1Chapter 27

2Experimental Investigation of Dynamic

3Behaviour of Cantilever Retaining Walls

4Panos Kloukinas, Augusto Penna, Anna Scotto di Santolo, Subhamoy

5Bhattacharya, Matthew Dietz, Luiza Dihoru, Aldo Evangelista,

6Armando L. Simonelli, Colin A. Taylor, and George Mylonakis

7Abstract The dynamic behaviour of cantilever retaining walls under earthquake

8action is explored by means of 1-g shaking table testing, carried out on scaled models

9at the Bristol Laboratory for Advanced Dynamics Engineering (BLADE), University

10of Bristol, UK. The experimental program encompasses different combinations of

11retaining wall geometries, soil configurations and input ground motions. The

12response analysis of the systems at hand aimed at shedding light onto the salient

13features of the problem, such as: (1) the magnitude of the soil thrust and its point of

14application; (2) the relative sliding as opposed to rocking of the wall base and the

15corresponding failure mode; (3) the importance/interplay between soil stiffness, wall

16dimensions, and excitation characteristics, as affecting the above. The results of the

17experimental investigations were in good agreement with the theoretical models used

18for the analysis and are expected to be useful for the better understanding and the

19optimization of earthquake design of this particular type of retaining structure.

P. Kloukinas (*) • G. Mylonakis

Department of Civil Engineering, Geotechnical Engineering Laboratory,

University of Patras, 26504 Patras, Greece

e-mail: pkloukin@upatras.gr; mylo@upatras.gr

A. Penna • A.L. Simonelli

Department of Engineering, University of Sannio,

Piazza Roma 21, 82100 Benevento, Italy

e-mail: aupenna@unina.it; alsimone@unisannio.it

A.S. di Santolo • A. Evangelista

Department of Civil and Environmental Engineering,

University of Naples Federico II, via Claudio 21, 80125 Napoli, Italy

e-mail: anscotto@unina.it; evangeli@unina.it

S. Bhattacharya • M. Dietz • L. Dihoru • C.A. Taylor

Department of Civil Engineering, University of Bristol,

Queen’s Building, University Walk, Bristol BS8 1TR, UK

e-mail: s.bhattacharya@bristol.ac.uk; m.dietz@bristol.ac.uk; Luiza.Dihoru@bristol.ac.uk;

colin.taylor@bristol.ac.uk

A. Ilki and M.N. Fardis (eds.), Seismic Evaluation and Rehabilitationof Structures, Geotechnical, Geological and Earthquake Engineering 26,

DOI 10.1007/978-3-319-00458-7_27, © Springer International Publishing Switzerland 2014

20 27.1 Introduction

21 Reinforced concrete cantilever retaining walls represent a popular type of retaining

22 system. It is widely considered as advantageous over conventional gravity walls as

23 it combines economy and ease in construction and installation. The concept is

24 deemed particularly rational, as it exploits the stabilizing action of the soil weight

25 over the footing slab against both sliding and overturning, thus allowing construc-

26 tion of walls of considerable height.

27 The traditional approach for the analysis of cantilever walls is based on the well-

28 known limit equilibrium analysis, in conjunction with a conceptual vertical surface

29 AD (Fig. 27.1b, c) passing through the innermost point of the wall base (vertical

30 virtual back approach). A contradictory issue in the literature relates to the calculation

31 of active thrust acting on the virtual wall back, under a certain mobilized obliquity

32 ranging naturally from 0 (a perfectly smooth plane) to φ (a perfectly rough plane).

33 Efforts have been made by numerous investigators to establish the proper roughness

34 for the analysis and design or this type of structures as reported by Evangelista et al.

concretewall (γw)

H

B

A

D

C

90 − f

t

b

B

D

H

V

H

V

ei

B

B´ = B – 2e

H´PAE

d E

PAE = 1–2Kg E (1 – av)g H'

2

C

A

a b

d

bodyforces

ah x Ww ah x Ws

equivalent wallinclination(ω = ω wall)

dry, cohesionlessbackfill (f, γ)

b - characteristic(ω = ω b )

vertical virtualback (ω = 0)

a - characteristic(ω = ω a )

