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Soil Dynamics and Earthquake Engineering 28 (2008) 99–117

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Static and dynamic behavior of hunchbacked gravity quay walls

Abouzar Sadrekarimia,�, Abbas Ghalandarzadehb, Jamshid Sadrekarimic

aDepartment of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USAbDepartment of Civil Engineering, University of Tehran, Tehran, IrancDepartment of Civil Engineering, University of Tabriz, Tabriz, Iran

Received 23 January 2006; received in revised form 2 April 2007; accepted 24 May 2007

Abstract

One of the parameters that can affect the lateral pressures behind a retaining wall is the back-face shape of the wall, which can be

controlled by the designer, and has not been investigated experimentally. Therefore, in order to study this behavior, a set of 1g shaking

table tests was carried out on hunched back gravity type quay walls made of concrete blocks. Crushed stone and silica sand were used in

the backfill and subsoil, respectively. The subsoil was prepared by moist tamping. The models were fully instrumented and beside each

earth pressure transducer a pore water pressure sensor was also installed behind the wall therefore the lateral effective stress acting on the

wall could be calculated. Tests were performed with various base accelerations on models with different subsoil relative densities. The

results show that the earth pressure increases at upper portions of the wall and decreases by the leaning slope at lower elevations.

Depending on the back-face shape of the wall the total thrust and overturning moment would be increased or decreased after an

earthquake. However, the hunched back-shape of the wall tends to raise the point of application of the total thrust exerted on the wall.

Other advantages of hunched back walls are demonstrated as well.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Quay wall; Hunched back wall; Point of application; Resultant thrust; Mode of failure; Earthquake; Lateral earth pressure distribution

1. Introduction

Quay walls are one of the most important coastalstructures which would suffer disastrous damages duringearthquakes; therefore, several studies have been carriedout on the pressures exerted on quay walls [1–11]. Matsuo[12] performed shaking table tests on retaining walls andfound that the dynamic component of pressure was actingat two-thirds of the wall height above the base of the wall.Similar behavior was observed by Jacobsen [13]. Ishii et al.[14] conducted shaking table tests on walls backfilled withsand. They observed phase differences as much as half ofthe shaking period between the input motion and themeasured lateral pressures. Furthermore, the maximumlateral pressure was equal to or less than Mononobe–Okabe’s [1,2] predictions and the dynamic lateral pressuredistribution was bow-shaped. By the means of shakingtable tests, Murphy [15] found that the failure plane during

e front matter r 2007 Elsevier Ltd. All rights reserved.

ildyn.2007.05.004

ing author. Fax: +1217 265 8041.

ess: asadrek2@uiuc.edu (A. Sadrekarimi).

shaking was much flatter than the static one. Nandaku-maran and Joshi [16] measured the dynamic increment ofearth pressure on flexible and rigid model walls andcorrelated the dynamic increment of the lateral earthpressure with the peak ground velocity and suggested aprocedure for computing the translational displacements ofrigid walls. Matsuo et al. [17] studied the earth pressureacting on retaining walls by large-scale prototype fieldtests. The walls were made of concrete and were 10m high.They observed that the lateral earth pressure distributionbehind the wall was not triangular and relatively largelateral pressures were measured at the lower part of thewall; however, the point of application of the resultantthrust was approximately at the one-thirds of wall heightfrom the base of the wall. Moreover, as the wall displacedthe lateral earth pressure dropped from its at-rest state tothe active state but it recovered gradually over time as thewall was left still. And therefore they recommendeddesigning retaining walls against the at-rest earth pressure.Sherif and Fang [18,19] did shaking table tests on modelrigid walls rotating about their base, and rotating about

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Fig. 1. Definitions of negative and positive back-slopes.

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their top. For the walls rotating about their base theyobserved that the static active lateral stress had a lineardistribution up to about 80% of the height of the wallhowever at deeper depths the stress distribution becamenon-linear and increased to the value of static at-rest stateat the base of the wall. During shaking and as the inputacceleration was increased the non-linearity of the lateralstress distribution also increased and high lateral stressesdeveloped near the top of the wall. They attributed this tothe smaller strength of the sand near the surface of thebackfill and hence its larger lateral stress transmissioncharacteristic. Furthermore, the point of application of thetotal dynamic thrust was observed to rise with increasingthe input acceleration. For the walls rotating about theirtop, the lateral pressures behind the wall initially droppedas the wall rotated from the at-rest condition andeventually reached an almost constant value, i.e. the activestate. The dynamic lateral pressures near the top of the wallincreased with increasing acceleration and this wasattributed to soil arching and those at the bottom of thewall were nearly zero. The point of application of the totaldynamic thrust was observed to rise from one-thirds of wallheight to 0.55 of wall height when the active state wasestablished. However, in contrast to their observation forwalls rotating about their base, for walls rotating abouttheir top the point of application of the total dynamicthrust was almost fixed and did not vary with inputacceleration. Sato et al. [20] found that the fluctuatingcomponents of the dynamic thrust acting on quay wallsand the inertia force of the wall were acting in oppositedirections while the excess pore pressure developed in thebackfill soil was small; however, these forces acted in thesame direction after the backfill soil liquefied. Kim et al.[21] proposed a model to estimate the magnitude and phasevariation of the dynamic thrust acting on the back of thequay wall. They evaluated the fluctuating and non-fluctuating components of the dynamic thrust separatelyand confirmed the behavior of their model by two shakingtable tests. They found that the Mononobe–Okabe [1,2]method overestimated the dynamic thrust as much as 4.5times for large excess pore water pressures. Nakamura [22]did centrifuge shaking table tests on model gravityretaining walls and observed significant difference betweenthe acceleration of the wall and the backfill and stated thatthe retaining wall would move simultaneously with theapplication of inertia force in the active direction andafterwards the backfill would move. Also the distributionof the earth pressure behind the wall was not triangularand its size and shape changed during the shaking period.

