor method;N = SPT blow count; qc= CPT tip resistance; =friction angle in effective

stresses; cu= undrained shear strength; C = coarse grained; F =fine grained soils; q/

r= deviator/radial stress

ratio; /v= shear/vertical stress ratio;N

c=number of cycles.

Test class Test type Consolidation Shear strain Frequency Stiffness Damping Strength

stress state [%] f[Hz] C F

SPT NVSG0

Penetration CPT qcVSG0 cu

Field Down-Hole Lithostatic VSG

0

Geophysical Cross-Hole < 103

10-100 VSG0 possible

SASW VRV

SG

0

Triaxial Axisymmetric > 102

0.01-1 q:aG q/

r:N

c

Cyclic Simple shear Axisymmetric > 102

0.01-1 :G WD /WSD /v :Nc

Torsional Axisymmetric 104

-1 0.01-1 :G0,G

Laboratory shear or true triaxial

Resonant Axisymmetric 104

-1 > 10 frG0,G H.p.,R.f.D

Dynamic column or true triaxial

Bender Axisymmetric < 103

> 100 VSG0

elements


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haviour of soil should be strongly considered indesigning any experiment involving geo-materials.

Recent developments in triaxial apparatusesallow stress-strain properties of soil to be ob-tained under a wide range of strain and strainrates (Tatsuoka et al., 1994; Santucci de Magistriset al., 1999). It must be emphasized, however,that only Youngs soil modulus can be directlyobtained from the triaxial apparatus, unlessreliable radial strain measurements and a propersoil model are available. A relationship betweenYoungs modulus and shear modulus is not easy

to acquire, even in the case of undrained tests(Vinale et al., 2001).

In general, while the Resonant Column test(RC) is relatively common in Italy (Cavallaroet al., 2001), a recent survey shows that thisapparatus has become less popular in Japan(Kuwano and Katagiri, 2001).

6. Analysis methods

Many approaches have been developed toanalyze the seismic behaviour of geotechnicalstructures. They can be classified on severalbases: geometry assigned to the soil-structuresystem (i.e. one-dimensional, two-dimensional,three-dimensional), constitutive model describ-ing the material stress-strain response (i.e.linearelastic, non linear elastic, elastoplastic with orwithout hardening), the modeling of the inter-action phenomena among different phasespresent in a soil (soil, water and air), the way inwhich the seismic loads are described (i.e.peakground acceleration, response spectrum, accel-eration time history). For the sake of simplicity,all the methods available in literature can begrouped into three main classes, including:

1) Simplified analyses, which allow forevaluating the safety factor of a soil-structuremass by simple global force equilibrium.

2) Simplified dynamic analyses, whichprovide the earthquake-induced displacement onthe basis of an assumed failure mode of the soil-structure system.

3) Full dynamic analyses, in order to evaluateboth magnitude of displacements and failuremodes.

Until the Sixties, among the simplifiedanalysis methods the pseudo-static approachrepresented the main tool used to assess theseismic safety of most geotechnical structures(retaining walls, embankments, earth dams, portstructures). Nowadays this method is still widelyused since it is imposed by several nationalregulations (in Italy, the D.M. 24/3/82) andbecause engineers have confidence in its use.Both the commercial codes that implement itand the quantitative definition of the requiredparameters are very simple.

In the pseudo-static approach, the dynamic

inertia forces induced by an earthquake areconsidered static actions proportional to the soilmass by a seismic coefficient (fig. 3). The valueof such a coefficient is determined on the basisof the expected peak ground acceleration in thearea where the structure is located. Nationalstandards generally prescribe the seismic coef-ficient value according to the seismic categoryof the site.

In the case of retaining walls (gravity andsheet pile walls), the pseudo-static approachrequires determination of both active and passiveearth pressures. They are usually estimated usingthe Mononobe-Okabe equation (Mononobe,1924; Okabe, 1924) obtained by modifying theCoulomb classical earth pressure solution toaccount for inertia forces.

One of the main limits of the pseudostaticmethod consists of considering the failure alonga well-defined sliding surface as the only typeof damage that an earth structure could sufferduring an earthquake. This assumption could bereasonable in the case of retaining walls, but itmight be misleading for other geotechnicalstructures. In the case of earth dams, for instance,

Fig. 3. Pseudostatic loads acting on a sliding mass.