ωwall

WsWw

PAE v

PAE h

SFsliding = H / Hult

SFbearing capacity =V / Vult

+ω

β

+ ah γ+ av γ

γ

+ye

4 2 2 2

Fig. 27.1 Pseudo-dynamic analysis of cantilever retaining walls for seismic loading: (a) Problem

under consideration, (b) seismic Rankine stress field characteristics, (c) Modified virtual back

approach by stress limit analysis, (d) Stability analysis according to Meyerhof (CEN 2003)

P. Kloukinas et al.

35(2009, 2010) and Kloukinas andMylonakis (2011). Nevertheless, the issue of seismic

36behaviour remains little explored. In fact many modern Codes, including the

37Eurocodes (CEN 2004) and the Italian Building Code (NTC 2008), do not explicitly

38refer to cantilever walls. The current Greek Seismic Code (EAK 2003) address the

39case of cantilever retaining walls adopting the virtual back approach in the context of

40a pseudo-static analysis under the assumption of gravitational infinite slope

41conditions (Rankine 1857) and various geometric constraints.

42Recent theoretical findings obtained by means of stress limit analysis

43(Evangelista et al. 2010; Evangelista and Scotto di Santolo 2011; Kloukinas and

44Mylonakis 2011) for the seismic problem of Fig. 27.1a indicate that a uniform

45Rankine stress field can develop in the backfill, when the wall heel is sufficiently

46long and the stress characteristics do not intersect the stem of the wall (ωβ < ωwall).

47Given that the inclination of the stress characteristics depends on acceleration level,

48a Rankine condition is valid for the vast majority of cantilever wall configurations

49under strong seismic action. This is applicable even to short heel walls, with an

50error of about 5 % (Huntington 1957; Greco 2001).

51Following the above stress limit analysis studies, closed-form expressions are

52derived for both the pseudodynamic earth pressure coefficient KAE and the resultant

53thrust inclination, δE (Fig. 27.1c), given by (Kloukinas and Mylonakis 2011):

δE ¼ tan�1 sinφ sin Δ1e � β þ ψ eð Þ1� sinφ cos Δ1e � β þ ψ eð Þ

� �(27.1)

54where Δ1e ¼ sin�1[sin(β + ψe)/sinφ] and ψe ¼ tan�1[ah/(1�av)] are the so-called

55Caquot angle and the inclination of the overall body force in the backfill. The same

56result for δE has been derived, in a different form, by Evangelista et al. (2009,

572010). In the case of gravitational loading (ψe ¼ 0), the inclination δE equals the

58slope angle β, coinciding to the classical Rankine analysis. In presence of a

59horizontal body force component, δE is always greater than β, increasing with

60ψe up to the maximum value of φ, improving consequently wall stability. The

61robustness of the above stress limit analysis becomes evident since under Rankine

62conditions and mobilized inclination δE, the stress limit analysis and the

63Mononobe-Okabe formula results coincide. These findings have been confirmed

64by numerical analysis results (Evangelista et al. 2010; Evangelista and Scotto di

65Santolo 2011).

66A second key issue in the design of the particular type of retaining systems deals

67with the stability analysis shown in Fig. 27.1d. Traditionally, stability control of

68retaining walls is based on safety factors against bearing capacity, sliding and

69overturning. Of these, only the first two are known to be rationally defined, whereas

70the safety factor against overturning is known to be misleading, lacking a physical

71basis (Greco 1997; NTC 2008; Kloukinas and Mylonakis 2011). It is important to

72note that the total gravitational and seismic actions on the retaining wall are resisted

73upon the external reactions H and V acting on the foundation slab. The combination

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

74 of these two actions, together with the resulting eccentricity e, determines the

75 bearing capacity of the wall foundation, based on classical limit analysis procedures

76 for a strip footing subjected to an eccentric inclined load (e.g. EC7, EC8). This

77 suggests that the wall stability is actually a footing problem and from this point of

78 view, understanding the role of the soil mass above the foundation slab and the soil-

79 wall interaction is of paramount importance. The above observations provided the

80 initial motivation for the herein-reported work.

81 27.2 Shaking Table Experimental Investigation

82 The dynamic behaviour of L-shaped cantilever walls was explored by means of 1-g

83 shaking table testing. The aim of the experimental investigation is to better under-

84 stand the soil-wall dynamic interaction problem, the relationship between design

85 parameters, stability safety factors and failure mechanisms, and the validation of

86 the seismic Rankine theoretical model. The test series were conducted to the Bristol

87 Laboratory for Advanced Dynamics Engineering (BLADE), University of Bristol,

88 UK. Details on the experimental hardware, materials, configurations and procedure

89 are provided in the ensuing.