All of these studies have been focused on walls withvertical back-slopes and very little data is availableregarding the effect of the wall’s back-face slope on theearth pressures. To directly reduce the earth pressurebehind a quay wall, the back-slope of the wall can be auseful design parameter to consider. The back slope of alandwards leaning wall which will be referred as a negativeback-slope (Fig. 1) here after and a positive back-slope

(Fig. 1) would, respectively, decrease and increase the earthpressures on the wall. This behavior can also be demon-strated by Coulomb’s lateral pressure relations [23]. Thus,a leaning wall would decrease the lateral pressure; however,taking into account the amount of materials used in a largeleaning wall and economical issues a hunched back wallwould be preferable since pressures at higher elevations ofthe wall are small and would not need to be reduced. Thistype of wall has not been thoroughly investigated and itsdynamic behavior has not been studied. Moreover, realseismic events are unpredictable and field conditions areoften characterized with significant uncertainties. Full-scalestructures are generally not adequately instrumented tocapture the complete scenario. A useful alternative is labo-ratory methods.Moreover the total lateral pressure behind a quay wall

can be divided into six components [21], which are:

1.

Hydrostatic pressure (pws). 2. Non-fluctuating dynamic water pressure (pnfdw). 3. Fluctuating dynamic water pressure (pfdw). 4. Static effective earth pressure (at-rest p0, or active

state ps).

5. Non-fluctuating dynamic effective earth pressure (pnfde)

and

6. Fluctuating dynamic effective earth pressure (pfde).

In order to have a better understanding of thesecomponents, Fig. 2 shows all of them.In this paper, the influence of a hunched back-slope of a

wall on lateral pressures is investigated through sixteen 1g

shaking table tests carried out on quay walls with twodifferent back-face shapes and the behavior of the walls isevaluated using the aforementioned components of lateralearth pressure.

2. Testing method and materials

The results of studies performed with 1g shaking tabletests agree well with those of centrifuge tests, suggesting a

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Fig. 2. Total lateral pressure components exerted on a quay wall:

(a) water pressure components and (b) lateral earth pressure components.

Fig. 3. Particle size distribution of the backfill and seabed soils.

A. Sadrekarimi et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 99–117 101

good applicability of the scaling relations for shaking tabletests and indicating that shaking table tests, if carefullyperformed, have a potential to be powerful means to studythe performance of complicated soil–structure interactionproblems [24,25]. In preparation of the models for thisstudy, the intention was to model a field structure as closeas possible as well as studying the mechanism of response.Therefore, every effort was taken to mimic a typical fieldstructure. Two types of hunchbacked walls were built andtested. Wall type I had a larger hunch and the breakingpoint of the hunch was at the mid-height of the wall, i.e.block number 6. Wall type II had a smaller hunch and thebreaking point of the hunch was at the lower one-third ofits height, i.e. block number 3.

2.1. Materials

Firoozkuh silica sand was used as the seabed in themodel tests. This sand has a uniform grading and its

physical properties are GS ¼ 2.658, emax ¼ 0.943, emin ¼

0.603 and D50 ¼ 0.3mm. In order to avoid liquefactioncoarse crushed limestone was used as the backfill soil. Thiscrushed stone had D50 ¼ 12mm, emin ¼ 0.670, emax ¼

0.960 and a permeability of 0.5m/s. The particle size distri-butions of these materials are plotted in Fig. 3. A 2-cm-thick rubble mound with a maximum grain size of 6mmwas used as the base beneath the quay walls, in order todistribute the weight of the wall uniformly on the seabedsand. Also quarry stone with a maximum size of 40mmwas used in front of the first row of blocks.

2.2. Concrete blocks

The walls were made of concrete blocks with a specificweight of 2400 kN/m3. The blocks had shear-keys on theirtop and bottom sides, which in addition to friction betweenthem prevented any relative sliding. The concrete blockswere cast in aluminum molds which were carefully designedand machined. Totally, 11 sections of each wall were builtto fill the 44 cm width of the model tank, and therefore 110concrete blocks were made for each type of wall. Finally, a44-cm-long concrete block cap was made and placed on topof each wall.

2.3. Instrumentations

To fully record the behavior of the model, miniaturepore water pressure (to measure pws+pnfdw+pfdw), totalearth pressure (to measure pws+pnfdw+pfdw+ps(orp0)+pnfde+pfde), acceleration transducers, and high-reso-lution LVDTs were used. The number and location of thetransducers were selected based on the desired data. On theback-face of the walls, pore water pressure transducerswere installed beside each earth pressure transducer inorder to calculate the effective lateral earth pressure. Thesetransducers were evenly installed in holes prepared forthem on the concrete blocks. They were installed on themiddle wall section on blocks B2, B4, B6 and B8 in walltype I and on blocks B1, B3, B5, B7 and B9 in wall type II.