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additional information is required aboutfreeboard loss and safety against liquefaction orfracture of dam elements (core or filter) thatassure water tightness. Literature documentsmany case histories of earth dams that failedeither partially or totally during earthquakes,even if the pseudo-static approach had given apositive result about their seismic safety. LowerSan Fernando Dam (Seed, 1979) and HebgenDam (Steinbrugge and Cloud, 1962) are twoclassic examples.

The simplified dynamic approach, firstintroduced by Newmark, still idealizes the soil-

structure system as rigid blocks of soil andstructural masses. Moreover, the method allowscomputation of the displacement of the slidingmasses by integrating the acceleration timehistory overcoming the so-called critical ac-celeration, i.e. the threshold acceleration thatcauses the block to slide (fig. 4). The seismicsafety of the earth structure is evaluated in termsof an acceptable permanent displacement ratherthan a factor of safety against global instabil-ity,as is typical in the pseudo-static approach.Simplified dynamic analyses, including theoriginal Newmark method (Newmark, 1965) andthe numerous Newmark-derived methods (i.e.Makdisi and Seed (1978) for embankments andearth dams; Yegian et al. (1991) for embank-ments; Franklin and Chang (1977) for dikes;Richards and Elms (1979) for gravity walls;Towahata and Islam (1987) for sheet pile walls;Steedman (1998) for gravity and sheet pile walls)can prove very useful when a performance-baseddesign philosophy is likely to be adopted toovercome the limitations of conventional seismicdesign.

Full dynamic analysis directly models theoverall soil-structure interaction problem,assuming that both soil and structure behaveascontinuum and deformable media. The spa-tial domain is discretized using a numericaltechnique (generally, finite element or finitedifference methods) and the differential equationgoverning the boundary value problem is solvedover the time or frequency domain. Since thesolution in the frequency domain is admissibleonly when the material linearity hypothesispersists, it is worth noting that the solution overthe time domain is mandatory when more

sophisticated constitutive models (inelastic orelastoplastic) are assumed for the soil-structuresystem. As discussed previously, the choicebetween a linear or non-linear material modeldepends on the expected level of earthquakemotion relative to the elastic limit of the soil-structure system.

Inside the class of full dynamic analysismethods, a more detailed distinction can be madein describing the interaction among the differentphasesair, water and soil skeleton of the soilconstituting the structure and its foundation.According to this point of view, the dynamicmethods can be further classified as: one-phase or total stress approach; simplified two-phase or simplified effective stress; coupled two- or three-phase approaches.

In the one-phase approach the interactionamong the soil phases is actually neglected, andthe soil is assumed to be an equivalent mono-phase continuum governed by dynamic equi-librium equations, continuity equations and

Fig. 4. Newmark sliding block approach.


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constitutive law. In particular, the constitutive lawrefers to the behavior of the whole soil skeleton-pore fluid system. Inside this category, theequivalent linear procedure has been the mostwidely used technique for computing the dyn-amic response of soil deposits, embankmentsand soil-structure interaction. This approachisimplemented in very popular codes, such asSHAKE (Schnabelet al., 1972), FLUSH (Lysmeret al., 1975) or QUAD-4 (Idriss et al., 1973).Notwithstanding the simplicity and popularity ofthe equivalent linear procedure, its main limi-tation lies in not providing any prediction of

earthquake induced permanent displacements. Asa matter of fact, the method is meaningless whenhigher strain levels are involved and permanentdisplacements should be forecast. Many attemptsin literature to overcome this limitation of theequivalent linear method are documented (Seed,1979).

In the simplified two-phase approaches, asemi-empirical law (excess pore water model)is introduced to evaluate the pore water pressureinduced by cyclic shear stresses. This law linksthe excess pore water pressure to the number andamplitude of the applied deviatoric cyclic stresses(Martin et al., 1975; Finn and Bathia, 1981;Dobry et al., 1985; Matasovic and Vucetic, 1992,1995). The effect of the excess pore water pres-sure is incorporated into the equivalent linearanalysis or into a direct non-linear analysis byreducing the actual stiffness of the soil. Such anapproach is implemented in computer codes asFLUSH-L (Ozutsumi et al., 2000) and TARA-3(Finn et al., 1986).