90 27.2.1 Experimental Hardware

91 27.2.1.1 Earthquake Simulator (ES)

92 The 6DOF ES consists of a 3 m � 3m cast aluminum platformweighing 3.8 tonnes,

93 with payload capacity of 15 tonnes maximum and operating frequency range of

94 1–100 Hz. The platform sits inside an isolated, reinforced concrete seismic block

95 that has a mass of 300 tonnes and is attached to it by eight 70 kN servo hydraulic

96 actuators of 0.3 m stroke length. Hydraulic power for the ES is provided by a set of

97 six shared variable volume hydraulic pumps providing up to 900 l/min at a working98 pressure of 205 bar, with maximum flow capacity of around 1,200 l/min for up to

99 16 s at times of peak demand with the addition of extra hydraulic accumulators.

100 27.2.1.2 Equivalent Shear Beam (ESB) Container

101 The apparatus, shown in Fig. 27.2a, consists of 11 rectangular aluminum rings,

102 which are stacked alternately with rubber sections to create a flexible box of inner

103 dimensions 4.80 m long by 1 mwide and 1.15 m deep (Crewe et al. 1995). The rings

104 are constructed from aluminum box section to minimize inertia while providing

105 sufficient constraint for the K0 condition. The stack is secured to the shaking table

P. Kloukinas et al.

106by its base and shaken horizontally lengthways (in the x direction). Its floor is

107roughened by sand-grain adhesion to aid the transmission of shear waves; the

108internal end walls are similarly treated to enable complementary shear stresses.

109Internal side walls were lubricated with silicon grease and covered with latex

110membrane to ensure plane strain conditions.

111This type of containers should be ideally designed to match the shear stiffness of

112the soil contained in it, as shown in Fig. 27.2b. However, the shear stiffness of the

113soil varies during shaking depending on the strain level. Therefore the matching of

114the two stiffnesses (end-wall and soil) is possible only at a particular strain level.

115The “shear stack” at the University of Bristol is designed considering a value of

116strains in the soil close to failure (0.01–1 %). Therefore it is much more flexible

117than the soil deposit at lower strain amplitudes; as a consequence, the soil will

118always dictate the overall behaviour of the container (Bhattacharya et al. 2012).

119Indeed the shear stack resonant frequency and damping in the first shear mode in the

120long direction when empty were measured prior to testing as 5.7 Hz and 27 %

121respectively, sufficiently different from the soil material properties.

12227.2.1.3 Instrumentation

123As seen in Fig. 27.3, 21 1-D accelerometers have been used to monitor the shaking

124table, the shear stack and the wall-soil system, with the main area of interest laying

125on the wall itself and the soil mass in its vicinity, as well as the response of the free

126field. 4 LVDT transducers were used to measure the dynamic response and perma-

127nent displacements of the wall and 32 strain gauges were attached on the stem and

128the base of the wall, on three cross sections, to monitor the bending of the wall. The

129signal conditioning was made via appropriate amplifier and filter modules and data

130acquisitions frequency was set at 1,024 Hz. Additionally to the 57 data channels

131employed overall, a grid of coloured sand was used for monitoring the settlement of

132the backfill surface.

Fig. 27.2 Equivalent shear beam container (“shear stack”)

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

133 27.2.2 Shaking Table Model Setup

134 27.2.2.1 Model Geometry

135 The dimensions of the model are illustrated in Fig. 27.3, with the type and the

136 positions of the instrumentation used. The model consists of an L-shaped retaining

137 wall supporting a backfill of thickness 0.6 m and length five times its thickness,

138 resting on a 0.4 m thick base soil layer (equal to the wall foundation width, B).

139 The properties of the soil layers and detailed description of the instrumentation and

140 the various wall configurations are provided in the below.

