Conti, Madabhushi, Viggiani - On the Behaviour of Flexible Retaining Walls Under Seismic Actions

8/12/2019 Conti, Madabhushi, Viggiani - On the Behaviour of Flexible Retaining Walls Under Seismic Actions

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Conti, R. et al. (2012). Geotechnique 62, No. 12, 10811094 [http://dx.doi.org/10.1680/geot.11.P.029]

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On the behaviour of flexible retaining walls under seismic actions

R . C O N T I , G . S . P. M A D A B H U S H I a n d G . M . B . V I G G I A N I

This paper describes an experimental investigation of thebehaviour of embedded retaining walls under seismicactions. Nine centrifuge tests were carried out on re-duced-scale models of pairs of retaining walls in drysand, either cantilevered or with one level of props nearthe top. The experimental data indicate that, for maxi-mum accelerations that are smaller than the critical limitequilibrium value, the retaining walls experience signifi-cant permanent displacements under increasing structur-al loads, whereas for larger accelerations the walls rotateunder constant internal forces. The critical accelerationat which the walls start to rotate increases with increas-ing maximum acceleration. No significant displacementsare measured if the current earthquake is less severethan earthquakes previously experienced by the wall. Theincrease of critical acceleration is explained in terms ofredistribution of earth pressures and progressive mobili-sation of the passive strength in front of the wall. Theexperimental data for cantilevered retaining walls indi-cate that the permanent displacements of the wall can bereasonably predicted adopting a Newmark-type calcula-tion with a critical acceleration that is a fraction of thelimit equilibrium value.

KEYWORDS: centrifuge modelling; diaphragm and in situ walls;dynamics; soil/structure interaction

La pre

sente communication de

crit une e

tude expe

rimen-tale sur le comportement de murs de soutenement encas-tres exposes a des secousses sismiques. On a procede aneuf essais centrifuges sur des maquettes de paires demurs de soutenement dans du sable sec, soit en porte-a-faux, soit avec un niveau detancons places a proximitede la partie superieure. Les donnees experimentales indi-quent que pour des accelerations maximales inferieures ala valeur dequilibre limite critique, les murs de soutene-ment subissent des deplacements permanentes significatifssous leffet de charges structurelles croissantes, tandisquen presence daccelerations plus importantes, les murstournent sous leffet de forces internes constantes. Lacce-leration critique a laquelle les murs commencent a tour-ner augmente avec une acceleration maximale croissante.Si le tremblement de terre en cours est moins severe queles tremblements de terre auxquels le mur a ete soumis,on ne mesure aucun deplacement significatif. Laugmenta-tion de lacceleration critique sexplique sous forme deredistribution des pressions de la terre et la mobilisationprogressive de la resistance passive sur lavant du mur.Les donnees experimentales pour des murs de soutene-ment en porte-a-faux indiquent quil est possible depredire de facon raisonnable les deplacements perma-nents du mur en adoptant un calcul du type Newmarkavec une acceleration critique qui est une fraction de lavaleur dequilibre limite.

INTRODUCTIONThe seismic design of earth-retaining structures is conven-tionally carried out using the pseudo-static approach, inwhich dynamic actions are represented as static DAlembertforces proportional to an equivalent acceleration, and theperformance of the system is quantified conventionally interms of a static safety factor against an assumed collapsemechanism. However, as noted by many authors (Iai & Ichii,1998; Iai, 2001; Callisto & Soccodato, 2010), the instanta-neous occurrence of limit conditions in the system during anearthquake does not necessarily imply the collapse of thestructure, but rather the occurrence of permanent displace-ments, provided that the behaviour of the system is ductile.

If the structure is designed using equivalent static actionscomputed using the maximum acceleration expected at thesite, no movement of the wall will occur during the earth-quake, as the system will never attain limit equilibriumconditions. This is safe, but may lead to unnecessarilyconservative and expensive design. On the other hand, if thepseudo-static actions are taken to be proportional to areduced equivalent acceleration, during the earthquake therewill be time intervals in which the safety factor is equal to1, and the structure will experience permanent displace-

ments. If the permanent displacement at the end of theearthquake is taken as a performance indicator, in the frame-work of performance-based design the choice of the equiva-lent acceleration to be used in the pseudo-static calculationscould be related to the maximum displacements that thestructure can sustain, with respect to different levels ofdesign earthquake motions.

The possibility of adopting a performance-based designfor retaining structures, even in the simple form just out-lined that is, by an appropriate reduction of the accelera-tion to be used in pseudo-static calculations dependscrucially on the ability to predict the displacements experi-enced by the wall during an earthquake. For gravity retaining

walls, the displacements are usually computed through thewell-established Newmark (1965) rigid-block analysis(Richards & Elms, 1979; Whitman, 1990; Zeng & Steed-man, 2000). Following this method, the relative displace-ments between the gravity wall and the soil are computed byintegrating twice the relative acceleration, a(t) ac, over thetime intervals in which the relative velocities are non-zero,where ac is a threshold or critical acceleration. This criticalacceleration, defined with respect to an assumed failuremechanism (generally sliding of the wall on its base),corresponds to the complete mobilisation of the soil strength(Elms & Richards, 1990), and for a rigid-perfectly plasticcontact between the foundation of the wall and the soil,depends solely on the geometry of the system and on the

strength of the soil.Experimental dynamic tests carried out on reduced-scale

models (Neelakantan et al., 1992; Richards & Elms, 1992)and dynamic numerical analyses (Callisto & Soccodato,

Manuscript received 21 March 2011; revised manuscript accepted 21March 2012. Published online ahead of print 3 September 2012.Discussion on this paper closes on 1 May 2013, for further details see

p. ii. SISSA, Trieste, Italy. University of Cambridge, UK. Universita di Roma Tor Vergata, Italy.