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The diaphragm diameter of the earth pressure and porepressure transducers were 25 and 20mm, respectively.Sand-filled small bags were placed on the diaphragm of theearth pressure transducers to distributed the pressuresuniformly and avoid stress concentrations caused by angu-lar grains. Water pressure transducers were also embeddedin different locations of the model soil. These embeddedpore water pressure transducers were fixed in place tomeasure the pore water pressure at the same location andnot to move with the surrounding soil during shaking. Two10-channel data loggers were used to record the measureddata and transfer them to a personal computer. Despite ofthe high-resolution transducers, due to deformations of themodel corrections were necessary for some of the mea-surements and even in some cases the measurements of a

Fig. 4. Schematic cross-section of the mod

particular transducer were completely rejected. Thesecorrections are presented in the Appendix with an exampleof the corrected data.

2.4. Model preparation

The Plexiglas model container which housed the soil andthe hunchbacked wall measured 179 cm long, 44 cm wideand 70 cm high, and was equipped with carbon dioxide andwater inlet and outlets. This container was fixed to theshaking table platform. The test preparation method wasintended to simulate a plane strain condition. The mainconcern in simulating a plane strain condition is to avoidthe side effects of the test container. This was accomplishedby polishing and lubricating the Plexiglas sides of the

els: (a) wall type I and (b) wall type II.

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Fig. 5. Schematic cross-section of models with non-uniform seabeds: (a) model QW08 and (b) model QW15.

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container before each test. Wet tamping was used todeposit Firoozkuh sand in the seabed. In this method, sandwas thoroughly mixed with 5% (of its dry weight) water,carefully rained in the container and tamped to the targetdensity. The moisture creates an apparent cohesion whichmakes it possible to achieve a wider range of densities andeasier tamping. The desired relative density (Dr) wasachieved by calculating the weight of wet sand requiredin a specified volume, marked every 5 cm on the Plexiglas,and tamping this amount of sand up to that volume. Aftercompleting the seabed, rubble mound under the wall waspoured and leveled, then the first row of the concreteblocks were placed followed by placing the quarry stonelayer in front of them. Afterwards carbon dioxide gas was

circulated from the bottom through the subsoil, followedby water. This technique was used to ensure bettersaturation of the seabed. Water was percolated with avery low discharge rate (0.02m3/h) to avoid disturbance ofthe controlled seabed by the upward gradient. The cross-section of the model was visible through the Plexiglas sidewalls of the container. A square grid of dyed sand wasdeposited adjacent to the side wall to show the deformationpattern of the subsoil. When water reached the desired levelthe water inlet was closed, and the remaining of theconcrete blocks were placed. Then the backfill soil waspoured in the container and the model was complete. Usingthe same pluviation method and drop height the backfillhad a relative density of 52% in all of the model tests. This

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Table 1

Specifications of the tests

Test no. Wall type Base

acceleration (g)

Seabed Dr (%)

QW1 I 0.25 90

QW2 I 0.35 90

QW4 I 0.40 90

QW5 I 0.34 60

QW5+ I 0.35 60

QW6 I 0.24 10

QW7 I 0.24 30

QW8 I 0.30 90–35–60

QW11 II 0.38 90

QW12 II 0.20 90

QW12+ II 0.36 90

QW13 II 0.24 35

QW14 II 0.12 35

QW14+ II 0.22 35

QW15 II 0.30 80–35–90

QW15+ II 0.35 80–35–90

Table 2

Failure modes of each test

Test

no.

Wall

type

No

significant

failure

Sliding Settle-

ment

Landwards

rotation

Over-

turning

QW1 I �

QW2 I �

QW4 I �

QW5 I �

QW6 I � � �

QW7 I � �

QW8 I � � �

QW11 II � �

QW12 II �

QW12+ II � �

QW13 II � � �

QW14 II �

QW14+ II � �

QW15 II � �

QW15+a II � �

aIn QW15+, some of the upper blocks of the wall toppled into the

water.

Fig. 6. Seabed relative density versus maximum base acceleration in each

test with different marks for different modes of failure.

Fig. 7. Maximum wall movement versus maximum base acceleration in

each test with different marks for each mode of failure. The seabed relative

density is noted beside each mark.

Fig. 8. Maximum effective lateral thrust versus maximum base accelera-

tion in each test with different marks for each mode of failure. The seabed

relative density is noted beside each mark.

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procedure was carried out in order to simulate a fieldconstruction procedure as nearly as possible. Fig. 4illustrates the cross-section of the models. In modelsQW08 and QW15, the seabed was made by depositing alooser layer between two denser layers, which are shown inFig. 5. The seabed was fairly uniform in the rest of themodels. The locations of total earth pressure transducers(designated by EP), water pressure transducers (PP),accelerometers (ACC) and displacement transducers(SLVDT and LVDT) are illustrated in Figs. 4 and 5. Infield constructions, usually the looser shallow seabed isexcavated in order to place the wall on the denser sub-soil and therefore a caved seabed profile was formed as inFigs. 4 and 5.

2.5. Performing the tests

A variety of models with different seabed densities weretested. Two types of wall back-shapes were considered. The

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Fig. 9. Maximum total overturning moment versus maximum base

acceleration in each test with different marks for each mode of failure.

The seabed relative density is noted beside each mark.

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input motion in all cases was a horizontal sinusoidalexcitation with a constant frequency of 2.8Hz, but withdifferent acceleration amplitudes. Total recording time was40.96 s and the shaking was applied for 10 s. Table 1 showsthe characteristics of each model test. Models QW5, QW12and QW14 which did not deform considerably during theshaking were shaken again with larger amplitude. Theseare denoted by a ‘+’ sign, i.e. QW5+, QW12+ andQW14+. The benefit of this was that the behavior of themodel could be compared during small and large earth-quakes without additional models. The apparent disadvan-tage was that soil density changed although slightly afterthe first shaking. Moreover, in order to evaluate the post-earthquake performance of a restored wall, test QW15+was performed just by filling the settled backfill to itsoriginal level, after shaking of model QW15.