141 The retaining wall was constructed from Aluminium 5,083 plates of thickness

142 32 mm. The width of the wall stem is 970 mm. A central wall segment of 600 mm

143 width was created by two 1 mm thick vertical slits penetrating 400 mm down into

144 the wall. The location of the slits was 185 mm from each side of the wall stem. The

145 base of the wall is subdivided into four 240 mm-wide aluminium segments that are

146 each secured to the wall stem using three M12 bolts. Properties of the aluminium

147 alloy are: unit weight γ ¼ 27 kN/m3, Young’s modulus E ¼ 70 GPa, Poisson’s

148 ratio ν ¼ 0.3.

zx

A1 A2

A7

A8A9A10A11

A3A4,5

A6

A13A14 A12

A15A16A17

A18

A19

A20 A21

D1

D3

D4

D2D: LVDT

A: Accelerometer

horizontal

vertical

1200

4800

1200200400900 900

300

300

300

600

400

1150

250

250

(+)

(+)

z

y

185600185

97032

32

570

b2 b1

Strain gaugepositions

88

50 front view(zy plane)

shaking table level

120 93

1 mmslits

400

wall model details

Configuration 1300

b2b1

7000

M12 bolts

Configuration 2250Configuration 3250

cross section(zx plane)

Fig. 27.3 Geometry and instrumentation of the shaking table model (dimensions in mm)

P. Kloukinas et al.

14927.2.2.2 Soil Material Properties

150The required soil configuration consists of a dense supporting layer and a medium

151dense backfill. The material proposed for both layers is Leighton Buzzard (LB)

152sand BS 881–131, Fraction B (D50 ¼ 0.82 mm, Gs ¼ 2,640 kg/m3, emin ¼ 0.486,

153emax ¼ 0.78). This particular soil has been used extensively in experimental

154research at Bristol and a wide set of strength and stiffness data is available (detailed

155references in Bhattacharya et al. 2012). The empirical correlation between peak

156friction angle φ and relative density Dr provided by the experimental work of

157Cavallaro et al. (2001) was used for a preliminary estimation of the soil strength

158properties.

159The packing density for each layer, determined from sand mass and volume

160measurements during deposition, and the corresponding predictions for the peak

161friction angles strength are summarized in Table 27.1. The base deposit was formed

162by pouring sand in layers of 150–200 mm from a deposition height of 0.6 m and

163then densifying by shaking. After densification, the height of the layer was reduced

164to 390 mm. The top layer was formed by pouring sand in axisymmetric conditions

165close to the centre of the desired backfill region, without further densification. The

166pouring was carried out by keeping the fall height steady, about equal to 200 mm, to

167minimize the densification effect of the downward stream of sand.

16827.2.2.3 Model Wall Configurations

169Three different Configurations (#1, #2, #3) for the wall model presented in Fig. 27.3

170were used to provide different response in sliding and rocking of the base. The

171characteristics of these configurations are shown in Table 27.2. After testing

172Configuration 1, the wall model was modified for Configuration 2. The wall heel

173was shortened by 50 mm and the toe was totally removed. In Configuration 3, the

174geometry of Configuration 2 was retained, after increasing the frictional resistance

175of the base interface from 23.5� to 28� (approximately equal to the critical state

t1:1Table 27.1 Soil properties

Soil layers Voids ratio, e Relative density, Dr Unit weight, γd kN/m3 Friction angle, φ a t1:2

Foundation 0.61 60 % 16.14 42� t1:3

Backfill 0.72 22 % 15.07 34� t1:4

t1:5aEstimated from Cavallaro et al. (2001)

t2:1Table 27.2 Pseudostatic critical accelerations and associated safety factors (SF)

Test

configuration

Critical acceleration

for SFsliding ¼ 1

SFBearing capacity at

critical sliding

acceleration

Critical

acceleration for

SFBearing capacity ¼ 1

SFsliding at critical

bearing capacity

acceleration t2:2

No 1 0.18g 7.45 0.35g 0.68 t2:3

No 2 0.14g 1.46 0.17g 0.93 t2:4

No 3 0.23g 0.44 0.17g 1.14 t2:5

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

176 angle), by pasting rough sandpaper. The interface friction angles were measured

177 in-situ by means of static pull tests on the wall. The differences between these three

178 Configurations, in terms of a pseudo-dynamic stability analysis according to EC7

179 (CEN 2003) are summarised in Table 27.2, ranging from a purely sliding-sensitive

180 wall (Configuration 1), to a purely rotationally sensitive one (Configuration 3).