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2010) have shown that a Newmark-type calculation may beadopted, at least qualitatively, to also interpret the dynamicbehaviour of cantilevered walls or retaining walls with onelevel of props, where the wall can rotate when a state oflimit equilibrium is attained in the adjacent soil. In New-marks analysis, as the internal forces in the structuralmembers cannot exceed the maximum value attained fora ac, the increments of permanent displacements com-

puted for a.

ac correspond to rigid rotations of the wall.For accelerations a , ac, corresponding to which the soilstrength is not yet fully mobilised, any displacements areassociated solely with the elastic bending deflection of thewall, induced by the dynamic increment of the horizontalcontact stresses in the soil. It is evident that this kind ofdisplacement cannot be taken into account by the rigid-blockanalysis (Zeng & Steedman, 1993). However, Callisto &Soccodato (2010) have shown that, for credible values oftheir bending stiffness EI, cantilevered walls can be consid-ered, for all practical purposes, as infinitely rigid. Therefore,according to the rigid-block model, both the permanentdisplacements of the walls and the maximum internal forcesinduced by an earthquake depend on the critical accelerationac, which describes intrinsically the strength of the system.

Three different methods are proposed in the literature tocompute the critical acceleration of embedded retainingwalls, all of them derived from a limit equilibrium analysis.As far as anchored sheet pile walls are concerned, Towhata& Islam (1987) compute the critical acceleration assuming atranslation mechanism of the wall and of the retained soilwedge, whereas Neelakantan et al. (1992) assume a rigidrotation of the wall about the anchor system. Finally, forcantilevered walls, Callisto & Soccodato (2010) compute thecritical acceleration with the Blum (1931) method, assuminga rigid rotation of the wall about a point close to the toe.

The rigid-block method provides a powerful tool to com-pute the permanent displacements of retaining walls duringan earthquake. However, it is apparent that, when applied to

embedded retaining structures, it does not describe the wholeobserved behaviour satisfactorily. Centrifuge dynamic testson reduced-scale models of cantilevered (Zeng, 1990) andanchored (Zeng & Steedman, 1993) sheet pile walls, duringwhich successive earthquakes were applied to the models,have shown that embedded walls may accumulate significantpermanent displacements concurrently with an increase ofthe internal forces in the structural members. As thesepermanent displacements correspond mainly to rigid rota-tions of the walls (Madabhushi & Zeng, 2007), it followsthat rigid permanent displacements of embedded walls mayoccur even before the strength of the soil is completelymobilised that is, in the rigid-block scheme, before thecritical acceleration is attained. Also, Callisto & Soccodato

(2007) have shown that the threshold acceleration that has tobe considered in a Newmark-type integration (to match the

permanent displacements resulting from dynamic numericalanalyses of cantilevered walls) is smaller than the criticalvalue computed from a limit equilibrium analysis.

This research is an experimental investigation of thephysical phenomena that control the dynamic behaviour ofembedded retaining walls, aimed at developing suitablesimplified procedures to compute permanent displacementsof this type of structure under seismic loading. Tests were

carried out on reduced-scale models of pairs of retainingwalls in dry sand, either cantilevered or propped againsteach other by one level of support near the top. Constructionsequences were not modelled, as the scope of the work wasnot to simulate exactly the behaviour of a structure in thefield, but rather to identify the main features of the responseof this type of structure to seismic actions.

EXPERIMENTAL WORKThe experimental programme was carried out in the 10 m

diameter Turner beam centrifuge of the University of Cam-bridge (Schofield, 1980); it included a total of nine tests onmodels of pairs of retaining walls, in dry sand reconstitutedat different values of relative density, six of which cantilev-ered and three of which propped against each other, atcentrifugal accelerations of 80g and 40g respectively. Themodels were prepared within two equivalent-shear-beam con-tainers (Zeng & Schofield, 1996; Brennan & Madabhushi,2002). The main geometrical quantities defining the problemunder examination, and the relative densities of the modelsare reported in Table 1 and Fig. 1. Two different values ofthe width of the excavation, B, were considered, as theresults of numerical analyses indicate that the distance be-tween the walls can affect the behaviour of the systemduring the dynamic transient (Callisto et al., 2007).

Retaining walls were modelled using aluminium alloyplates with a bending stiffness at prototype scale similar tothat of a prototype tangent concrete pile wall with a

diameter of 400 mm. For propped walls, two square alumi-nium rods with an axial stiffness of about 1 3 106 kN/m atprototype scale, connected to the walls by cylindrical hingesallowing rotation in the vertical plane, were located at adistance of 195 mm from each other; see Fig. 2.

A standard fine silica sand was used to form the models,namely Leighton Buzzard, Fraction E Sand 100/170. Thespecific gravity of the sand is GS 2.65, its maximum andminimum void ratios are 1.014 and 0.613 respectively, andits critical friction angle is cv 328 (Tan, 1990; Jeyatharan,1991). Further details of the mechanical behaviour of thesand under monotonic, cyclic and dynamic loading condi-tions can be found in Visone & Santucci de Magistris(2009) and Conti & Viggiani (2011).

