SERIES · SERIES 227887 DYNCREW Project ix List of Figures Figure 2.1 Pseudo-dynamic analysis of...

SEVENTH FRAMEWORK PROGRAMME

Capacities Specific Programme

Research Infrastructures

Project No.: 227887

SERIES

SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR

EUROPEAN SYNERGIES

Work package [WP8 – TA4 EQUALS]

DYNCREW

Experimental Investigation of the Dynamic Behaviour of Cantilever

Retaining Walls

- Final Report -

User Group Leader: Prof. A. Evangelista

Revision: Final

July, 2013

SERIES 227887 DYNCREW Project

i

ABSTRACT

The document reports the outcomes of an experimental test campaign, under 1-g shaking table

testing, for the validation of the performance of cantilever retaining walls to dynamic loading.

Cantilever retaining walls represent a popular type of retaining system, widely considered

advantageous over conventional gravity walls as it combines economy and ease in construction

and installation. Apart from few available limit analysis solutions, the seismic behaviour of this

type of walls is little explored. In the frame of the research presented in this report, a systematic

investigation on scaled wall models was carried out at the Earthquake and Large Structures

Laboratory (EQUALS) - University of Bristol. The experimental program encompasses different

combinations of retaining wall geometries, soil configurations and input ground motions (white

noise, sine dwells and actual recorded motions from the Italian and American database). The

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

problem, such as: (1) the magnitude of the soil thrust and its point of application; (2) the relative

sliding as opposed to rocking of the wall base and the corresponding failure mode; (3) the

importance/interplay between soil stiffness, wall dimensions, and excitation characteristics, in

affecting the above. The data obtained by the experimental investigations were in good

agreement with the results by the theoretical models used for the analysis and are expected to be

useful for the better understanding and the optimization of earthquake design of this particular

type of retaining structure.

Keywords: Cantilever Retaining Walls, Earthquake Design, Dynamic Earth Pressures, Soil-

Structure-Interaction, Experimental Analysis, Shaking Table Testing


ii


iii

ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Union Seventh

Framework Programme [FP7/2007-2013] for access to EQUALS, University of Bristol under

grant agreement n° 227887 [SERIES].


iv


v

REPORT CONTRIBUTORS

University of Naples Federico II Aldo Evangelista

Anna Scotto di Santolo

University of Sannio Armando Lucio Simonelli

Augusto Penna

Pamela Imbriale

Carmine Lucadamo

University of Patras George Mylonakis

Panos Kloukinas

University of Bristol Matt Dietz

Colin Taylor


vi


vii

CONTENTS

CONTENTS .....................................................................................................................................v

List of Figures .............................................................................................................................. xiii

List of Tables ............................................................................................................................ xxxi

1 The DYNCREW Project ...............................................................................................................1

1.1 INTRODUCTION .................................................................................................................1

2 The experimental program ............................................................................................................1

2.1 THEORETICAL BACKGROUND ......................................................................................2

2.2 EXPERIMENTAL DESIGN AND SETUP ..........................................................................4

2.2.1 The Earthquake Simulator .............................................................................................4

2.2.2 The Equivalent Shear Beam container (shear “stack”) .................................................5

2.2.3 Instrumentation and recording hardware .......................................................................7

2.2.4 Shaking table model geometry and instrumentation ...................................................10

2.2.5 Soil material and soil layers properties .......................................................................15

2.2 EXPERIMENTAL PROCEDURE .....................................................................................19

2.3.1 Model Configurations ..................................................................................................19

2.3.2 Iterative testing procedure ...........................................................................................20

2.3.3 White noise testing ......................................................................................................21

2.3.4 Dynamic testing with harmonic, sinusoidal excitation ................................................21

2.3.5 Dynamic testing with real earthquake records ............................................................22

3 Experimental results....................................................................................................................24

3.1 DYNAMIC PROPERTIES OF THE MODEL ...................................................................24


viii

3.2 EXPERIMENTAL RESULTS FOR DISPLACEMENTS, SEISMIC LOADS

AND FAILURE MECHANISMS EXPERIMENTAL DESIGN AND SETUP ................37

4 Interpretation of displacements in the light of sliding block theory predictions ........................47

5 Interpretation of dynamic bending moments ..............................................................................57

6 Conclusions .................................................................................................................................64

References ......................................................................................................................................66

Appendix .......................................................................................................................................69


ix

List of Figures

Figure 2.1 Pseudo-dynamic analysis of cantilever retaining walls for seismic loading: (a)

Seismic Rankine stress field for the problem under consideration, (b) Seismic Rankine

stress tensor and stress, (c) Modified virtual back approach by stress limit analysis, (d)

Stability analysis according to Meyerhof (EC 7) ......................................................................... 3

Figure 2.2 The shaking table of EQUALS – BLADE (University of Bristol, (UK) .................. 5

Figure 2.3 General and inside aspect of the Equivalent Shear Beam container (“shear

stack”) (a) side walls lubricated with silicone grease and covered with latex membrane, (b)

wooden floor and (c) transverse walls roughened by sand-grain adhesion ................................. 6

Figure 2.4. Schematic diagram of the EBS container (Bhattacharya et al., 2012) ..................... 7

Figure 2.5 Illustration of the model and experimental equipment during the first phase of

testing ........................................................................................................................................... 9

Figure 2.6 Details of the experimental setup (Second phase of testing): (a) longitudinal

aspect of the model, (b) wall face instrumentation (Configurations No2 & No3), (c),(d)

pairs of accelerometers on shaking table and upper ring, (e) backfill accelerometer, (f) sand

pouring procedure, (g), (h) back - covered with rough sandpaper - and front view of the

wall (Configuration No1) ............................................................................................................. 9

Figure 2.7 Illustration of geometry and instrumentation of the shaking table model

(dimensions in mm) .....................................................................................................................10

Figure 2.8 Geometry and assembling of the retaining wall model (dimensions in mm) ............12

Figure 2.9. Strain gauges positions .............................................................................................13