In the coupled two-phase approaches theconstitutive law refers only to the soil skeleton.To account for the presence of the pore fluid, thecontinuity equation of the water is incorporatedas well. The stress-strain behaviour of the soilcan be described by different constitutive lawsaccording to the level of sophistication required:linear elastic, hypoelastic, elastoplastic withkinematic or combined hardening. In this ca-tegory, the effective stress methods implementingelastoplastic models based on the concept ofcombined hardening (isotropic and kinematic)have proven very powerful in computing residualdisplacements and/or evaluating the structureresponse beyond the elastic strain level (Prevost,

1985; Muraleetharan et al., 1988; Iai et al., 1998;Benzenati, 1993; Sica et al., 2001). In the caseof earth dams, for instance, these methods allowevaluation of the structures safety against mosttypes of earthquake-induced damage: freeboardloss, liquefaction due to excess pore water pres-sures and post seismic effects.

The choice of analysis approach should bebased on the principle that structures requir-inghigher performance (structures with highexposure) should be designed/verified usingmore sophisticated methods. In light of this,simpler approaches may be used for preliminary

design, screening purposes or to evaluate earthstructure response in case of low seismic ex-citation levels.

Since earth dams can be quite complex geo-technical structures, the next section will focuson seismic response evaluation by applying someof the outlined analysis procedures to a real casehistory.

7. Some issues regarding earth dams

The structural complexity of earth dams andthe high risk associated with them due to majorsocial, economic and environmental conse-quences of failure, require very reliable analysistools to study their performance, especially whencarrying out a safety assessment involving seis-mic loads.

Principal damage that earth dams may sufferduring an earthquake consists of (Seed, 1979): settlements and fractures of the dam body; freeboard loss up to the limit of overtopping; global instability of upstream and downstream slopes; reduction of shear strength up to liquefaction of construction and/or of foundation soils; differential displacements between embankment, abutments and spillway; failure of outlet works crossing the dam body; disruption of dam by major fault movement in foundation; overtopping of the dam produced by soil

masses sliding into reservoir.Permanent displacements induced by earth-

quakes can be considered the integral effect ofvolumetric and deviatoric plastic strains devel-


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oped within the dam embankment. Deviatoricstrains produce, as an isolated effect, the so called

lateral spreading of the dam body. Significantcrest settlements produce freeboard loss up toovertopping (fig. 5). Even if this limit is not reac-hed, differential settlements may induce othercritical types of damage such as fractures withinthe dam body, which could then jeopardize thewater tightness of the structure.

Global failure induced by earthquakes mightoccur if the shells are so steep that even staticconditions are close to instability. Seismic forcesalways produce an increase in instability loadsand for some soils a decrease of shear strengthas well.

The failure mechanism may involve eitherthe dam body and/or the foundation soils.

Other types of damage could derive fromstrength reduction of soils induced by excessporewater pressure. The latter might cause twodifferent phenomena: liquefaction and cyclicmobility.

Liquefaction consists of a cyclic shear stressprocess that induces a reduction in strength notcompatible with static stability conditions actingat the end of the cyclic process itself. Cyclicmobility refers instead to a similar process wherestrength reduction is consistent with static sta-bility. Liquefaction induces high deformation inthe earth structure even up to collapse eitherduring or after the seismic event. Rapid col-lapseoccurred, for instance, in the Lower SanFernando Dam (1971) and in the Hebgen Dam(1959) several seconds after the end of theearthquake. Liquefaction phenomena occurredalso in more than ten small irrigation dams inAkiba (Japan) during the Oga earthquake (1939).In most cases failure occurred some hours afterthe seismic event.

Cyclic mobility, on the other hand, producespermanent deformations only during the seismicevent. Additional plastic strains develop onlywhen shear stresses (static + seismic induced)exceed the soil shear strength. Plastic defor-mations and related permanent settlementsdepend on cyclic number and amplitude of shearstresses. Vulnerability to liquefaction of soilsused as construction materials depends on theintrinsic soil properties and on the adoptedconstruction technique. It has been observed(Seed, 1979) that hydraulic fill dams are moreprone to liquefaction than dams constructed using

compaction. Differential movements betweendam body, abutments and spillway could causeinternal fractures where water could find lessresistance to seepage during post-seismic stages,giving rise to so-called piping. These effectsare very difficult to diagnose and are dangerousbecause piping could progress until abrupt failureof the dam.