Instrumentation was used to measure accelerations of thewalls and at different locations in the model and on its

Table 1. Centrifuge model tests on pairs of cantilevered (CW) and propped (PW) walls (model scale)

Test Dri: % Drf: % h: mm d: mm s: mm tw: mm Z: mm B: mm

CW1 84 85 50 [4] 50 [4] 3.14 [0.25] 200 [16] 75 [6]CW2 53 59 50 [4] 50 [4] 3.14 [0.25] 200 [16] 75 [6]CW3 73 74 50 [4] 50 [4] 3.14 [0.25] 200 [16] 100 [8]CW4 55 62 50 [4] 50 [4] 3.14 [0.25] 200 [16] 100 [8]CW5 49 53 50 [4] 50 [4] 3.14 [0.25] 200 [16] 75 [6]CW6 69 75 50 [4] 50 [4] 3.14 [0.25] 200 [16] 100 [8]PW1 78 81 140 [5.6] 60 [2.4] 9 [0.3] 6.0 [0.24] 400 [16] 150 [6]

PW2 42 52 140 [5.6] 60 [2.4] 9 [0.3] 6.0 [0.24] 400 [16] 150 [6]PW4 44 59 140 [5.6] 60 [2.4] 9 [0.3] 6.0 [0.24] 400 [16] 200 [8]

Figures in brackets [ ] are prototype scale: m.

1082 CONTI, MADABHUSHI AND VIGGIANI


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boundaries, bending moments and horizontal displacementsof the walls, and axial loads in the props. Ground andcontainer accelerations during the dynamic stages of the testswere measured using miniature piezoelectric accelerometers;horizontal and vertical accelerations of the walls wererecorded using MEMS accelerometers, capable of measuringthe dynamic acceleration as well as the static accelerationdue to gravity and centrifuge swing-up. The bending mo-ments and the horizontal displacements of the walls weremeasured using six strain gauges glued to the middle sectionof each wall, and linear variable differential transducers(LVDTs). The axial load in the props was measured by twominiature load cells located in the mid section of eachsquare rod.

The dynamic input was provided by a stored angularmomentum (SAM) actuator (Madabhushi et al., 1998b).During each test, the model was subjected to a series oftrains of approximately sinusoidal waves (Table 2) withdifferent nominal frequencies f and amplitudes amax, and a

constant duration of 32 s for cantilevered walls and 16 s forpropped walls, at prototype scale. As an example, Fig. 3shows the acceleration time histories and the Fourier ampli-tude spectra of the five earthquakes that were applied at thebase of model PW2; the nominal frequencies were between1 Hz and 1.5 Hz, and the maximum acceleration, corre-sponding to earthquake EQ5, was equal to 0.41g. Theapplied signal is not perfectly harmonic, both because itsamplitude is not constant and because, although the nominalfrequency is predominant, significant energy content is asso-ciated also with secondary frequencies. Brennan et al.

B

h

d

tw

Z

(a)

s

(b)

B

h

d

tw

Z

Fig. 1. Problem geometry

Table 2. Earthquake features (prototype scale)

Test CW1 CW2 CW3 CW4 CW5 CW6 PW1 PW2 PW4

EQ1 f: Hz 0.50 0.38 0.50 0.38 0.50 0.50 1.00 1.00 1.00amax: g 0.08 0.05 0.07 0.07 0.09 0.06 0.23 0.21 0.22Ia: m/s 0.34 0.23 0.45 0.30 0.42 0.30 1.36 0.95 1.29

EQ2 f: Hz 0.75 0.50 0.75 0.50 0.75 0.75 1.50 1.50 1.50amax: g 0.17 0.07 0.16 0.07 0.16 0.11 0.36 0.30 0.31Ia: m/s 1.75 0.38 1.79 0.46 2.04 1.13 5.40 3.09 3.85

EQ3 f: Hz 0.63 0.63 0.63 0.63 0.63 0.63 1.25 1.25 1.25amax: g 0.10 0.13 0.11 0.12 0.11 0.11 0.38 0.36 0.37Ia: m/s 0.88 1.01 1.15 1.15 1.03 0.81 5.82 4.31 5.44

EQ4 f: Hz 0.75 0.75 0.75 0.75 0.75 0.75 1.50 1.50 1.50amax: g 0.18 0.15 0.16 0.15 0.19 0.17 0.42 0.35 0.39Ia: m/s 2.93 1.96 2.18 3.05 3.25 2.18 6.53 4.22 4.68

EQ5 f: Hz 0.63 0.63 0.63 0.63 0.63 0.63 1.25 1.25 1.25amax: g 0.17 0.14 0.13 0.16 0.16 0.19 0.48 0.41 0.45Ia: m/s 2.03 1.85 1.89 2.62 2.18 1.96 9.08 5.69 8.12

Fig. 2. Test PW2: photograph of model from the top, showinglocation of props

BEHAVIOUR OF FLEXIBLE RETAINING WALLS UNDER SEISMIC ACTIONS 1083


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(2005) report that such an extended frequency content

corresponds to effective mechanical actions on the model,related to the higher vibration modes of the SAM actuator.

In this paper, accelerations are positive rightwards, andthe horizontal displacements of the walls are positive to-wards the excavation. Moreover, all results are presented atprototype scale, unless explicitly stated.