Figure 2.10 Comparison of dynamic bending deformation recorded at the strain gauges at

the bottom of the cantilever (slab connection area) .....................................................................14


x

Figure 2.11 Friction angle of Leighton Buzzard Sand as a function of mean effective stress

and relative density (from Bhattacharya et al., 2012) ..................................................................16

Figure 2.12 Empirical correlations for dynamic soil properties of LB sand derived from the

laboratory dynamic tests of Cavallaro et al. (2001) .....................................................................18

Figure 2.13 Dynamic soil properties of LB sand measured experimentally by shaking

table testing at EQUALS (from Dietz & Muir Wood, 2007) ......................................................19

Figure 2.14 Harmonic base excitation at the frequency of 7Hz and amplitude 0.05g ...............22

Figure 2.15. Scaled seismic signals imposed as base acceleration ............................................23

Figure 2.16 Comparison between the authentic and modified Sturno record .............................24

Figure 3.1 Accelerometer positions for white noise testing evaluation .....................................25

Figure 3.2 Transfer functions from the wall response in Configuration No1 – wall placed

on the foundation layer before backfill construction ..................................................................27

Figure 3.3 Transfer functions from the foundation layer response in Configuration No1 –

before backfill construction ........................................................................................................28

Figure 3.4 Transfer functions from the wall response in Configuration No1 – after backfill

construction .................................................................................................................................29

Figure 3.5 Transfer functions from the backfill response in Configuration No1 .......................30

Figure 3.6 Transfer functions from the wall response in Configuration No3 – wall placed

on the foundation layer before backfill construction (*refers to the soil prism behind the

wall) .............................................................................................................................................31

Figure 3.7 Transfer functions from the wall response in Configuration No3 after the

construction of the backfill ..........................................................................................................32

Figure 3.8 Transfer functions from the backfill response in Configuration No3. ......................33

Figure 3.9. Variation of earth pressure coefficient K0 at very low confining stress (from

Chu & Gan, 2004) .......................................................................................................................34

Figure 3.10. Increase of the soil shear modulus with depth, based on empirical relations .........35

Figure 3.11 Resonant frequency of the two-layered medium with properties: H1 = 0.4m,

Vs1 = 157m/s, H2 = 0.6m, Vs2 = 113m/s ......................................................................................36

Figure 3.12. Elastic parameters of the soil layers of the problem ...............................................37

Figure 3.13. Measurements of wall displacement and rotation for all configurations and


xi

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 No1, No2 and No3, respectively ...........41

Figure 3.14. Comparison of typical experimental results for Configurations No1 and No3

under harmonic-sinusoidal excitation: (a) measured wall accelerations, (b) corresponding

wall displacements, (c) positive acceleration distribution (maximum inertial forces towards

the backfill), (d) negative acceleration distribution (maximum inertial forces towards the

wall) .............................................................................................................................................42


under seismic excitation: (a) measured wall accelerations, (b) corresponding wall

displacements, (c) positive acceleration distribution (maximum inertial forces towards the

backfill), (d) negative acceleration distribution (maximum inertial forces towards the wall) .....43

Figure 3.16. Typical experimental results for Configuration No2: (a) measured wall

accelerations for harmonic sinusoidal and seismic excitation, (b) corresponding wall

displacement, (c) positive acceleration distribution (maximum inertial forces towards the

backfill), (d) negative acceleration distribution (maximum inertial forces towards the wall) ....44


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. .......................................45


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 ........................................46

Figure 3.19. Backfill surface settlement distribution at failure: (a) initial grid geometry -

dimensions in mm, (b),(c) settlement distributions for Configurations No2 and No3,

respectively. .................................................................................................................................47

Figure 4.1. Gravity retaining wall on rigid base examined against (a) sliding according

Richards & Elms, (1979) and (b) rotation about the toe (point O) according to Zeng &


xii

Steedman, (2000) .........................................................................................................................48

Figure 4.2. Comparisons of experimental permanent displacement and rotation with the

predictions of sliding/rotating block theory – Configuration No1 under harmonic loading .......51


predictions of sliding/rotating block theory – Configuration No3 under harmonic loading ......52

Figure 4.4.Comparisons of experimental permanent displacement and rotation with the

predictions of sliding/rotating block theory – Configuration No1 under seismic loading .........53


predictions of sliding/rotating block theory – Configuration No3 under harmonic loading ......54

Figure 4.6. Comparisons of time histories for experimental permanent displacement and

rotation with the predictions of sliding/rotating block theory – Configuration No1 under

harmonic loading 0.19g and 0.23g and under seismic loading 0.35g and 0.55g .........................55

Figure 4.7. Comparisons of time histories for experimental permanent displacement and

rotation with the predictions of sliding/rotating block theory – Configuration No3 under

harmonic loading 0.19g and 0.23g and under seismic loading 0.35g and 0.55g .........................56

Figure 5.1 Inertial and contact forces contributing dynamic bending moment on the

cantilever wall ..............................................................................................................................58

Figure 5.2 Stress variation in the backfill during dynamic loading ............................................58

Figure 5.3. Comparisons of experimental and theoretical dynamic bending moments for

Configuration No1 under harmonic loading of amplitude 0.15g, 0.19g and 0.23g ....................60

Figure 5.4 Comparisons of experimental and theoretical dynamic bending moments for

Configuration No1 under seismic loading of PGA 0.17g, 0.35g and 0.55g ................................61


Configuration No3 under harmonic loading of amplitude 0.15g, 0.19g and 0.23g ....................62


Configuration No3 under seismic loading of PGA 0.17g, 0.35g and 0.55g ................................63


xiii

List of Tables

Table 2.1. Instrumentation summary........................................................................................... 8

Table 2.2 Soil properties .............................................................................................................17

Table 2.3. Pseudostatic critical accelerations and associated safety factors (SF) with

respect to sliding and bearing capacity ........................................................................................20


xiv


1

1 The DYNCREW Project

1.1 INTRODUCTION

The document reports the experimental study of the dynamic response of cantilever retaining

walls under 1-g shaking table testing, conducted at the Earthquake and Large Structures