3. Results and discussions

3.1. Mode of failure

The failure mode of a quay wall can be divided into fourcategories which are settlement, sliding, landwards rota-tion, and overturning (seawards rotation). None or more ofthese modes may happen. The modes of failure of each testare presented in Table 2 which along with Table 1 show thesignificance of seabed relative density on the mode andextent of failure. In models QW08, QW15 and QW15+where a layer of loose sand was embedded between twolayers of dense sand, the loose layer was the controllinglayer increasing the deformations. Furthermore, the modeof failure and its extent was different in the two types ofwalls, i.e. wall type I rotated but wall type II overturnedmore than the rotation of wall type I. During modelpreparation, the backfill soil settles under its own weight,and mobilizes a down-drag force which depends on thefriction between the wall and the backfill soil. This forceplus the weight of the soil resting on the positive back-slope

of the wall tends to stabilize the wall so that it resistsoverturning, and it adds to the normal force acting on thebase of the wall, helping to prevent sliding and overturning.The rotation of wall type I in contrast to the overturning ofwall type II indicates this stabilizing effect of the over-burden soil.

3.2. Overall behavior of the wall

The relative density of the seabed, wall movement,thrust, overturning moment and acceleration are plottedagainst each other in Figs. 6–9. In theses plots, wall types Iand II are indicated by solid and hollow marks, respec-tively. The tests in which no significant failure wasobserved are shown by square marks, those where the wallonly slid are shown by triangles and those where more thanone type of failure mode happened, i.e. sliding, settlementand rotation/overturning are shown by lozenges. Also thetests which the excitation was applied for the second timeare marked by a ‘+’ sign beside their relative densityvalues. Fig. 6 depicts the relative density of the seabedversus maximum acceleration applied to the model. Withrespect to the above convention, this plot can be dividedinto zones of different modes of failure and therefore themode of failure for any other combination of relativedensity and maximum base acceleration can be predictedfrom this plot.Maximum wall movement is plotted against maximum

base acceleration in Fig. 7. According to this plot, the wallmoved more with a larger base acceleration and a softerseabed. Moreover, the models which were shaken for thesecond time moved less; this was due to the denser seabedcaused by the first time shaking and since the densificationwas not measured the relative density is denoted by a plussign meaning that the relative density could be larger. Themodels with layered seabeds moved farther which confirmsthe significance of the loose layer. Also within the samerelative densities of the seabed and similar ranges of baseaccelerations, wall type II moved more than wall type I.This was because of the larger thrust exerted on wall type IIdue to its larger portion of positive back-face slope andsmaller portion of negative back-face slope.The maximum effective thrust is plotted versus max-

imum base acceleration in Fig. 8. It shows that themaximum effective thrust on the wall increased with thebase acceleration, irrespective of the type of the wall. Therelative density of the seabed and the mode of failure weretwo factors which also influenced the maximum effectivelateral thrust on the wall. A softer seabed (i.e. lowerrelative density) increased the thrust exerted on the wall. Inother words within a similar mode of failure, softer theseabed larger the maximum effective lateral thrust was onthe wall. In addition, as explained earlier, a larger thrustwas exerted on wall type II.Maximum total overturning moment exerted on the wall

is plotted versus maximum base acceleration in Fig. 9.Similar to the effective lateral thrust, the total overturning

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moment increased with base acceleration and also withinthe same failure mode the overturning moment increasedas the seabed density decreased. Comparing the over-turning moments on the walls with seabed relative densitiesof 35% with 35%+, 90% with 90%+ and 80–35–90%with 80–35–90%+ which had the same mode of failure, itcan be concluded that shaking the model for the secondtime densified the seabed hence the overturning momentacting on the wall was smaller in those tests. However,models with seabed relative densities of 60% and 60%+cannot be compared, since their modes of failures weredifferent. Furthermore, comparing the overturning mo-ments on wall types I and II shows that a larger momentwas applied on wall type II, this was due to the largerportion of the upper positive back-face slope in wall type II

Fig. 10. Effective lateral earth pressure distributions before and after the ex

(g) QW13, (h) QW14, (i) QW14+ and (j) QW15.

which increased the thrust acting on the wall as well aselevating its point of application.

3.3. Lateral pressure distribution behind the wall

Lateral effective pressure distribution behind the wall,before (p0) and after (ps) the shaking, are plotted in Fig. 10,in which the horizontal dashed line represents themaximum sea level, i.e. the level up to which the modelswere filled with water. In plotting these distributions, theupper portion of the distribution diagram was extended tozero since the earth pressure at the surface of the backfilland the water pressure at the water table would be zero.The lower portion beyond the lowest transducers waslinearly extrapolated down to the base of the wall level.

citation: (a) QW2, (b) QW4, (c) QW5, (d) QW5+, (e) QW8, (f) QW12,

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Fig. 10. (Continued)

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Along with each distribution its resultant thrust, and pointof application are also shown where the bold fontrepresents the active case and the regular font is the at-rest case. The point of application of the resultant thrustwas calculated by equilibrium of moments at toe of thewall. The number in parenthesis is the overturning momentby that thrust in Nm. Because of space limitations not allof the tests are presented in Fig. 10, although the omittedtest results were similar to what is presented except formodel QW15+, which due to the toppling of the upper-most block, the results were not interpretable.