OBSERVED BEHAVIOURPropped wall PW2

Test PW2 was carried out on a loose sand model of proppedwalls; see Table 1. The sand had an initial relative densityDr 42% corresponding to a unit weight d 14.37 kN/m

3

and a void ratio e 0.84. The relative density measured at the

end of the test was Dr 52%. Fig. 4 shows a cross-section ofthe model and the layout of the instrumentation, whichincluded 15 miniature piezoelectric accelerometers (A), twoLVDTs (LV) on the right wall, at 20 mm and 100 mm from thetop of the wall, six strain gauges (SG) on each wall, and twoload cells (LC) in the mid-sections of the props, for a total of31 transducers. The acceleration recorded by accelerometerA1, placed on the lower frame of the ESB box, is consideredas the input during the dynamic stages.

Figure 5 shows the time histories of the axial load meas-ured in one of the two props (LC1); of the bending momentsin the two walls, measured by transducers SG2, SG3 andSG4, located at 2.4 m, 3.5 m and 4.7 m from the top of thewalls; and of the free-field accelerations (A4, A5 and A6),

during earthquake EQ1. For sake of clarity the plot islimited to the time interval between 5 s and 10 s. The phaseshift between the acceleration time histories measured at twodifferent locations can be computed as j 2f t, where

t is the time for the wave to propagate from one accel-

erometer to the other, and f is the nominal frequency of theinput signal. During earthquake EQ1 the maximum phaseshift between accelerometers A5 and A6, located approxi-mately at the bottom and the top of the walls, is only 228,with a ratio of the height of the wall and the wavelengthH/ 0.16. As the wavelength depends on the shear stiff-ness of the soil, Vs/f, the ratio H/ increases for strongerearthquakes. However, the maximum value of H/ attainedduring all the tests in the experimental programme wasalways less than about 0.2, corresponding to a maximumacceleration phase shift between the bottom and the top ofthe wall of less than 608. It follows that, even if theacceleration is amplified, the soil wedge behind the retainingwall is accelerated approximately in phase (Steedman &

Zeng, 1990). The bending moments induced at differentlevels in the retaining walls are substantially in phase withone another, and with the accelerations recorded in the soilat the bottom of the wall (Figs 5(b) and 5(c)). As expected,when the accelerations in the model are maximum (right-wards), the bending moments in the right wall are alsomaximum, while the bending moments in the left wall areminimum (tt1). On the other hand, when the model isaccelerated leftwards, the bending moments on the left wallincrease while the bending moments on the right wall de-crease (tt2). The frequency of the bending moment timehistories in the two walls is therefore the same as thenominal frequency of the input signal (1 Hz). As far as theaxial load in the props is concerned (Fig. 5(a)), the signal

recorded by the load cell is maximum when the accelerationclose to the soil surface (A6) is both maximum and mini-mum. Consistently with the dynamics of the observed phe-nomenon, axial loads in the props increase when the soil is

A:g

a:g

A:g

a:g

A:g

a:g

A:g

a:g

A:g

a:g

amax 030 g

amax 036 g

amax 035 g

amax 041 g

222018161412108642 12108642

06

04

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t: s

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: Hzf

0

002

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002

004006

008

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008

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EQ1

EQ2

EQ3

EQ4

EQ5

amax 021 g

100 Hzf

150 Hzf

125 Hzf

150 Hzf

125 Hzf

Fig. 3. Test PW2: acceleration time histories and Fourier spectra of input signals



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Load cell

LVDT

Piezoelectric accelerometerUnit: mm (model scale)A1

190

175

A2

A3

400

901532020

675

150243

9 LC1/LC2

LV1

LV2

A9

A8

A7

20

80

A6

A5

60

30

210

A14

A15

A13A10

A11

A12

140

200

60

A4

Fig. 4. Test PW2: layout of transducers

t1 638 s t2 797 s

5 6 7 8 9 10

t: s(a)

5 6 7 8 9 10t: s(b)

5 6 7 8 9 10t: s(c)

5 6 7 8 9 10t: s(d)

M:kNm/m

M:kNm/m

a:g

140

160

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N:kN

30

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03

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0

01

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A5A6

A4

SG3SG4

SG2

Fig. 5. Test PW2, earthquake EQ1: (a) axial load in one prop; bending moment on (b) right and(c) left wall at z 3.5 m; (d) accelerations in free-field conditions measured between 5 s and 10 s



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accelerated both towards the right (maximum inertia forceson the right wall) and towards the left (maximum inertiaforces on the left wall). It follows that the frequency atwhich the internal forces vary in the prop system is twicethe nominal frequency of the input signal. Moreover, theobserved behaviour implies that the two walls interact withone another during the dynamic event.

Figures 6(a) and 6(b) show the bending moment distribu-

tions in the two walls at the end of the swing-up stage(static) and after each earthquake (residual); Fig. 6(c) showsthe horizontal deflection of the right wall, computed fromthe LVDT measurements and double integration of the straingauges recordings; Fig. 6(d) shows the time histories of theaxial load in one prop during the five earthquakes applied;and Fig. 6(e) shows the accelerations measured close to thesoil surface (A6). As expected, the static bending momentsin the walls are symmetric, with a maximum of about45 kNm/m, while the non-symmetrical distribution observedat the end of the earthquakes (Figs 6(a) and 6(b)) is due tothe asymmetry of the accelerations applied to the model.Dynamic bending moments increase with increasing maxi-

mum acceleration, such that the maximum dynamic bendingmoment of EQ3 and EQ5 are smaller than those measuredduring EQ2 and EQ4 respectively. Residual bending mo-ments progressively increase during the sequence of earth-quakes, and are much larger than their static values, with ameasured increase of about 6070% at the end of earth-quake EQ1, and about 100120% at the end of the test.Moreover, while the maximum permanent increments of the

bending moments occur after earthquakes EQ1 and EQ2,during subsequent events the maximum increments are about5% and 10% in the left and right walls respectively. Itfollows that, during earthquake EQ4, the right wall rotateswithout significant variations of the internal forces.