8. The case history of El Infernillo Dam

The El Infiernillo Dam (fig. 6) has been se-lected in this study as a case-history samplebecause it is a high zoned dam (H

max= 145 m)

located in a highly seismic area (i.e.the Balsasriver zone around 300 km SW of Mexico City).The region is characterized by significant seis-micity fed by the subduction mechanism of thePacific plate under the American continent.

Since its construction, the El Infiernillo Damhas experienced several earthquakes, amongwhich two strong-motion events (on 14/03/1979and 19/09/1985). With reference to the earth-quakes of 14/03/1979 (Richter magnitude equalto 7.6 and epicentral distance of 134 km) and19/09/1985 (Richter magnitude of 8.1 and epi-central distance of 68 km), accelerogramsrecorded both on the rock abutments of the damand at reference points along the dam maximumcross section (crest and downstream shell) areavailable, together with some measurements ofearthquake-induced permanent displacements.These field observations have been used in thisstudy to verify the reliability of the selectedanalysis methods to evaluate the seismic per-formance of the dam.

Fig. 5. Typical earthquake-induced damages to earthdams.


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8.1. Simplified analysis

The stability analysis has been performedusing the modified Bishop method (Bishop,1955). The method is based on searching for thesafety factor along pre-defined potential circularslip surfaces by a limit equilibrium analysis. Atrial and error procedure was adopted to identifythe location of the slip surface having theminimum safety factor, both in the upstream andin the downstream rockfill shells of the dam. Thepseudostatic inertial forces were assumed to actin an outward direction to sliding (i.e. in theupstream and downstream directions, respec-tively, for the upstream and downstream shell)in order to maximize the effect of the activeforces that induce sliding. The analysis wasperformed under the hypothesis of steadyseepage inside the dam with the reservoir levelfixed at its operational maximum. As a conse-quence, the buoyance unit weight was adoptedin the computation regarding the upstream shell,while the actual unit weight of the constructionsoils was considered in searching for the slipsurfaces within the downstream side.

The seismic coefficient was assumed equal to0.1, the peak ground acceleration during the14/03/1979 earthquake at the rock base of thedam.

From the two sets of analyses, it appears thathigher instability is located in the upstream shell

of the structure. Potential sliding surfaces areconcentrated in the upper part of the dam closeto the external boundary. The minimum safetyfactor was 1.7, an acceptable value for assuringglobal stability of the dam.

8.2. Simplified dynamic analysis

Among the simplified dynamic methodsavailable in literature, the Newmark approachwas selected to evaluate the permanent displace-ment of the El Infiernillo Dam induced by the14/03/1979 earthquake.

As indicated before, this method requiresthe determination of the critical accelerationassociated with an assumed sliding surface. Theselected surface in this case had the lowest safetyfactor in the pseudostatic analysis and involveda dangerous failure mechanism involving theovertopping of the reservoir water.

Figure 7 shows the adopted sliding surfacefor the upstream side of the dam. Figure 8 showsthe reduction of the safety factor with increasingseismic coefficient. This plot was obtained bycomputing the pseudostatic safety factor (S

F) for

different values of the seismic coefficient. Incorrespondence to the unit safety factor (S

F=1),

a critical seismic coefficient (kc) of 0.32 was

evaluated. This means that if the average ac-celeration along the slip surface overtakes the

Fig. 6. Main cross section of El Infiernillo Dam.


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critical value of 0.32 g(acrit

= kcg), the sliding

mass will start moving as a rigid block.The left hand side of fig. 7 shows the variation

of the peak horizontal acceleration along the damaxis. This plot was obtained by assuming linearvariation of acceleration from the measured valueof 0.1 gat the dam base up to the value of 0.36 gthat was recorded at the dam crest during the

14/03/1979 seismic event. Therefore, an aver-age value of 0.31 g could be reasonably at-tributed as the unique peak acceleration alongthe whole sliding surface. Since the drivingacceleration is lower than the computed criticalacceleration, the Newmark method does notpredict any irreversible displacement withinthe dam.