Laboratory (EQUALS) which is part of the Bristol Laboratories of Advanced Dynamics

Engineering (BLADE), at the University of Bristol. The experiments were carried out during a

total testing period of five weeks, divided into two phases: a preparative phase of two weeks

(December 2010) and the main testing period of three weeks (June 2011), under the

collaboration of research teams from Universities of Naples and Sannio (Italy) and University of

Patras (Greece), within the SERIES project (Seismic Engineering Research Infrastructures for

European Synergies). The experimental program involves testing on scaled wall models founded

on compliant base, under different combinations of retaining wall geometries, soil configurations

and input ground motions. The initial motivation of this experimental study was the validation of

relevant stress limit analysis solutions (Evangelista et al, 2009, 2010; Evangelista & Scotto di

Santolo, 2011; Kloukinas & Mylonakis, 2011). The results aimed at shedding light onto salient

features of the dynamic response and can be useful for the better understanding and the

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

2 The experimental program

Reinforced concrete cantilever retaining walls represent a popular type of retaining system. They

are widely considered advantageous over conventional gravity walls as they combine economy

with ease in construction and installation. The concept is deemed particularly rational, as it

exploits the stabilizing action of the soil weight over the footing slab against both sliding and


2

overturning, thus allowing construction of walls of considerable height. For walls of this type,

structural weight is not a predominant parameter as equilibrium depends mainly on backfill

action and resistance of foundation soil.

2.1 THEORETICAL BACKGROUND

The traditional approach for analyzing cantilever walls is based on the well-known limit

equilibrium analysis, in conjunction with a conceptual vertical surface AD (Fig. 2.1a,c) passing

through the innermost point of the wall base (vertical virtual back approach). A contradictory

issue in the literature relates to the calculation of active thrust acting on the virtual wall back,

under a certain mobilized obliquity ranging, naturally, from 0 (for a perfectly smooth plane) to φ

(for a perfectly rough plane). Efforts have been made by numerous investigators to establish the

proper roughness for the analysis and design or this type of structures as reported by Evangelista

et al (2009, 2010) and Kloukinas & Mylonakis (2011). Nevertheless, the issue of seismic

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

(Eurocode 8-Part 5, 2004) and the Italian Building Code (NTC, 2008), do not explicitly refer to

cantilever walls. The current Greek Seismic Code (EAK, 2003) addresses the case of cantilever

retaining walls adopting the virtual back approach in the context of a pseudo-static analysis

under the assumption of gravitational infinite slope conditions (Rankine, 1857) and various

geometric constraints.

Recent theoretical findings obtained by means of stress limit analysis (Evangelista et al 2010;

Evangelista & Scotto di Santolo, 2011; Kloukinas & Mylonakis, 2011) indicate that a uniform

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

stress characteristics do not intersect the stem of the wall (wall). Given that the inclination

of the stress characteristics depends on acceleration level, a Rankine condition is valid for the

vast majority of cantilever wall configurations under strong seismic action. This is applicable

even to short heel walls, with an error of about 5% (Huntington, 1957; Greco, 2001).

Following the aforementioned stress limit analysis studies, closed-form expressions are derived

for both the pseudo-dynamic earth pressure coefficient KAE and the resultant thrust inclination, E

(Figure 2.1c), given by (Kloukinas & Mylonakis 2011):

11

1

sin sintan

1 sin cos

e e

E

e e

(2.1)


3

where 1e = sin-1

[sin(+e)/sin] ande = tan-1

[ah/(1-av)] are the so-called Caquot angle and the

inclination of the overall body force in the backfill. The same result for E has been derived, in a

different form, by Evangelista et al (2009, 2010). In the case of gravitational loading (e = 0), the

inclination E equals the slope angle , coinciding with the classical Rankine analysis. In

presence of a horizontal body force component, E is always greater than increasing with e

up to the maximum value of , consequently improving wall stability. The robustness of the

above stress limit analysis becomes evident, since under Rankine conditions and mobilized

inclination E, the stress limit analysis and the Mononobe-Okabe formula results coincide. These

findings have been confirmed by numerical analysis results (Evangelista et al. 2010; Evangelista

& Scotto di Santolo, 2011).

Figure 2.1 Pseudo-dynamic analysis of cantilever retaining walls for seismic loading: (a)

Seismic Rankine stress field for the problem under consideration, (b) Seismic Rankine stress

tensor and stress, (c) Modified virtual back approach by stress limit analysis, (d) Stability

analysis according to Meyerhof (EC 7)


4

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

stability analysis shown in Figure 2.1d. Traditionally, stability control of retaining walls is based

on safety factors against bearing capacity, sliding and overturning. Of these, only the first two

are known to be rationally defined, whereas the safety factor against overturning is known to be

misleading, lacking a physical basis (Greco, 1997; NTC, 2008; Kloukinas & Mylonakis, 2011).

It is important to point out that the total gravitational and seismic actions on the retaining wall

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

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

the wall foundation, based on classical limit analysis procedures for a strip footing subjected to

an eccentric inclined load (e.g. EC7, EC8). This suggests that the wall stability is actually a

footing problem and from this point of view, understanding the role of the soil mass above the

foundation slab and the soil-wall interaction is of paramount importance.

2.2 EXPERIMENTAL DESIGN AND SETUP

In the following paragraphs, the shaking table equipment, the experimental design and setup, the

material properties and the testing procedure are described in detail.