181 A set of characteristic pictures of model details and installation procedures are

182 presented in Fig. 27.4.

183 27.2.3 Experimental Procedure

184 Each model Configuration was tested under the same dynamic excitation, described

185 in detail in the following paragraphs. Two different input motions, harmonic and

186 earthquake, were used in the form of sequential, increasing amplitude time

187 histories. The dynamic properties of the soil layers and the soil-wall interactive

188 system were investigated by means of the white noise exploratory procedure

189 described below. This kind of testing was repeated after every severe yielding of

190 the system to track for significant changes in the dynamic response and properties.

191 27.2.3.1 White Noise Excitation

192 During white noise exploratory testing, a random noise signal of bandwidth

193 1–100 Hz and RMS acceleration ¼ 0.005g was employed. During each exploratory

Fig. 27.4 Details of the experimental setup: (a) longitudinal aspect of the model, (b) wall face

instrumentation – Config. 2, (c),(d) pairs of accelerometers on shaking table and upper ring,

(e) backfill accelerometer, (f) sand pouring procedure, (g), (h) back and front view of the wall

P. Kloukinas et al.

194series test, and simultaneous data acquisition, system transmissibility was moni-

195tored using a two-channel spectrum analyser. The analyzer computes the frequency

196response function (FRF) between the input and the output signals of interest.

197Natural frequency and damping values for any resonances up to 40 Hz (i.e. within

198the seismic frequency range) were determined for well-defined resonances using

199the output of the analyser’s curve fitting algorithm by means of a least-squares error

200technique. Additionally, transfer functions can be determined between any pair of

201data channels to get a clear view of the system dynamics.

20227.2.3.2 Harmonic Excitation

203This type of input acceleration was imposed by sinusoidal excitation consisting of

20415 steady cycles. To smoothen out the transition between transient and steady-state

205response, the excitation comprises of a 5-cycle ramp up to full test level at the

206beginning of the excitation, and a 5-cycle ramp down to zero at the end. With

207reference to frequency and acceleration level, a set of five frequencies (4, 7, 13, 25

208and 43 Hz) was used at low acceleration amplitude of 0.05g, to study the dynamic

209response of the system. The excitation frequency of 7 Hz was then selected for a

210series of harmonic excitations with increasing amplitude, until failure. The

211conditions of the excitation are considered to be essentially pseudostatic, as the

212above frequency is much smaller than the resonant frequencies of the system, with

213respect to both the free field and the soil-wall system.

21427.2.3.3 Earthquake Excitation

215Three earthquake records from the Italian and American database were selected for

216the earthquake testing. Specifically, the Tolmezzo record from the Friuli, 1976

217earthquake, the Sturno record from Irpinia, 1980 and the Northridge record from

218Los Angeles, 1994. The authentic signals were scaled by a frequency scale factor

219of 5, derived from the scaling law n0.75, which is valid for 1-g modelling (Muir

220Wood et al. 2002), assuming a geometrical scale factor of n ¼ 9, corresponding to a

221prototype of 5.4 m high. The frequency-scaled signals were applied at low acceler-

222ation amplitude of 0.05g to measure the dynamic response of the model and then the

223Sturno record was selected for carrying out increasing amplitude dynamic testing,

224until failure in sliding or rocking of the retaining wall.

22527.3 Experimental Results and Discussion

226Some characteristic experimental measurements are presented in Figs. 27.5, 27.6,

22727.7, 27.8 and 27.9, for the observed failure mechanisms, accelerations, dynamic

228and permanent displacements and bending moments, organized in sets of graphs

229suitable for direct comparisons. Most of the results presented herein mainly relate to

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

230 Configurations 1 and 3, for they exhibit yielding near similar acceleration conditions

231 but in different modes. Limited results are presented for Configuration 2, which is

232 significantly weaker compared to the others, failing almost simultaneously in foun-

233 dation sliding and rotation (i.e., bearing capacity) mode, thus is less important for

234 comparison reasons.