In these plots, the break in the slope of the lateralpressure distribution diagram at the water table reflects theconversion from dry unit weight to submerged unit weightcontribution in the lateral earth pressure. Moreover, theslope of the at-rest pressure distribution diagram hasdecreased with depth, this is because of that the at-restlateral earth pressure coefficient (K0) in a given soil oftendecreases with depth [26]. According to the above figures,the point of application of the resultant thrust either beforeor after shaking was higher than the conventional one-thirdof the height (i.e. 14.7 cm) in vertical back-face walls. Thiswas because of the hunched back-face of the wall.

Moreover, the sharp drop of the lateral earth pressurewas partly due to the arching effect at the breaking point ofthe wall’s back-slope. Non-uniform deformations in anearth mass, resulting from some restraints preventing freemovements in it, would cause additional shearing stresses.

These extra shear stresses would tend to keep the movingparts in place and therefore decrease the thrust acting onthem. Therefore, the sliding surface would not form freelyand stress distribution along the back of the wall would notbe hydrostatic [27].The pressures after shaking became larger on positive

back-slope elevations of the wall and smaller on negativeback-slope portions; this means that the static activepressure was larger than the at-rest pressure on the positiveback-slope portions of the wall and was smaller on thenegative back-slope portions of the wall. This phenomenonis consistent with Coulomb’s lateral earth pressure theory[23], which results in lateral earth pressure coefficientslarger than the at-rest value where the back-slope of thewall is positive and lower coefficients when it is vertical ornegative. This increase of the pressure on positive back-slope levels and decrease on negative back-slope levelselevated the point of application of the resultant thrustbehind wall type I. In wall type II, the pressure distributionon the positive back-slope portion of the wall changed in away that the points of application of the resultant thrustswere fairly at the same location. In wall type I which aremodels QW2, QW4, QW5, QW5+, QW6 and QW8, theincrease in pressure at higher levels was compensated bythe decrease at the lower levels resulting in a less resultantthrust and overturning moment despite of the fact that thepoint of application of the resultant had raised. However,in wall type II which are models QW12, QW13, QW14,

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QW14+ and QW15, the decrease in pressures or in otherwords the negative back-slope portion of the wall was notenough to compensate the increased pressure on thepositive back-slope portions of the wall resulting in alarger resultant thrust and overturning moment behind thewall. Therefore, the hunched back-face in wall type II wasunable to reduce the pressures and overturning momentsafter the shaking. The densification of the backfill soil alsocontributed to the increased pressures after the excitation,but its effect was less significant than the at-rest to activeconversion, since the pressures on negative back-slopeportions of the wall were decreased despite of thedensification effect.

The distribution of total lateral pressure and each of itscomponents at the moment during shaking when the total

Fig. 11. Distribution of total lateral earth pressure and it is components at th

(d) QW6, (e) QW8, (f) QW12, (g) QW13, (h) QW14, (i) QW14+ and (j) QW

lateral thrust was at maximum are plotted in Fig. 11 forselected tests. The total lateral thrust and its point ofapplication are also shown in these graphs. Deriving eachcomponent was performed in the following manner: thepore water pressure time history recorded by the porepressure transducers was deducted from the total lateralpressure time history recorded by the total earth pressuretransducers; therefore, the effective lateral pressure timehistory which is ps+pnfde+pfde was obtained. By smooth-ening the effective lateral pressure time history, the non-fluctuating lateral earth pressure time history that isps+pnfde was obtained which could not be furtherseparated from each other because as well as pnfde, ps alsochanged during a test. Furthermore, the fluctuating part ofeffective lateral pressure (pfde) time history was obtained by

e moment of maximum lateral earth thrust: (a) QW1, (b) QW2, (c) QW5,

15.

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Fig. 11. (Continued)

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subtracting the non-fluctuating part (pnfde+ps) from thetotal effective lateral pressure (ps+pnfde+pfde) time history.pnfdw and pfdw were also obtained in the same manner, andsince pws was constant throughout the test or at least itcould be calculated therefore deriving pnfdw was possible.

Fig. 11 shows that the total lateral pressure during theexcitation was distributed in the same manner as thepreviously discussed static pressure distributions, i.e.increased lateral pressure on the positive back-slopeand decreased lateral pressure on the negative back-slope. This was also true for the non-fluctuating andfluctuating dynamic effective pressure distributions. Con-sequently, on the positive back-slope portions of thewall (upper levels), the non-fluctuating and fluctuatingdynamic effective lateral pressure components were muchlarger, but on the negative back-slope elevations (lowerlevels) the static water pressure was the largest componentof the total lateral pressure. The non-fluctuating andfluctuating dynamic water pressures were significantlysmaller because of the large permeability of the coarsebackfill material.

3.4. Non-fluctuating effective lateral earth pressure

(ps+pnfde)

Time histories of the non-fluctuating effective lateralearth pressures recorded by each couple of total earthpressure and pore water pressure transducers are plotted in

Fig. 12. This figure shows that the at-rest pressures on thenegative back-slope portions of the walls (elevations lowerthan 24 cm in wall type I and 12 cm in wall type II) droppedto the active pressures. However, in some case, thedensification of the backfill soil partially compensated thisdrop. Furthermore, the rapid increase in the earth pressureimmediately after the start of shaking can be attributed tothe effect of negative excess pore water pressure generateddue to the displacement of the wall, i.e. the backfill soildilated under the low stress levels in the 1g model tests andby the temporarily undrained conditions the dilativebehavior of the backfill reduced the pore water pressures.On the other hand, the at-rest pressures recorded by thetransducers located on the positive back-slope portions ofthe walls increased considerably.