2.2.1 The Earthquake Simulator

The EQUALS-BLADE Earthquake Simulator, shown in Figure 2.2, consists of a 3m x 3m cast

aluminium platform weighing 3.8tons and capable of shaking a maximum payload of 15tons at

an operational frequency range of 0-100Hz. The platform has the shape of an inverted pyramid

consisting of four sections having a honeycomb-like network of stiffening diaphragms giving it

high strength and bending stiffness. The platform surface is an arrangement of 5 aluminium

plates with a regular grid of M12 bolt holes for attaching to the platform body and for mounting

of specimens. The platform sits inside a reinforced concrete seismic block that has a mass of

300tons. The block is located in a pit in the Earthquake Engineering Laboratory and is isolated

from the rest of the laboratory by a 20mm cork filled gap running between the block and the rest

of the laboratory. Hydraulic power for the ES is provided by a set of 6 shared variable volume

hydraulic pumps providing up to 900litres/min at a working pressure of 205bar. The maximum

flow capacity can be increased to around 1200litres/min for up to 16 seconds at times of peak

demand with the addition of extra hydraulic accumulators. The platform is attached to the block

by eight hydraulic actuators arranged so as to make best use of the available space. The


5

horizontal actuators are attached to the block by concrete filled steel box sections and to the

platform by smaller closed triangular brackets. The vertical actuators are connected directly to

the block and platform. Each actuator has a dynamic capacity of 70kN and has a maximum

stroke of 300mm. The four vertical actuators each have a static section to carry the static loads of

the platform plus specimen.

Figure 2.2 The shaking table of EQUALS – BLADE (University of Bristol, UK)

2.2.2 The Equivalent Shear Beam container (shear “stack”)

The apparatus, shown in Figure 2.3, consists of eleven rectangular aluminium rings, which are

stacked alternately with rubber sections to create a hollow yet flexible box of inner dimensions

4.80m long by 1m wide and 1.15m deep (Crewe et al, 1995). The rings are constructed from

aluminium box section to minimize inertia while providing sufficient constraint for the K0

condition. The stack is secured to the shaking table by its base and shaken horizontally

lengthways (in the x direction). Its floor is roughened by sand-grain adhesion to aid the

transmission of shear waves; the internal end walls are similarly treated to enable complementary

shear stresses. Internal side walls are lubricated with silicon grease and covered with latex

membrane to ensure plane-strain conditions.

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

contained in it, as depicted in Figure 2.4. However, the shear stiffness of the soil varies during

shaking depending on the strain level. Therefore the matching of the two stiffnesses (end-wall


6

and soil) is possible only at a particular strain level. The “shear stack” at the University of Bristol

is designed considering a value of strain in the soil close to the failure (0.01–1%). Therefore it is

much more flexible than the soil deposit at lower strain amplitudes and, as a consequence, the

soil will always dictate the overall behaviour of the container (Bhattacharya et al, 2012). Indeed

the shear stack resonant frequency and damping in the first shear mode in the long direction

when empty were measured prior to testing as 5.7Hz and 27% respectively, sufficiently different

from the soil material properties.

Figure 2.3 General and inside aspect of the Equivalent Shear Beam container (“shear stack”) (a)

side walls lubricated with silicone grease and covered with latex membrane, (b) wooden floor

and (c) transverse walls roughened by sand-grain adhesion

(a)

(b)

(c)


7

Figure 2.4 Schematic diagram of the EBS container (Bhattacharya et al, 2012)

2.2.3 Instrumentation and recording hardware

Three basic types of instruments were used for the measurement of accelerations, displacements

and strains. An outline of the instrumentation employed is provided in Table 2.1, and some

characteristic aspects are shown in Figures 2.5 and 2.6. 21 1-D accelerometers were used to

monitor the shaking table, the shear stack and the wall-soil system, with the main area of interest

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

4 LVDT transducers were used to measure the dynamic response and permanent displacements

of the wall. 4 INDIKON type, non-contact displacement transducers, were used for monitoring

the settlement of the backfill surface during the first phase of testing, but were eliminated during

the second phase, because of restrictions in their operational range (~10mm). Alternatively, a

grid of coloured sand was used for this purpose. Additionally, 32 strain gauges were attached on

the stem and the base of the wall, on three cross sections, to monitor the bending of the wall.

Overall, apart from the INDIKON transducers, 57 data channels were employed. The number

and the positions of the instrumentation are shown in detail in the drawings of the sequent

paragraph, where the experimental model design and setup are analyzed.

An RDP 600-type modular electronics system will supply the excitation voltage for the

displacement transducers and the strain gauges. The signal conditioning of the LVDTs was made

via the RDP 611 amplifier modules. These amplifiers allow optimisation of both the excitation

voltage and gain and can impart DC offsets in order to zero signals. The completion of the bridge

and the excitation voltage for the strain gauges was made via RDP 628 strain gauge amplifier

modules. The SETRA accelerometer signals were amplified by a set of Fylde 245GA mini-

amplifiers. These have multiple gain, variable sensitivity and offset options. The amplified


8

signals were supplied to a FERN EF6 multi-channel programmable filter that was set at a

common cut-off frequency of 80Hz on all channels (low pass Butterworth filter).

Signals generated by test instrumentation were supplied to ADC boards of type MSXB 028

manufactured by Microstar Laboratories, which are capable of simultaneous sampling and hold

from 64 channels of 16bit. Data collection was controlled with the SIMACQ v.3.00 software, at

a sampling rate of 1024Hz, except of the white noise tests sample at 256Hz. Data from the

seismic tests were stored in self processing MATLAB (.m) files. (MathWorks Inc., 1995).

Table 2.1. Instrumentation summary

Measured

Parameter Transducer Type Description Purpose

Acceleration Type

SETRA 141A

High output capacitance

type sensor with inbuilt

pre-amplifier.

Calibrated range: +/8g.

Operating frequency: 0-

3000 Hz

Used to measure the

horizontal and vertical

accelerations of the

shaking table, the shear

box, the wall and in the

backfill

Displacement

Τype

RDP DCTH LVDT

Linear variable

displacement

transformers

Range: +/ 12.5, +/ 50

and +/75mm

Used to monitor the

horizontal and vertical

displacement of the wall

Type

INDIKON

Non-contact displacement

transducer. Operation

based on eddy effect.

Range: 0-30 mm

Used to monitor the

settlement of the free

surface of the backfill. The

transducers will be

attached to plates resting

on a Perspex pad with

roughened underside

surface.

Strain

Strain gauge type

EA-13-120LZ-120

(Vishay Ltd)

Linear strain gauge

pattern, 3 mm length

Used to measure bending

strain of wall at various

elevations (on Y direction).