The horizontal displacements measured on the right wallat the end of the static stage are 6 mm and 13 mm for LV1and LV2 respectively (Fig. 6(c)). During the dynamic stagesthe wall rotates progressively towards the excavation, with afinal value of measured displacements of 8 mm and 54 mmfor LV1 and LV2 respectively. However, whereas the hor-izontal displacements of the wall increased during earth-quakes EQ1, EQ2 and EQ4, earthquakes EQ3 and EQ5 did

8

6

4

2

00 20 40 60 80 100

M: kNm/m

z:m

Left wall

(a)

M: kNm/m

100 80 60 40 20 0 120100 80 60 40 20 0 20

u: mm

Right wall

(b) (c)

LV1Static

EQ1

EQ2

EQ3

EQ4

EQ5

LV2

100

150

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350

0 30 60 90 120 150

N:kN

t:s

(d)

LC1

EQ1 EQ2 EQ3 EQ4 EQ5

06

04

02

0

04

06

0 30 60 90 120 150

a:g

t:s

(e)

A6

02

Fig. 6. Test PW2: (a), (b) bending moment distributions on the two walls; (c) horizontal displacements of right wall at end ofstatic stage and of each earthquake; time histories of (d) axial load in one prop and (e) accelerations measured close to surface



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not produce significant displacements (u 2 mm for LV2),even if their peak accelerations were larger than those ofEQ1 and EQ2 respectively. Table 3 reports the maximumaccelerations and the Arias intensities of the signals recordednear the top (A6) of the soil layer. The maximum accelera-tions increase between the first and last earthquake, withEQ3 and EQ5 having substantially the same values of amaxas EQ2 and EQ4 respectively, while the Arias intensities

measured during earthquakes EQ3 and EQ5 are significantlysmaller than those measured during the previous earthquakesEQ2 and EQ4. It appears that the permanent horizontaldisplacements of the walls depend on the entire accelerationtime history, and not just the current earthquake intensity.

The axial load in the prop at the end of the static stage(Fig. 6(d)) is about 130 kN. During the five earthquakes,great transient dynamic increments were measured, approxi-mately proportional to the current accelerations applied tothe model, but, as already observed in terms of bendingmoments in the walls, only at the end of earthquakes EQ1and EQ2 was a significant permanent increase of the axialload observed.

Cantilevered wall CW1Test CW1 was carried out on a dense sand model of

cantilevered walls; see Table 1. The sand had an initialrelative density Dr 84%, corresponding to a unit weightd 15.80 kN/m

3 and a void ratio e 0.68. The relativedensity measured at the end of the test was Dr 85%.Fig. 7 shows a cross-section of the model and the layout ofthe instrumentation, which included 16 miniature piezoelec-tric accelerometers, two LVDTs on the left wall, at 9 mmand 20 mm from the top of the wall, six strain gauges oneach wall and one horizontal MEMS accelerometer on the

top of each wall. As before, the acceleration recorded byaccelerometer A1 is considered as the input during thedynamic stages.

Figure 8 shows the time histories of the horizontal dis-placements of the left wall, together with the free-fieldaccelerations measured close to the soil surface, during thefive earthquakes applied. The initial displacements corre-spond to the end of the swing-up stage (static), and are

equal to 29 mm and 25 mm for LV1 and LV2 respectively.During the dynamic stages, the displacements of the wallprogressively increase towards the excavation, up to a finalvalue of 78 mm and 63 mm for LV1 and LV2 respectively.As already observed for test PW2, significant displacementsoccur during earthquakes EQ1, EQ2 and EQ4, whereasduring earthquakes EQ3 and EQ5 the walls do not experi-ence significant displacements, even if their peak accelera-tions were larger than those of EQ1 and EQ2 respectively.However, the maximum accelerations and Arias intensitiesmeasured near the top of the soil layer during earthquakesEQ3 and EQ5 (Table 3) are smaller than those of earth-quakes EQ2 and EQ4 respectively. This seems to suggest,again, that the permanent displacements of the walls dependon the entire acceleration time history, and not just on thecurrent earthquake intensity.

Figure 9(a) shows the horizontal deflection of the rightwall, computed from the LVDT measurements and doubleintegration of the strain gauges recordings, and correspondingto a rotation of the wall about a pivot point close to the toe,and Figs 9(b) and 9(c) show the bending moment distributionsin the two walls at the end of the swing-up stage (static) andafter each earthquake (residual). Static bending moments arenot perfectly symmetrical because of experimental problems(e.g. the action exerted by the electrical connections from thestrain gauges, rendering bending moments at the top of thewalls non-zero), and the non-symmetrical distribution ob-served at the end of the earthquakes is due mainly to theasymmetry of the input earthquake loading. At the end of the

static stage the maximum bending moments are 37 kNm/mand 23 kNm/m, increasing to about 69 kNm/m and 23 kNm/mafter the five earthquakes, for the left and right walls respec-tively. Bending moments show the same trend as displace-ments. Each time the current earthquake intensity and thecurrent bending moment during shaking are larger than forthe previous applied earthquakes, such as for earthquakesEQ1, EQ2 and EQ4, permanent increments of residual bend-ing moments occur. By contrast, even strong earthquakes,such as EQ3 and EQ5, do not produce permanent incrementsof the internal forces if a stronger earthquake has occurredbefore. It follows that residual bending moments in the walls,like permanent displacements, depend on the entire accelera-tion time history.