235 In Fig. 27.5, measured settlement profiles at the state of failure are plotted

236 together with the assumed failure mechanisms for Configurations 2 and 3. The

237 following are worthy of note: First, these failure mechanisms were observed only

238 for transient earthquake loading, whereas in the case of harmonic excitation, the

239 settlement profile could not clearly reveal the emergence of the main failure planes,

240 as it had more-or-less a smooth parabolic shape. This can be explained in view of a

241 non-uniform settlement and deformation mechanism and stronger dynamic effects

242 imposed by earthquake loading. Although there is actually not a “rigid block”

243 response in the retained soil mass, the experimental findings show that the earth-

244 quake excitation induces a more uniform acceleration distribution within the

245 retained soil mass, which corresponds to a more uniform stress field, as assumed

246 in the pseudo-static analyses. Second, the assumed failure mechanisms confirm the

247 estimations based on the material properties, the stability analysis and the yield

248 accelerations presented in Tables 27.1 and 27.2 respectively.

249 The measurements of system displacement for all tested configurations are

250 summarized in Fig. 27.6. The total, cumulative settlement and rotation of the

251 wall, for each series of sequential input motions are presented in Fig. 27.6a, b,

252 and the incremental displacements for each input motion are presented in

253 Fig. 27.6c–e, indicating different behaviour of the wall models under the same

254 input. The measurements confirm the predictions for the expected failure modes

255 and the levels of critical acceleration. The sliding failure is clearly visible in

256 Configuration 1, as is the bearing capacity failure in Configuration 3. Configuration

257 2 although designed to be weaker in sliding, also exhibits significant rotational

258 deformations caused by the high eccentricities induced by the seismic thrust.

259 Rotational deformations are also observed in Configuration 1 for high acceleration

Fig. 27.5 Backfill surface settlement distribution at failure: (a) initial grid geometry – dimensions

in mm, (b),(c) settlement distributions for Configurations 2 and 3, respectively

P. Kloukinas et al.

260levels, revealing that walls resting on a compliant base exhibits local bearing

261capacity failure near the toe, due to high compressive stress concentration. This

262observation elucidates the importance of properly designing retaining structures to

263avoid developing significant rotational response.

264Results from Configurations 1 and 3 under harmonic excitation are plotted

265together in Fig. 27.7.

Fig. 27.6 Measurements of wall displacement and rotation for all configurations and various base

excitations. (a) Cumulative footing rotation versus sliding (LVDT-D1), (b) Cumulative footing

settlement (LVDT-D4) versus sliding, (c), (d) and (e) Incremental wall displacement (LVDTs

D1-D2-D3) for configurations 1, 2 and 3, respectively

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

Fig. 27.7 Comparison of typical experimental results for Configurations 1 and 3 under harmonic-

sinusoidal excitation: (a) measured wall accelerations, (b) corresponding wall displacements,

(c) negative acceleration distribution (maximum inertial forces towards the wall), (d) increment

of wall displacement (LVDTs D1-D2-D3) and (e) peak seismic increment of bending moment for

positive and negative acceleration

P. Kloukinas et al.

266The following can be observed: First the response of each Configuration is as

267expected. A translational response mode is evident in Configuration 1 and a rocking

268one in Configuration 3, respectively. Sliding discontinuities are obvious on the

269acceleration time histories of Configuration 1 (Fig. 27.7a), at a critical acceleration

270slightly higher than that of Table 27.2. Note that the translational yield acceleration

271is not steady, but always increases after every successive yielding, as even a small

272rotation causes penetration of the wall toe into the foundation soil thus increasing

273passive resistance. On the other hand, Configuration 3 starts rotating at initiation of

274yielding, without any evidence of sliding discontinuities on the recorded

275accelerogram. Second, in both cases the wall stem appears to have an amplified

276response, mainly because of foundation rocking and secondarily of pure bending of

277the stem. Naturally, this is more evident in Configuration 3. Third, both models

278exhibit a consistent, repeatable, behaviour with respect to yielding.

279The same results for earthquake loading on Configurations 1 and 3 are presented

280in Fig. 27.8. In this case, the input motion contains higher effective peak

281accelerations, but the number of important strong cycles (half cycle pulses) is

282only three. The sliding failure is again clearly visible in Configuration 1, as is the

283bearing capacity failure in Configuration 3 caused by the high eccentricities

284induced by seismic thrust. An important notice about the failure modes arising

285from the combination of the two comparisons is that the bearing capacity failure is

286more affected by the input acceleration level, whereas the behaviour of pure sliding

287mechanisms is mainly controlled by the time interval of the strong motion, as

288known from sliding block theory. Accordingly, rotational mechanisms appear to

289be more critical under strong earthquakes, even though they are strong enough

290against sliding (Figs. 27.7d and 27.8d). Moreover, some rotational deformation is

291also observed in Configuration 1 for high acceleration level, revealing that any wall

292resting on a compliant base exhibits local bearing capacity failure near the toe, due

293to concentration of high compressive stresses. This observation elucidates the

294importance of properly designing retaining structures to avoid development of

295significant rotational response.