9

Figure 2.5 Illustration of the model and experimental equipment during the first phase of testing

Figure 2.6 Details of the experimental setup (Second phase of testing): (a) longitudinal aspect of

the model, (b) wall face instrumentation (Configurations No2 & No3), (c),(d) pairs of

accelerometers on shaking table and upper ring, (e) backfill accelerometer, (f) sand pouring

procedure, (g), (h) back - covered with rough sandpaper - and front view of the wall

(Configuration No1)


10

2.2.4 Shaking table model geometry and instrumentation

The model geometry adopted, shown in Figure 2.7, had to take under consideration the

dimensions of the shear box, the dynamic problem simulation feasibility and restrictions of the

shaking table equipment. Based on the forgoing, a maximum height of 1m of soil material was

selected, separated into the retained backfill of 0.6m (equal to the height of the wall, Η) and the

foundation soil layer of 0.4m (equal to the wall footing width, Β). The length of the retained

backfill was selected 5 times its height, whereas the corresponding free length in front of the wall

was 3 times the wall height. These dimensions were deemed sufficient to eliminate the boundary

effects and to ensure free field conditions in the middle of the backfill.

zx

4800

H

H

B

1150

shaking table

5H3H

B

H H H HHHH

backfill

"free field"

conditions

foundation layer

"free field"

conditions

Rankine prismatic

failure mechanismarea

foundation

failure

mechanismarea

zx

A1 A2

A7

A8A9A10A11

A3A4,5

A6

A13A14 A12

A15A16A17

A18

A19

A20 A21

D1

D3

D4

D2

D: LVDT

A: Accelerometer

horizontal

vertical

12001200200400900 900

300

300

300

600

400

250

250

(+)

(+)

shaking table

nodes of the surface deformation

measurment grid

Figure 2.7 Illustration of geometry and instrumentation of the shaking table model (dimensions

in mm)


11

In Figure 2.7, the positions of the instrumentation (LVDT and accelerometers) in the model are

presented, which were kept the same during the whole testing procedure. The soil layer

parameters were also kept the same and will be presented in a next paragraph. The only

modification of the model geometry and setup relate to the geometry of the wall itself, which

was designed to exhibit different behaviour, between sequential testing cycles. The different wall

geometries adopted are presented in the table embedded in Figure 2.8. The retaining wall model

was made of Aluminium alloy 5083 plates with properties: unit weight γ = 27kN/m3, Young’s

modulus E = 70GPa, Poisson’s ratio = 0.3.

The material density of the model wall is similar to those of prototype concrete walls, while the

dimension proportions of the model followed the common construction analogies used in

practice (geometrical similarity). As shown in Figure 2.8, the 32mm thick plates are connected

with M12 bolts. The efficiency of this connection system, with respect to the total fixity

conditions demand, proved to be very good, as shown in the bending moment diagrams of Figure

2.10. The width of the stem of the wall is 970mm. A central wall segment of 600mm width was

created by two 1mm thick vertical slits penetrating 400mm down into the wall, to ensure the

response of the central segment under plane strain conditions, independently from possible

problems at the boundaries. The locations of the slits were 185mm from each side of the wall

stem. Following the same concept, the base of the wall is subdivided into four 240mm-wide

aluminium segments, that are each secured to the wall stem via three M12 bolts.

The positions of the 32 strain gauges are depicted in the drawings of Figure 2.9. The instruments

were placed symmetrically, at the same positions on both slab faces (1) on the central wall line,

and (3) on a second section close to the edge, for an extra control of the plane strain condition

requirement. Generally, the selection of the 32mm thick slab for the cantilever beam, followed

the criterion to keep the bending deformations close to the operational level of the instruments

( 2a d wM t D ~10-5

, where 3 212(1 )w w wD E t v ), in order to be measured, but at the same

time to simulate a relatively rigid wall. This is why no strain gauges were place at the upper

200mm of the wall stem, where strain lever due to bending is expected much smaller than the

instrumentation operational level (in the order of 10-6

).

Even under the design concept described above, the wall-soil relative flexibility parameter

3

w wd GH D (Veletsos & Younan, 1994, 2000; Giarlelis & Mylonakis, 2010), yields values

from 15 to 20, depending on the soil stiffness. These values correspond to a relatively flexible


12

32

32

570

b2

b1

Confi

gura

tion Νο

1

b2

b1

298

250

250

70 0 0

Confi

gura

tion Νο

2

Confi

gura

tion Νο3

wal

l

cross

sec

tion

(zx

-pla

ne)

185

600

185

fron

t vie

w

(zy

-pla

ne)

1 m

m

slit

400

M12 b

olt

s

400

240

240

240

240

400

1 m

m

slit

12

34

5

602

Alu

min

ium

alo

y 5

083 p

late

s

14

- fo

undat

ion p

late

s, d

imen

sions:

240 x

400 x

32

to

5-

canti

lever

wal

l pla

te, dim

ensi

ons:

570 x

970 x

32

model

modif

icat

ions:

pla

n v

iew

(xy

-pla

ne)

970

Figure 2.8 Geometry and assembling of the retaining wall model (dimensions in mm)


13

cantilever wall, not usually the case for the prototype retaining walls of this type. In practice, the

cantilever wall thickness increases with depth, from a minimum width at the load-free end on the

top, prescribed from constructional codes (t/H ratio equal to 0.05 or even smaller), to a notably

higher width at the base, designed to carry the shear force and the bending moment of the fixity

area. This usually leads to trapezoidal cantilever wall cross sections, providing high bending

stiffness.

y

185600185

970

back view

120 93

x

y

x

y

z

y

185 600 185

970

front view

12093

z

86

88

88

88

20

20

2050

50

plan view bottom

view

SG1

SG2

SG3

SG4

SG5

SG6

SG7

SG21

SG22

SG23

SG24

SG25

SG26

SG14

SG13

SG12

SG11

SG10

SG9

SG8

SG20 SG32 SG28 SG16

SG17

SG18

SG19

SG29

SG30

SG15SG31 SG27

Figure 2.9 Strain gauges positions

In Figure 2.10 time histories recorded at the strain gauges of the slab connection area, for the

typical case of harmonic excitation with PGA 0.1g, are presented. The efficiency of the plates

connection system to provide total fixity conditions is obvious, as the opposite strain gauges

provide the same bending moment readings, being on opposite faces (tension-compression) at


14

the stem and the footing plate (see SG8-SG15 comparison). Minor exception is the strain gauges

pair SG16-SG20, placed at the short cantilever of the wall toe, which cannot bend but penetrates

the underlying soil. Additionally, the instrument SG1 exhibits an electrical anomaly, commonly

observed at the internal instruments being in contact to the soil mass.