Table 3. Tests PW2 and CW1: maximum accelerations and Ariasintensity close to top of soil layer (A6)

EQ Test PW2 Test CW1

amax: g Ia: m/s amax: g Ia: m/s

1 0.22 2.09 0.11 0.422 0.36 14.43 0.23 2.433 0.37 9.87 0.15 1.084 0.44 22.61 0.26 4.075 0.46 13.41 0.25 2.65

LVDT

MEMS accelerometerPiezoelectric accelerometerUnit: mm (model scale)

200

223 20

560

75

M3

A12

50

100

A11

M4

20 83

LVDT1LVDT2

A9 A6

A8

A7 A5

A15

20

50

20

110

A17

A16A1050

A4 A1

A2

118

88

A3

30110

Fig. 7. Test CW1: layout of transducers



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DISCUSSION OF RESULTSFigure 10 shows, for all the centrifuge tests and all the

applied earthquakes, the maximum values of the axial forcein the props (Fig. 10(a)) and of the bending moments in the

two walls (Figs 10(b) and 10(c)), and the horizontal displa-cements of the walls (Figs 10(d) and 10(e)), as a function ofthe horizontal acceleration measured close to the soil surface(A6). Structural loads are normalised by the corresponding

static values in order to provide a direct comparison betweensoil models with different relative densities, and hence unitweight and peak friction angle; displacements are expressedas a percentage of the height of the wall. Figs 10(f) and

10(g) also show the critical acceleration, ac, of the proppedwalls, computed with the method proposed by Neelakantanet al. (1992), and of the cantilevered walls, computed withthe Blum (1931) method, for different values of the peak

0 60 120 180 240 300

t: s(a)

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:mm

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friction angle, p, and of the relative density, Dr: In bothmethods the critical acceleration is computed as the value ofacceleration corresponding to full mobilisation of the shearstrength of the soil and limit equilibrium of moments aboutthe position of the prop, for propped walls, or the pivotpoint, for cantilevered walls. The peak friction angle wascomputed as (Bolton, 1986)

jp jcv 5 Dr 10ln p9 1 (1)

where cv 328 is the critical-state friction angle of thesand, and p9 78 kPa is the mean effective stress at mid-

height of the sand layer. In the limit equilibrium analysis, afriction angle 128 was assumed at the contact betweenthe soil and the wall (Madabhushi & Zeng, 2007). Thecritical acceleration computed for cv is equal to 0.24gand 0.13g for propped and cantilevered walls respectively,while for the relative densities measured in the centrifugetests (40%


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pseudo-static acceleration a, again normalised by the corre-sponding static values. As observed above, in all the centri-fuge tests the accelerations measured behind the walls areapproximately in phase, so that uniform accelerationsthroughout the soil wedge behind the wall were assumed inthe pseudo-static analyses, without taking soil deformabilityinto account (Steedman & Zeng, 1990). Four different valuesof the friction angle were considered, 328, 388, 418, 508,

representative of the critical-state friction angle and of thepeak friction angle at three different values of the relativedensity of the soil.

Maximum bending moments and axial forcesAs expected, the maximum values of the axial forces in

the props and of the bending moments in the walls increasewith the amplitude of the accelerations applied to the models(Figs 10(a), 10(b) and 10(c)).

As far as propped walls are concerned, experimental dataare in reasonable agreement with the limit equilibriumvalues for models in both dense and loose sand. Moreover,for accelerations larger than about 0.4g, the maximum

values of the structural loads measured in the loose sandmodels do not experience significant variations. This is inagreement with the limit equilibrium prediction for the samemodels, as the critical acceleration computed for relativedensity Dr 42% is ac 0.44g; following the pseudo-staticapproach, for a ac the passive resistance of the soil infront of the walls is completely mobilised, and the internalforces in the structural members cannot increase further(Callisto & Soccodato, 2010). On the other hand, for canti-levered walls, measured bending moments are always largerthan the pseudo-static values, particularly for dense models.This may be because, in this case, the displacements inducedin the surrounding soil are generally greater than thoseexperienced by the propped walls, and hence the increase in

bending moments during stronger dynamic events is dueboth to the inertial forces acting on the soil and to theprogressive reduction of the mobilised soil friction anglewith increasing soil strains, not taken into account in thepseudo-static analysis.

Displacements of the wallsUnlike structural loads, horizontal displacements of the

walls do not show an increasing trend with the amplitude ofthe applied accelerations (Figs 10(d) and 10(e)); moreover,they are not zero, even at accelerations that are smaller thanthe critical value computed using limit equilibrium solutions.The measured displacements correspond mainly to rigid

rotations of the wall, either about a point close to its bottom(CW tests), or about the prop (PW tests). They are accom-panied by an increase of the loads in the structural membersif the acceleration is below the critical value computed bylimit equilibrium, whereas they occur without any changesin the structural loads if the critical value of the accelerationis exceeded, as is the case for some of the earthquakesapplied to the models of propped walls.