Fig. 7. Sliding surface adopted in the Newmark analysis for the upstream shell of the El Infiernillo Dam.

Fig. 8. Pseudostatic safety factor variation with increasing seismic coefficient along the sliding surface.


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8.3. Full dynamic analysis

The dynamic analysis was performed usinga two-phase coupled approach implemented inthe finite element program GEFDYN (Aubry andModaressi, 1996). The approach is based on theu-p formulation of the Biot generalized con-solidation theory (Zienkiewicz and Shiomi,1984).In particular, the overall dynamic equilibrium andthe pore water flow equations were combinedwith Hujeuxs elastoplastic kinematic hardeningconstitutive law (Hujeux, 1985). This law de-scribes some relevant features of the soil response

under monotonic and cyclic loading conditions(hysteresis, liquefaction, cyclic mobility andratcheting). Since in a coupled effective stressmethod the predictions of the dynamic analysisare strongly affected by the pre-seismic condi-tions of stress and pore water pressure distri-bution within the structure, it was necessary tosimulate all stages of the dams history up untilthe actual seismic event: construction, firstimpounding, service operations.

In this study, the model parameters charac-terizing the materials of the El Infiernillo Dam

were evaluated from the laboratory tests per-formed at the time of dam construction (conven-tional drained and undrained monotonic triaxialtests and oedometer tests) and on a back-analysisprocedure of dam observed behaviour (Sica,2001). The dam geometry was discretized inabout 400 2D quadratic elements (fig. 9). Theacceleration time-history used as input motionat the base of the finite element model is thehorizontal accelerogram (upstream-downstreamdirection) recorded on the outcropping rockduring the 14/03/1979 earthquake.

At the end of the seismic excitation, the

effective stress analysis gives a deformed shapeof the dam like that shown in fig. 10. Themaximum vertical settlement computed at theend of the earthquake is around 9 cm at the damcrest; the maximum horizontal displacement inthe upstream direction is about 8 cm and 4 cm inthe downstream direction. These results areconsistent with the observed deformed mode ofthe dam after the same earthquake (Resendizetal., 1982).

As far as the excess pore water pressures areconcerned, the analysis gives a maximum pore

Fig. 9. Mesh geometry of the El Infiernillo Dam adopted in the f.e.m. analysis.

Fig. 10. Deformed mesh geometry of the El Infiernillo Dam after the 14/03/1979 earthquake simulation.


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water pressure ratio inside the dambody of about 20%, a value far enough from thethreshold limit of 100% at which soil liquefactionmay occur.

In conclusion, the effective stress analysisprovided the required information about the damsafety in terms of:

1) overtopping: the computed freeboard loss,equal to the seismic induced vertical displa-cement at the dam top, is only 1% of the availablefreeboard (10m);

2) liquefaction: the computed pore waterpressure ratio r

u is less than 100%;

3) shell stability: the computed horizontaland vertical displacements at the end of theearthquake are very small (less than 10 cm) com-pared to the transverse dimension of the dam.

9. Conclusions

To properly analyze the seismic behaviourof geotechnical structures, a complete method-ology typically employs several steps. First, adetailed evaluation of the regional seismicityshould be performed in order to define theearthquake motion at the base formation wherethe structure is located. Next, the specific hazardof the site should be assessed by consideringeither local amplification of ground motion andother problems like soil liquefaction, groundrupture or landslides. Finally, the soil-structureinteraction analysis should be performed. Sincethe whole methodology cannot be described in asingle paper, this report focuses only on somerelevant aspects of the final step.

The first point highlighted in the paper isa close interconnection between various techni-cal branches (from seismology to geology, en-gineering and land planning) and governmentpolicy in seismic risk analysis. This means thatthe seismic response of geotechnical structuresshould be considered just one component of thewider topic of earthquake disaster risk protectionand prevention.

The second aspect emphasized in this paperis the importance of proper knowledge of themechanical properties of the materials con-stituting the structure and its subsoil. This is acrucial problem for geotechnical engineers

because it requires both high technical skill andeconomic resources for suitable in situ andlaboratory investigation.