Figure 2.10 Comparison of dynamic bending deformation recorded at the strain gauges at the

bottom of the cantilever (slab connection area)


15

2.2.5 Soil material and soil layers properties

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

The soil material is the same for all soil layers, consisting of dry, yellow Leighton Buzzard (LB)

sand BS 881-131 (silica sand with sub-rounded grain shape), Fraction B (Dmin = 0.6mm, Dmax =

1.18mm, D50 = 0.82mm, Gs = 2640Mg/m3, emin = 0.486, emax = 0.78), at different compaction

levels. This particular soil has been used extensively in experimental research at Bristol and a

wide set of density and stiffness data is available (Stroud, 1971; Tan, 1990; Cavallaro et al,

2001). Further information and references are provided in Bhattacharya et al (2012).

The base deposit was formed by pouring sand in layers of 150-200 mm from a deposition height

of 0.6m and then densifying by shaking. After densification, the height of the layer was reduced

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

centre of the desired backfill region, without any further densification. The pouring was carried

out by keeping the fall height steady, approximately equal to 200mm in order to minimize the

densification effect of the downward stream of sand.

The packing density of the soil material is a parameter of major importance during 1-g shaking

table testing. It is known that the soil behaviour is non-linear, strongly depending on the isotropic

stress (first invariable of the stress tensor ij[ / 3]p trace ), which in small scale models is

ordinarily less than 5kPa. At this low stress level, soils exhibit an important dilative behaviour,

resulting to higher apparent friction angles, φpeak = φcrit + 0.8ψ (Bolton, 1986), compared to the

prototype. It is also known that the critical friction angle is not altered with density variations.

Thus, the only way for minimizing the error in the peak friction angle, is by controlling soil

dilatancy by reducing soil density. The specific technique has been proposed by various

researchers (Kelly et al, 2006; Leblanc et al, 2010). Figure 2.11 shows the variation of peak

friction angle with mean effective isotropic stress (p′) for silica sand of various relative densities

based on Eq. (2.1), following the stress-dilatancy work of Bolton (1986).

3 9.9 ln 1cv Dr p (2.2)

where φcv, is the critical friction angle, estimated at 34.3ο in the graph, and p’ is the isotropic

confining stress (in kPa). Based on this approach, if 120kPa of mean effective prototype stress at

50% relative density is to be modelled in a small scale laboratory model at 25kPa stress, the sand


16

is to be poured at about 39% relative density ensuring that peak friction angle is the same. On the

other hand, this approach raises two major restrictions: First, there is a minimum density beyond

which sand cannot be poured. Second, a very loose soil mass is extremely sensitive to dynamic

densification during seismic excitation. This effect was noticed during the retaining wall

experiment, but its effect was kept generally small due to the following reasons: (1) the

foundation layer that was common in all cases, was relatively dense from the beginning, (2) the

backfill behind the wall was replaced after every cycle of strong shaking and failure of the model

and (3) the uniform, coarse-grained sand with rounded grain shape selected for the model,

provided a relatively stable structure, less sensitive to dynamic compaction.

Figure 2.11 Friction angle of Leighton Buzzard Sand as a function of mean effective stress and

relative density (from Bhattacharya et al, 2012)

Apart from soil mechanical properties, the low confining stress level of the shaking table model,

affects the dynamic soil properties, yielding lower stiffness modulus G, which obeys a parabolic

variation relatively to the isotropic stresses of the form n

G p , where the n is about 0.5. This

effect is taken under consideration during the shaking table model design through appropriate

scaling laws. Secondarily, the shear modulus G is also a function of soil density. These features

are presented and commented later on, at the paragraph where the investigation of the dynamic

properties of the model is explained and the results of the dynamic white noise testing are


17

interpreted. This particular soil has been used extensively in experimental research at Bristol and

a wide set of density and stiffness data is available (Stroud, 1971; Tan, 1990; Cavallaro et al,

2001). Further information and references are provided in Bhattacharya et al, (2012). Laboratory

testing by Cavallaro et al (2001) provided the following empirical correlation between friction

angle φ and relative density Dr, which was used for a preliminary estimation of the soil strength

properties:

deg 0.238 % 28.4Dr

(2.3)

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

during the deposition, and the corresponding predictions of Eq. (2.3) are summarized in Table

2.2 with the corresponding estimation of the peak friction angle.

Table 2.2 Soil properties

Soil layers Thickness

(mm)

Voids

ratio, e

Relative density,

Dr (%)

Unit weight

(kN/m3)

Friction angle, φ(o)

Cavallaro et al (2001)

Foundation 390 0.61 60 16.14 42

Backfill 600 0.72 22 15.07 34

Extremely important for the soil-wall system behaviour are the mechanical properties of the

interfaces, which are of two kinds: a) smooth interface with direct contact of sand on the

aluminum plate, and b) rough interface created by pasting rough sandpaper on the wall surface.

The critical friction angles of the interfaces were measured directly on the model with static pull

tests. The resulting values are:

Smooth soil-wall interface (Aluminum - soil): δ = 23.5ο

Rough soil-wall interface (sandpaper - soil): δ = 28.5ο

It can be observed that the roughened interface yields a friction close to the soil critical state

angle of Eq. (2.3), as expected for a totally rough surface. More information referring to the LS

sand behaviour on interfaces, as well as the corresponding dilatancy angles, can be found in the

experimental work of Lings & Dietz (2005) and Dietz & Lings (2006).