The fact that the displacements are not proportional to themaximum acceleration is consistent with the observation thatstrong earthquakes can produce negligible displacements ifthey are applied after the retaining structure has undergone astronger event, as shown in detail for tests CW1 and PW2.If the critical acceleration is defined as the value of the

acceleration at which the wall starts to rotate, rather than thevalue of the acceleration at which the soil strength is fullymobilised and the moment safety factor is 1 (limit equili-brium), the observations imply the existence of a sort of

hardening effect, in which the critical acceleration mayincrease during an earthquake.

Figure 11 shows the acceleration time histories recordedat the soil surface, on the left, and the measured horizontaldisplacements of the left wall, on the right, for all earth-quakes of test CW1. A Newmark calculation was carried outfor each earthquake, in which the critical acceleration acwas found by trial and error to match the computed dis-

placement and that measured at the end of each earthquake.Inspection of Fig. 11 reveals that the displacement timehistories obtained using a constant value of the criticalacceleration are completely different from the observed ones.The only way in which the displacement time histories canbe back-calculated using a Newmark analysis is to admitthat the critical acceleration varies during the earthquakes.For the first earthquake, the initial value of the criticalacceleration is close to zero, whereas for each successiveearthquake the initial critical acceleration is the same as thefinal value computed at the end of the previous earthquake.The data in Fig. 11 also indicate that the critical accelerationrequired to match the observed displacement time historiesincreases very rapidly at the beginning of the earthquake(first peak of the imposed acceleration), and then only veryslowly during the rest of the earthquake.

The final value of the critical acceleration at the end ofthe five applied earthquakes is ac 0.196g, smaller than thelimit equilibrium value computed using the peak value ofthe friction angle (ac 0.69g). It is evident that, had theNewmark analysis been carried out using the latter, thedisplacements of the wall would have been zero; in otherwords, the pseudo-static analysis predicts that the wall is notin a state of limit equilibrium during any of the appliedearthquakes, as the available strength of the soil is not fullymobilised. On the other hand, using the critical accelerationcorresponding to the friction angle at constant volume(ac 0.13g) the Newmark displacements computed duringearthquake EQ1 would have been zero, while those com-

puted for earthquakes EQ2, EQ4 and EQ5 would have beenmuch larger than measured.

A Newmark-type calculation was also carried out for allearthquakes applied in the tests on cantilevered walls, inwhich LVDTs measurements were available to obtain theconstant values of critical acceleration ac required to matchthe measured permanent displacement at the end of eachearthquake. Fig. 12 shows the computed values of ac as afunction of the maximum acceleration amax, both normalisedby the limit equilibrium value of the critical acceleration,ac,eq:lim, for those earthquakes in which significant displace-ment were measured that is, which were stronger than anypreviously applied earthquake. The data indicate that thecritical acceleration increases linearly with the maximum

acceleration applied in the test, and all data plot very closelyto the same line, independently of the relative density of themodel.

The question arises why, for embedded retaining walls,does the critical acceleration increase during an earthquake?Zeng (1990) explained this phenomenon with the densifica-tion of the sand under dynamic loading, resulting in aprogressive increase of the strength and of the stiffness ofthe backfill. In the centrifuge tests performed, however, theobserved increase of critical acceleration cannot be ex-plained solely in terms of sand densification: as an example,the total variation ofDrmeasured in test CW1 was only 1%,whereas the variation of relative density required to explainthe increase of ac obtained by back-analysis of the observed

displacements would be of the order of 2030%.It is felt that the reason why the critical acceleration

increases during an earthquake is connected to redistributionof earth pressures and progressive mobilisation of the pas-



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ac 0089 g

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Newmark ( 0082 )ac g

Measured (LV1)





Fig. 11. Test CW1: (a) accelerations measured close to soil surface (A6) and critical acceleration; (b) measured andcomputed horizontal displacement of wall



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sive strength in front of the wall. In fact, when the activepressure behind the wall increases as a result of seismicloading, equilibrium of moments requires a larger proportionof the passive earth pressure to be mobilised in front of thewall, which can happen only with a progressive rotation ofthe structure towards the excavation, resulting in finitedisplacements well before the strength of the soil is fullymobilised. This is completely different from the case of arigid block or a gravity retaining wall sliding on its base,where the contact is rigid-perfectly plastic, and full mobilisa-tion of the strength occurs with zero relative displacements.

The displacements required to mobilise a larger proportion

of the passive strength are inelastic that is, they are notrecovered when the acceleration decreases and thereforeno further rotations occur if the acceleration applied issmaller then the maximum value experienced by the wall. Itfollows that ac increases rapidly as the acceleration increasesfrom zero to its maximum value (first peak), and then shouldbe constant if the maximum value of the acceleration is notexceeded again. In the dynamic inputs applied in the cen-trifuge, the maximum acceleration is always reached duringthe first peak; the small increase of ac observed duringsuccessive peaks may well be due to sand densification, assuggested by Zeng (1990). This physical interpretation alsoexplains why the critical acceleration at the beginning of thefirst earthquake is close to zero (any increase of the active

pressure above its static value requires a larger proportion ofthe passive strength to be mobilised in front of the wall),and why the critical acceleration at the beginning of eachsuccessive earthquake is the final value computed for theprevious one. Once the passive strength of the soil in frontof the wall is fully mobilised, and hence the critical accel-eration has reached its maximum, limit equilibrium value,the wall will rotate without any changes of critical accelera-tion other than those connected to small hardening due todensification, or even small softening due to the progressivereduction of soil strength from its peak value towards itscritical-state value as displacements increase.