3.5. Point of application of the effective lateral earth thrust

Point of application of the effective lateral earth thrustnormalized by the height of the wall (solid marks) and wallacceleration (hollow marks) on the secondary vertical axisare plotted versus effective lateral earth thrust in Fig. 13. Inall of the models, the effective lateral thrust reached amaximum at extreme accelerations (either positive ornegative) and decreased as the acceleration decreased.The effective lateral thrust was greatest when the wall wasresisting the forward movement; that is when the inputacceleration was negative (landwards) and the inertia force

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Fig. 12. Time histories of the non-fluctuating effective lateral earth pressures on the wall: (a) QW1, (b) QW4, (c) QW5, (d) QW8, (e) QW12 and (f) QW15.

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acting on the wall was in the opposite direction.Furthermore, the normalized point of application of theeffective lateral thrust fluctuated in the range of 0.3–0.65which is within the middle one-third of wall’s height.Moreover, as the point of application dropped or rose, theeffective lateral thrust increased and this increase wasgreatest when the point of application dropped. This wasdue to the fluctuating dynamic effective lateral earth thrust(Pfde), rocking motion of the wall and the out of phasefluctuation of the pore water and the coarse backfill soil.

3.6. Point of application of the resultant water thrust

Similar to the effective lateral earth thrust, the point ofapplication of the resultant water thrust normalized by the

total depth of the water behind the wall (solid marks)and wall acceleration (hollow marks) on the secondaryaxis, are plotted versus the magnitude of the resultantwater thrust in Fig. 14. Due to the out of phase fluctuationof the pore water and backfill particles the behavior wasopposite the behavior observed for the lateral effectiveearth thrust. The resultant water thrust approached itsminimums at extreme accelerations (either positive ornegative) and increased to its maximum when the absoluteacceleration was smaller. In other words, the resultantwater thrust was less when the wall was acceleratingforward; as this forward acceleration decreased and thewall started to resist the movement, the water thrustincreased however because of the large permeability ofthe coarse backfill the excess pore water pressure dissipated

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Fig. 13. Wall acceleration and normalized point of application of the effective lateral earth thrust versus its magnitude: (a) QW4, (b) QW5, (c) QW5+,

(d) QW11, (e) QW14+ and (f) QW15.

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and the water thrust decreased as the wall reached itsmaximum resistance. After the maximum resistance of thewall was reached, the resistance decreased and the waterthrust increased slightly until the wall started acceleratingforward and the water thrust decreased to its minimum.Therefore, different paths were followed by the resultantwater thrust by increasing and decreasing of wall accelera-tion. The normalized point of application of the resultantwater thrust rose as its magnitude increased. This wasbecause of the fluctuating dynamic water thrust (Pfdw)which acted at a higher elevation than the elevation ofthe hydrostatic thrust and since it fluctuated betweennegative and positive values; therefore, the normalizedpoint of application of the resultant water thrust roseand fell.

3.7. Effect of weight of the wall on the seabed excess pore

water pressure

The time histories of the excess pore water pressure ratioðru ¼ uexcess=s0v0 Þ are plotted for models QW6, QW7, QW8and QW13 in Fig. 15. The pore pressure transducer PP5was located under the wall and PP6 and PP8 were locatedfarther away from the wall. These time histories show thatthe excess pore water pressure ratio was significantlysmaller under the wall. This was due to the weight of thewall, otherwise the shaking was able to develop larger ru.Similar behavior was observed in centrifuge and 1g shakingtable tests on foundations supported by sandy deposits andwas explained by the shear induced dilative soil response ofthe saturated soil below the footing and the inability of the

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Fig. 14. Wall acceleration and normalized point of application of the resultant water thrust versus its magnitude: (a) QW2, (b) QW5+, (c) QW6,

(d) QW11, (e) QW12+ and (f) QW13.

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earlier liquefied free-field soil to provide lateral stressesmore than its initial vertical effective stress to the foun-dation soil [28–34].

3.8. Settlement of the backfill soil

The surface settlement profile observed on the backfillsoil in models QW2, QW5, QW13, QW14 and QW15 isnormalized by the maximum settlement of each case and isplotted versus the distance from the top of the wall in Fig.16. This figure shows that the normalized settlement wasconsiderably smaller just behind the wall in QW2 and QW5and it reached maximum at a farther distance from the wallthan in models QW13, QW14 and QW15. This was due tothe larger hunch of the wall tested in models QW2 andQW5, which reduced the settlement at the immediate

margin behind the wall. In other words, wall type I had aregion immediately behind it, which was safer to locateindustrial and coastal structures such as cranes, roads, railsand cargo. Such a safety margin could have reduced thedamages of cranes and pavements behind the quay wallsduring the 1995 Kobe Earthquake. However, such a regionof safety was not developed in wall type II because of itssmaller hunch.

4. Conclusions

This study presents the static as well as seismic behaviorof hunched back quay walls by 16 shaking table experi-ments. The back-face slope of a hunchbacked wall wasdivided into two parts where the elevations below the

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Fig. 15. Time histories of the seabed excess pore water pressure ratios: (a) QW6, (b) QW7, (c) QW8 and (d) QW13.

Fig. 16. Normalized settlement profile of the backfill soil measured from

top of the wall.