At last, the dynamic properties of the soil material is well described through empirical curves for

the G/G0 ratio degradation and the increase of damping ratio D (%), derived from the

experimental study of Cavallaro et al (2001):


18

0

( ) 1

1 (%)

G

G

(2.4)

0

( )

( )(%)

G

GD e

(2.5)

where: α = 20, β = 0.9, η = 134 and λ = 4.6. The specific curves, plotted in Figure 2.12, have

been derived from laboratory resonant column tests under confining stress levels ranging from

50 - 150kPa, which is much higher than those corresponding to the shaking table conditions.

This leads to an overestimation of the damping ratio D, as shown by Dietz & Muir Wood (2007),

who measured the dynamic soil parameters directly on the shaking table model. Their

experimental curves are presented in Figure 2.13. These experimental studies were conducted at

the same soil material (LB sand, 14-25) and at the same density Dr close to 60%.

Figure 2.12 Empirical correlations for dynamic soil properties of LB sand derived from the

laboratory dynamic tests of Cavallaro et al (2001)


19

Figure 2.13 Dynamic soil properties of LB sand measured experimentally by shaking table

testing at EQUALS (from Dietz & Muir Wood, 2007)

2.3 EXPERIMENTAL PROCEDURE

2.3.1 Model Configurations

The experimental procedure was repeated for three different Configurations (No1, No2 and No3)

for the wall model presented in Figure 2.8 to provide different response in sliding and rocking of

the base. These configurations are summarized in Table 2.3. In Configuration 2, the wall heel

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

Configuration 2 was adopted, after increasing the frictional resistance of the base interface from

23.5o to 28

o (approximately equal to the critical state angle), by pasting rough sandpaper. The

interface friction angles were measured by means of static pull tests on the wall. The differences

between these three configurations, in terms of a pseudo-dynamic stability analysis according to

EC7 and EC8, are summarised in Table 4, ranging from a purely sliding-sensitive wall

(Configuration 1), to a purely rotationally sensitive one, mobilizing a bearing capacity failure

mechanism (Configuration 3). Configuration No2, represents a more complex, intermediate

mechanism, yielding simultaneously to sliding and bearing capacity.


20

Table 2.3. Pseudostatic critical accelerations and associated safety factors (SF) with respect to

sliding and bearing capacity

Test configuration

Critical

acceleration for

SFsliding = 1

SFBearing capacity

at critical sliding

acceleration

Critical

acceleration for

SFBearing capacity = 1

SFsliding

at critical

bearing capacity

acceleration

Configuration No1 0.18g 7.45 0.35g 0.68



2.3.2 Iterative testing procedure

The experimental procedure described in this paragraph corresponds mainly to the more

systematic second phase of testing (June 2011), whereas the tests of the first phase were mainly

useful to the calibration and better preparation of the testing model of the second phase. Every

testing Configuration was subjected to the same series of dynamic tests, described below step-

by-step:

1) Placement of the wall on the foundation layer and investigation of its dynamic

behaviour by means of white noise testing.

2) Backfill construction and repetition of white noise testing to investigate both the

backfill and the combined soil-wall system response.

3) Harmonic-sinusoidal dynamic testing at various excitation frequencies and increasing

amplitude, until yielding of the wall and sufficient plastic deformation of the system is recorded.

4) Removal of the backfill, reposition of the wall on site and repetition of steps 1 and 2.

5) Dynamic excitation of the system with real earthquake signals, scaled in frequency

and increasing amplitude, until yielding of the wall and sufficient plastic deformation of the

system.

6) Removal of backfill and wall, placement of the next wall Configuration and repetition

of the whole procedure (steps 1 - 6)

The most time consuming part of the procedure described above is the removal and

reinstallation of the backfill and the wall, demanding the handling of a great amount of sand

(approximately 2.6tons) and the dismantling-reconnection-check of a great number of

instruments and cable connections. Given the time restrictions of the 3 weeks available for

testing, some modifications of the program were necessary: (a) In the case of Configuration No

1, the plastic deformation of the system during the harmonic excitation was kept relatively small


21

(1/100 of wall height) and the earthquake loading continued to the same specimen. The

elimination of step 4 was deemed reasonable since harmonic testing had been performed

extensively during the first testing phase (December 2010). (β) The backfill was totally removed

only once, at the end of Configuration No1. At the end of all testing cycles, only the soil prism

behind the wall was removed and replaced, with special care for the temporary support of the

rest backfill. These modifications provided significant time economy for the completion of the

whole experimental program.

2.3.3 White noise testing

During white noise exploratory testing, a random noise signal of bandwidth 1-100Hz and RMS

acceleration = 0.005g was employed. During each exploratory series test, and simultaneous data

acquisition, system transmissibility was monitored using a two-channel spectrum analyser

(Advantest 9211C). The analyzer computes the frequency response function (FRF) between the

input and the output signals of interest (A1 accelerometer on the shaking table and A6 on the top

of wall stem respectively). The frequency response function is applied to the product between the

signal data and a Hanning window function (rectangular). Natural frequency and damping values

for resonances up to 40Hz (i.e. within the seismic frequency range) were determined for well-

defined resonances using the output of the analyzer’s curve fitting algorithm by means of a least-

squares error technique. Some characteristic outputs of the curve fitting algorithm are provided

in the Appendix.

For the interpretation of the dynamic behaviour of the system, more transfer functions between

any selected pair of channels need to be calculated using a Matlab code. These results are

presented in the ensuing, together with an interpretation of the resulting resonant frequencies.