Residual bending momentsConsistent with previous experimental evidence for gravity

(Andersen et al., 1991), cantilevered (Zeng, 1990; Madab-hushi & Zeng, 2007) and anchored (Zeng, 1990; Whitman

& Ting, 1993; Zeng & Steedman, 1993; Watabe et al.,2006) retaining walls, high residual bending moments weremeasured after the earthquakes, corresponding to about8090% of the maximum values recorded during shaking.According to Whitman (1990) and Zeng (1990), residualmoments are associated with the tendency of the sand todensify when vibrated, which in turn implies that the hor-izontal stresses remain locked behind the wall even after the

earthquake, similarly to what happens during compaction ofa backfill. Only when the previous maximum horizontalstress is again exceeded that is, a stronger earthquake isapplied to the structure will permanent deformations beinduced that will cause still higher residual earth pressure onthe wall (Zeng, 1990). However, as already discussed interms of displacements, the variations of relative densitymeasured in the centrifuge tests cannot fully justify theobserved behaviour of embedded walls. Once again, webelieve that the observed behaviour may be justified bystress redistribution and progressive mobilisation of the soilstrength on the passive side of the wall produced by theearthquake, as confirmed by preliminary numerical analyses(Conti, 2010).

CONCLUSIONSThe experimental results discussed in this paper show that

both propped and cantilevered retaining walls experiencenearly rigid permanent displacements even for maximumaccelerations that are smaller than the critical limit equili-brium value corresponding to full mobilisation of the soilstrength. For cantilevered retaining walls the magnitude ofthe horizontal displacement of the top of the wall can be upto 12% of the total height of the wall, whereas for proppedretaining walls the horizontal displacement of the toereaches about 0.51% of the total height of the wall,depending on soil relative density. These values are largerthan allowable displacements of embedded retaining walls

quoted in many recommendations and codes of practice,such as PIANC (2001), the US Navy (Ferritto, 1997) andItalian (NTC, 2008), and cannot be predicted using a New-mark analysis with the limit equilibrium value of the criticalacceleration, as in this case zero displacements would becomputed.

In this experimental research, the maximum accelerationexceeded the limit equilibrium critical value only for testson propped walls. In this case the retaining walls experi-enced even larger permanent displacements, of the order of1.5% of the total height of the wall, under constant structur-al loads. A Newmark analysis carried out using the limitequilibrium value of the critical acceleration would yielddisplacements that are much smaller than observed, as it

would overlook the displacements experienced by the wallbefore the acceleration reaches the limit equilibrium criticalvalue.

In a performance-based design approach, it may berequired that the permanent displacement of the structureunder an earthquake of given maximum acceleration becomputed. A practical solution to the problem of predictingthe permanent displacements may be that of using a New-mark analysis with a value of the critical acceleration that isa fraction of the limit equilibrium value. The experimentaldata for cantilevered retaining walls indicate that the perma-nent displacements of the wall at the end of each earthquakecan be reasonably predicted adopting a Newmark-type calcu-lation with a critical acceleration that is 72% of the limit

equilibrium value, independently of soil relative density.However, the data refer only to cantilevered walls in drysand with approximately the same safety factor under staticconditions, and subjected to maximum accelerations less

a

ac

c,eq

.lim

/

a ac max072

a amax c,eq.lim/

100806040200

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Test CW 3

Test CW 5

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Fig. 12. Newmark analysis of CW test results: required value of

critical acceleration as a function of maximum acceleration



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than the limit equilibrium critical value. Further research isrequired to investigate the appropriate value of critical accel-eration to be used in a Newmark-type calculation to predictcorrectly the permanent displacements of propped walls, ofwalls with different static safety factors and of walls sub-jected to maximum accelerations larger than the limit equili-brium critical acceleration. Finally, the experimental workwas limited to retaining walls in dry sand, and further testing

is required to clarify the role of the presence of the porewater, for either saturated or unsaturated soils.

ACKNOWLEDGEMENTThe work presented in this paper was partly funded by the

Italian Department of Civil Protection under the ReLUIS20052008 research project.

NOTATIONA Fourier spectrum amplitudea acceleration

ac critical value of acceleration

ac,eq:lim limit equilibrium value of critical accelerationamax maximum value of accelerationDr relative density

Drf final relative densityDri initial relative density

d depth of embedmentEI bending stiffness of walls

e void ratiof nominal frequency

GS specific gravityg gravity acceleration (9.81 m/s2)

H total wall height (h+ d)h excavation depth

Ia Arias intensityM bending moment

Mmax maximum value of bending moment

Mst static value of maximum bending momentN axial load

Nmax maximum value of axial loadNst static value of axial loadp9 mean effective stress

s distance of props from top of the wallt time

t time intervaltw wall thicknessu horizontal displacement

u increment of horizontal displacementVS shear wave velocity

Z thickness of sand layer friction angle at soil/wall contactd dry unit weight wavelength

friction angle phase shift of acceleration time historiescv constant-volume friction anglep peak friction angle

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Conti, Madabhushi, Viggiani - On the Behaviour of Flexible Retaining Walls Under Seismic Actions