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breaking point of the hunch were named negative back-slopes and the elevations above the break were named aspositive back-slopes. The results show that the negativeback-slope reduces the lateral earth pressures and thepositive back-slope increases them, which is consistent with

Coulomb’s lateral earth pressure theory. This made a verydifferent pressure distribution pattern behind the hunch-backed wall in comparison to the typical triangular patternwhich develops behind vertical back-face walls, causing thestatic thrust both before and after an earthquake to act at ahigher level behind the hunchbacked wall.The behavior of the wall showed that the relative density

of the seabed had a significant effect on the extent of failureof the wall and depending on the back-face shape, the wallrotated or overturned. A larger thrust and overturningmoment were applied on a wall with a softer seabed. Also itwas observed that if a wall survived an earthquake it wouldbecome more stable and would move less if the sameearthquake happened again and this is due to subsoildensification. Furthermore, depending on the height of thenegative and positive back-slopes of the wall, the staticactive thrust and overturning moment after an earthquakewould be larger or smaller than those before the excitation.Moreover, larger the negative back-slope portion of thewall, smaller would be the effective thrust and overturningmoment on the wall during the excitation.The effective lateral thrust reached its maximum when

the wall was resisting against the movement, i.e. when the

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input acceleration was landwards. The point of applicationof this thrust fluctuated within the mid-third of wall’sheight. The behavior of the resultant water thrust wasopposite and approached its maximum when the wallstopped accelerating. The point of application of theresultant water thrust rose as its magnitude increased.

All in all, in order to have a safer hunchback wall, thenegative and positive back-slope parts should be chosencarefully. In addition to this advantage of a hunchbackwall, is the stabilizing effect of the weight of the soil leaningon the positive back-slope of the wall which reduces slidingand overturning of the wall. Also there is a region of safety

Fig. A1. Corrected acceleration

Fig. A2. Corrected displacement

just behind a hunchbacked wall that has a comparativelyless settlement where industrial and coastal structures canbe located. Larger the hunch of the wall greater is this safearea behind the wall.

Appendix. The data recorded by the transducers were

corrected as described here

A.1. Acceleration

Most often during the shaking, the accelerometers tiltedas a result of liquefaction of the surrounding soil.

time histories of test QW06.

time histories of test QW06.

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Fig. A3. Corrected pore water pressure time histories recorded in test QW06.

Fig. A4. Corrected total lateral earth pressure time histories recorded in test QW06.

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Consequently, acceleration was recorded in the tilteddirection and included a static bias which was a componentof gravity. Assuming an accelerometer inclination of y,degrees, the measured acceleration would be as follows:

a ¼ g sinðyÞ þ ahor cosðyÞ. (A.1)

In which ahor is the horizontal acceleration and g is theacceleration of gravity. Filtering the recorded accelerationtime-history, the static bias, which is g sin(y) and conse-quently y was obtained and by subtracting this bias fromthe recorded acceleration, ahor cos(y) and thus ahor was

calculated at each time step. Furthermore, in the testswhich the upper block toppled, the readings of theacceleration transducer located on the top of the wall, i.e.ACC2 and ACC3 in wall types I and II, respectively, wererejected. The corrected acceleration time histories in testQW06 are presented in Fig. A1.

A.2. Displacements

The rotation or overturning of the wall caused errors inthe measured settlements. Therefore, the settlements were

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corrected by some geometrical analyzes where rotation ofthe wall was obtained from the acceleration transducerattached to the toe of the wall. Moreover, the settlement ofthe wall inclined the string of potentiometer-type displace-ment transducers which were measuring the horizontalmovement of the wall. This caused some errors in theirmeasurements and thus their readings were corrected usingthe settlement and rotation of the wall. The correcteddisplacement time histories of test QW06 are shown inFig. A2.

A.3. Pore water pressure

Because of the limited volume of the model container,the static pore water pressures increased as the wall andbackfill soil settled and hence more volume of materialswere submerging in water. However, this would nothappen in the field and the error is caused only due tothe limited space of the model tank. Thus, all of the waterpressure readings were corrected for this error so that thebefore and after shaking pore water pressures were thesame in the fixed embedded transducers, and for the porewater pressure transducers installed on the wall the staticpore water pressure only increased because of the settle-ment of the wall which causes the transducer to settle too.In a field quay wall, water depth can be raised instantly byevents such as tsunamis, but such cases were not intendedto be evaluated in this study. The pore water pressure timehistories of test QW06 corrected for this error are presentedin Fig. A3.

A.4. Total earth pressure

The same kind of correction applied to pore waterpressure readings was also applied to total earth pressuremeasurements. Corrected total earth pressure time historiesof test QW06 are shown in Fig. A4.

References

[1] Mononobe N, Matsuo M. On the determination of earth pressures

during earthquakes. In: Proceedings of the world engineering

congress, vol. 9. Tokyo; 1929. p. 177–85.

[2] Okabe S. General theory of earth pressure and seismic stability of

retaining wall and dam. J Jpn Soc Civil Eng 1924;10(5):1277–323.

[3] Ichihara M, Matsuzawa H, Kawamura M. Earthquake resistant

design of quay walls. In: Proceedings of the sixth world conference on

earthquake engineering, vol. 2, New Delhi; 1977. p. 265–74.

[4] Richard R, Elms DG. Seismic behavior of gravity retaining walls.

J Geotech Eng Div 1979;105(GT4):449–64.

[5] Sherif MA, Ishibashi I, Lee CD. Earth pressure against rigid retaining

walls. J Geotech Eng Div 1982;108(GT5):679–95.