296From the acceleration distributions of Figs. 27.7c and 27.8c, it can be observed

297that the earthquake loading results to conditions closer to the assumptions of

298pseudostatic analysis, as a soil mass moving together with the wall is evident,

299especially for the rotational mode of Configuration 3. Contrary to earthquake

300excitation, wall and soil under harmonic loading appear to respond in a quite

301different way. At last, the peak seismic increment of bending moments is compared

302in Figs. 27.7e and 27.8e. A noteworthy observation is that the earth pressure on the

303wall stem increases when the system moves towards the backfill, that is for an

304acceleration not critical for overall stability. On the other hand, at yielding acceler-

305ation of the system, earth pressure on the stem is minimum. This is in agreement

306with the findings of the analysis presented by Green et al. (2008) on a full scale

307numerical model and the experimental and numerical results of Al Atik and Sitar

308(2010). Comparing Configurations 1 and 3, it can be clearly identified that rota-

309tional modes induce lower earth pressure on the wall but different distribution

310leading to higher point of application of the thrust.

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

Fig. 27.8 Comparison of typical experimental results for Configurations 1 and 3 under seismic

excitation: (a) measured wall accelerations, (b) corresponding wall displacements, (c) negative

acceleration distribution (maximum inertial forces towards the wall), (d) increment of wall

displacement (LVDTs D1-D2-D3) and (e) peak seismic increment of bending moment for positive

and negative acceleration

P. Kloukinas et al.

311Finally, the response of Configuration 2 to harmonic and earthquake excitation

312with PGA ¼ 0.17g presented in Fig. 27.9, exhibits a similar behaviour to both

313Configurations 1 and 3, resulting to simultaneous sliding and rotational failure. As

314seen from both the acceleration time histories (Fig. 27.9a) and the failure

315mechanisms (Fig. 27.9b) the sliding failure mode prevails, which is consistent to

316the critical accelerations estimated in Table 27.2.

31727.4 Conclusions

318A series of shaking table tests on scaled models of cantilever retaining walls were

319conducted in the BLADE laboratory at the University of Bristol. The initial

320motivation of this experimental study was the validation of recent stress limit

321analysis solutions for the seismic design of this type of retaining structures

322(Evangelista et al. 2009, 2010; Kloukinas and Mylonakis 2011) in conjunction

323with the absence of any specific, relative regulations in established seismic codes,

324including EC8. Special issues related to stability design and response of walls

325founded on compliant base, were also incorporated. Preliminary interpretation of

326the experimental findings confirms the predictions of the theoretical analysis, with

327reference to the failure mechanisms and the critical yield accelerations of the

328system. Pseudo-static stability analysis proves to behave adequately for both

Fig. 27.9 Typical experimental results for Configuration 2: (a) measured wall accelerations for

harmonic sinusoidal and seismic excitation, (b) negative acceleration distribution (maximum

inertial forces towards the wall)

27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls

329 harmonic and seismic excitation, although important dynamic effects are evident in

330 the first case, dealing with the response of the backfill and the wall stem. On the

331 other hand, earthquake loading results to conditions closer to the assumptions of the

332 pseudo-static analysis, which are the uniform distribution of the acceleration and

333 the “rigid block” response of the backfill. Finally, the responses of the various wall

334 configurations confirm the equivalent footing analysis of wall stability and high-

335 light the importance of a proper design of walls founded on compliant base with

336 respect to sliding and rocking.

337 Acknowledgments The research leading to these results has received funding from the European

338 Union Seventh Framework Programme (FP7/2007–2013) for access to the Bristol Laboratory for

339 Advanced Dynamics Engineering (BLADE), University of Bristol, UK under grant agreement n�

340 227887 [SERIES].

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27 Experimental Investigation of Dynamic Behaviour of Cantilever Retaining Walls