It was further pointed out that for geo-technical structures, determination of soilproperties should be adapted to the analysismethod chosen to study seismic response. Thischoice is not simple, especially if one considersthat national standards, except for some specificand recent releases, are usually not exhaustiveon the safety evaluation of structures underseismic actions. In general, they account for theamplification of the ground motion due to site

conditions in a very rough manner, and suggestonly simplified analysis methods.

Conventional approaches provide infor-mation on the structures capacity to resist adesign seismic force, but they are not able topredict structural performance during and afterthe earthquake. Theperformance-based designapproach, first developed for buildings, is nowa-days proposed for geotechnical structures aswell. A comprehensive report on this topic, ori-ented towards port structures, can be found inInternational Navigation Association (2001).Extracted from that report are the followingpoints:

1) deformations in ground and foundationsoils, together with corresponding structuraldeformation and stress states, are key designparameters;

2) conventional limit equilibrium-basedmethods are not well-suited to evaluate theseparameters, and

3) some residual deformation may be ac-ceptable.

In performance-based design, appropriatelevels of design earthquake motions must bedefined along with acceptable levels of structuraldamage. For design purposes, two levels ofearthquake motions are typically used:

Level L1: earthquake motion that is likelyto occur during the life-span of the structure(probability of exceeding is 50 %).

Level L2: earthquake motion associatedwith rare events that typically involve very strongground shaking (probability of exceeding is 10 %).

The acceptable level of damage is set ac-cording to some specific structural (predictedamount of damage) and operational (level of loss

( )r uu = / vo

'


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of serviceability, time and cost for restoration)factors.

Once the design earthquake levels and ac-ceptable damage levels have been properly defined,the required performance of a structure may berepresented by a performance grade determined bythe importance of the structure (critical and keystructures, primary structures, ordinary structuresand small, easily restorable structures).

The principal steps taken in performance-based design are summarized in the flowchart offig. 11.

It is apparent that for geotechnical structures,

appropriate damage criteria should be related tothe deformation mode of the structure itself. Asa consequence, sophisticated analyses should beadopted to model structure performance ade-quately.

In this paper, the seismic behaviour of anearth dam was analyzed as a sample geotechnicalstructure. Even if this case history was examinedfrom a verification rather than design viewpoint,the study is very explanatory of the capabilityof a coupled dynamic analysis in predictingstructure performance during and after a selectedearthquake. In particular, this type of analysismethod allows forecasting of seismically induceddisplacements in the dam body with good ac-curacy, as verified by comparing analyticalresults with monitoring data. Figure 12 reportsthe computed vertical displacements profiles at

three locations along the dam axis. On the rightside hand of the figure the residual displacementsare plotted together with the measured ones,showing good agreement between the analysisprediction and observed behaviour.

Fig. 11. Steps required for the seismic behaviour analysis of a geotechnical structure using a performance-designbased approach (modified after International Navigation Association, 2001).


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It is worth emphasizing that while the pseudo-static method does not directly predict dis-placements, no seismically-induced movementswere forecast by the simplified dynamic analysesusing the Newmark method. In any case, the

critical slip surface given by the pseudostaticapproach, found by trial and error, lies very closeto the area in which maximum plastic sheardeformations were detected by the full dynamicanalysis (fig. 13).

Fig. 13. Contour plot of plastic shear strains at the end of the 14/03/1979 earthquake.

Fig. 12. Time histories of vertical displacement at three points along the dam axis.


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Acknowledgements

The authors wish to give thanks to Prof. H.Akihama, Nihon University, and Prof. A. Ra-polla, University of Naples, scientific organizersof the Kyoto and Kobe meeting, for offering usthe opportunity to contribute our findings in ahigh level meeting that was useful for exchangingopinions with several experts in the area ofnatural disaster mitigation. A vote of thanksshould be given to Prof. M. Nakashima and hisstaff at Kyoto University for the tremendouseffort in organizing the symposium; to Dr. A.

Volpi, scientific attach at the Italian Embassyin Japan and the Italian Embassy in Japan, forthe care and the support received; to Mr. M. DiGianni, Honorary Consul of Japan in Naples, andto all participants in the symposium for theirfriendship and frank exchange of ideas.

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