[6] Fang YS. Dynamic earth pressure against rotating walls. PhD thesis,

University of Washington at Seattle, Washington; 1983.

[7] Bolton MD, Steedman RS. Modeling the seismic resistance of

retaining structures. In: Proceedings of the 11th international

conference on soil mechanics and foundation engineering. San

Francisco; 1985. p. 1845–8.

[8] Uwabe T, Moriya M. Shaking table model tests of sliding gravity-

type retaining walls during earthquake. In: Proceedings of the ninth

world conference on earthquake engineering, vol. 3. Tokyo; 1988.

p. 1125–32.

[9] Sato M, Shamoto Y, Goto S, Katsura Y, Kimata H. Centrifuge

reproduction of seismic liquefaction damage to caisson type quay

wall and its neighboring pile foundations. In: Proceedings of JSCE

symposium on Hanshin-Awaji earthquake disasters. Tokyo; 1996.

[10] Miura K, Kohama E, Kurita S, Ohtsuka N, Yoshida N. Behavior of

gravity type quay wall during earthquake observed in model shaking

table test. In: Proceedings of the seventh international offshore and

polar engineering conference, vol. 1, Honolulu; 1997. p. 683–8.

[11] Ghalandarzadeh A, Orita T, Towhata I, Yun F. Shaking table

tests on seismic deformation of gravity quay walls. Soils Found 1998:

115–32 [special issue].

[12] Matsuo H. Experimental study on the distribution of earth pressure

acting on a vertical wall during earthquakes. J Jpn Soc Civil Eng

1941;27(2).

[13] Jacobsen LS. Kentucky project report No. 13, Tennessee Valley

Authority Series, 1951; Appendix D.

[14] Ishii Y, Arai H, Tsuchida H. Lateral earth pressure in an earthquake.

In: Proceedings of the second world conference in earthquake

engineering, vol. 1. Tokyo; 1960. p. 211–30.

[15] Murphy VA. The effect of ground characteristics on the seismic

design of structures. In: Proceedings of the second world conference

on earthquake engineering. Tokyo; 1960. p. 1.

[16] Nandakumaran P, Joshi VH. Static and dynamic active earth

pressures behind retaining walls. Bull Ind Soc Earthquake Technol

1973;10(3).

[17] Matsuo M, Kenmochi S, Yagi H. Experimental study on earth

pressure of retaining wall by field tests. Soils Found 1978;18(3):

27–41.

[18] Sherif MA, Fang YS. Dynamic earth pressures on rigid walls rota-

ting about the base. In: Proceedings of the of eighth world con-

ference on earthquake engineering, vol. 6. San Francisco; 1984.

p. 993–1000.

[19] Sherif MA, Fang YS. Dynamic earth pressure on walls rotating about

top. Soils Found 1984;24(4):109–17.

[20] Sato M, Watanabe H, Takeda T, Shimada M. Simplified method to

evaluate caisson type quay wall movement. In: Proceedings of the

12th world conference on earthquake engineering. New Zealand;

2000.

[21] Kim S, Kwon O, Kim M. Evaluation of force components acting on

gravity type quay wall during earthquakes. Soil Dyn Earthquake Eng

2004;24:853–66.

[22] Nakamura S. Re-examination of Mononobe–Okabe theory of gravity

retaining walls using centrifuge model tests. Soils Found 2006;46(2):

135–46.

[23] Golder HQ. Coulomb and earth pressure. Geotechnique 1948;1:

66–71.

[24] Gibson AD, Scott RF. Comparison of a 1g and centrifuge model

dynamic liquefaction test: preliminary results. In: Proceedings of the

conference on earthquake geotechnical engineering IS-Tokyo ’95.

Tokyo; 1995.

[25] Hayashi K, Fujii N, Murakami T, Houjyou K. Direct comparison of

gravity model and centrifuge model for the seismic problem.

J Geotech Eng Jpn Soc Civil Eng 1997;41(582):207–16.

[26] Clough GW, Denby GM. Self-boring pressuremeter study of San

Francisco bay mud. J Geotech Eng Div 1980;106(GT1):45–63.

[27] Kezdi A. Lateral earth pressure. Foundation engineering handbook.

2nd ed. Van Nostrand Reinhold; 1991.

[28] Van Laak PA, Elgamal AW, Dobry R. Design and performance of an

electro-hydraulic shaker for the RPI centrifuge. In: Centrifuge’94.

1994; 1: 139–144.

[29] Whitman RV, Lambe PC. Earthquake like shaking of a structure

founded on saturated sand. In: Proceedings of the international

conference on geotechnical centrifuge modeling, vol. 1. Paris; 1988.

p. 529–38.

[30] Liu L, Dobry R. Seismic response of shallow foundations on

liquefiable sand. J Geotech Eng Div 1997;123(6):557–67.

ARTICLE IN PRESSA. Sadrekarimi et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 99–117 117

[31] Adalier K, Elgamal AW, Martin GR. Foundation liquefaction

countermeasures for earth embankments. J Geotech Geoenviron Eng

1998;124(6):500–17.

[32] Adalier K, Elgamal AW. Seismic response of adjacent saturated

dense and loose sand columns. Soil Dyn Earthquake Eng 2002;22(2):

115–27.

[33] Koga Y, Matsuo O. Shaking table tests of embankments resting on

liquefiable sandy ground. Soils Found 1990;30(4):162–74.

[34] Sadrekarimi A, Ghalandarzadeh A. Evaluation of gravel drains and

compacted sand piles in mitigating liquefaction. Ground Improve

2005;9(1):1–14.