2.3.4 Dynamic testing with harmonic, sinusoidal excitation

This type of input acceleration was imposed by sinusoidal excitation consisting of 15 steady

cycles. To smoothen out the transition between transient and steady-state response, the excitation

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

ramp down to zero at the end. An example of the harmonic excitation signals is presented in

Figure 2.14. With reference to frequency and acceleration level, a wide range of excitation

frequencies (from 1 to 58Hz, every 3Hz) and various amplitudes was tested during the first

testing phase (December 2010). At the second phase of testing (June 2011) the excitation


22

frequencies were restricted to a set of 5 frequencies (4, 7, 13, 25 and 43Hz), used initially at a

low acceleration amplitude of 0.05g, for studying the dynamic response of the system. An

excitation frequency of 7Hz was then selected for a series of harmonic excitations with

increasing amplitude, until failure. These conditions are essentially pseudostatic, as the above

frequency is much smaller than the resonant frequencies of the system.

Figure 2.14 Harmonic base excitation at the frequency of 7Hz and amplitude 0.05g

2.3.5 Dynamic testing with real earthquake records

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

earthquake testing:

a) The Sturno record from Irpinia, 1980 earthquake (Mw= 6.9, PGA=0.321g), characterized by a

long strong motion duration of 16.2s and energy transfer to a wide range of frequencies from

0.25 to 10Hz (predominant frequency of 0.44Hz).

b) The Tolmezzo record from Friuli, 1976 earthquake (Mw=6.5, PGA=0.315g) with a smaller

duration of 4.92s, frequency range from 0.8 to 5Hz and predominant frequency of 1.5Hz.

c) The Northridge record from Los Angeles, 1994 earthquake (Mw = 6.7, PGA =0.47g), with

duration of 10.3s and narrow frequency range of 0.14 to 0.7Hz

The reproduction of these signals at the shaking table demanded an iterative matching process,

for calibrating of the displacement input of the table actuators. This procedure was performed

after the first phase of testing (December 2010), just before the removal of the model from the

shaking table, in order to have the same mass and geometrical conditions. The reproduction of

the signals was not 100% accurate, due to the large weight and eccentricity of the model.


23

The authentic signals were scaled by a frequency scale factor of 5, assuming a geometrical scale

factor of n = 9 corresponding to a prototype of 5.4m high and applying the scaling law n0.75

,

which is valid for 1-g modelling (Muir Wood et al., 2002). The frequency-scaled signals were

applied at a low acceleration amplitude of 0.05g to measure the dynamic response of the model

and then the Sturno record was selected for carrying out increasing amplitude dynamic testing,

until failure in sliding or tilting of the retaining wall. The specific signal was selected because of

the long duration and wide frequency range. Time histories and corresponding Fourier spectra

are presented in Figure 2.15, whereas in Figure 2.16 the differences between the authentic (red

dashed line) and the modified Sturno record used as excitation signal (continuous black line) are

presented, in terms of acceleration, velocity and displacement time histories and Fourier spectra.

Figure 2.15 Scaled seismic signals imposed as base acceleration


24

Figure 2.16 Comparison between the authentic and modified Sturno record

3 Experimental results

3.1 DYNAMIC PROPERTIES OF THE MODEL

Estimation of the dynamic model parameters was based on the interpretation of the white noise

testing results and their validation through empirical and theoretical relations from the literature.

In Figures 3.2 to 3.8 the transfer functions calculated at the positions shown in Figure 3.1, for

Configurations No1 and No3, during various phases of model construction, are presented. The

resulting resonant frequencies are noted on the graphs.


25

A1

A8A9A10A11

A5

A6

A18

A20

A15

Figure 3.1 Accelerometer positions for white noise testing evaluation

From Figure 3.2, referring to dynamic response of the wall without the backfill in Configuration

No1, the frequencies 25.5Hz and 23.5Hz clearly appear. The first one corresponds to the

predominant frequency of a fixed cantilever beam with length L = 0.57m according to Eq. (3.1)

(Clough & Penzien, 1993) for Ε = 70GPa, m = 0.864kN/m (mass of the cantilever beam per m of

length) and Ι=2.73*10-6

m4 the moment of inertia for the 32mm thick cross section, of 1m width.

2

1 4

1.87525.6

2

EIf Hz

mL (3.1)

This frequency (estimated both theoretically and experimentally), reduces to 23.5Hz when the

response of the wall is examined, as the cantilever beam is fixed to a rectangular footing that is

not completely rotationally constrained. The same frequency further reduces to 17Hz, in the case

of Configuration No3, when the footing dimensions decrease and the system is even more free to

rotate (Figure 3.6). In that specific case, the rocking frequency of the foundation is predominant

for the system - not of the cantilever beam. This explains why the frequency of 25.5Hz is not

measured. At the foundation soil layer, before the backfill construction, the frequencies of 72 Hz

(free field) and 77Hz (under the wall) were measured. When the backfill is added, the

frequencies of 36, 47 and 52-55Hz, appear at all cases and have to be interpreted in terms of the

system vibrating mode. Finally, from the accelerometers on the rings of the shear box, an extra

frequency of 12 – 13.5Hz was recorded, corresponding to the resonant frequency of the container

full of soil, which naturally exhibits a stiffer behaviour.

Beginning from the foundation layer and the resonant frequencies of 72 and 77Hz, the relation

G0 = 16ρH 2

f connecting the resonant frequency with the shear wave propagation velocity Vs and

accordingly with the shear modulus at low strains G0, yields the values of 20.5GPa and 23.5GPa


26

respectively. The soil under the wall is naturally slightly stiffer than at the free field, due to the

additional confining stress imposed from the self weight of the wall. There are many empirical

equations available in soil mechanics literature, describing the parabolic relation of G0 with the

isotropic confining stress. Suitable formulas derived for rounded silicate sands that can be used

for comparisons have been proposed from Hardin & Black (1966), Hardin & Drenvich (1969)

(Eq. 3.2) και Iwasaki et al. (1978) (Eq. 3.3) among others.

2

0

(2.973 )3230

1

eG p

e

(3.2)

20.4

0

(2.17 )9000

1

eG p

e

(3.3)

In the above equations, 01 2 / 3vp K . A more detailed analysis of this topic can be found

in Ishihara (1996).


27

Figure 3.2 Transfer functions from the wall response in Configuration No1 – wall placed on the

foundation layer before backfill construction


28

Figure 3.3 Transfer functions from the foundation layer response in Configuration No1 – before

backfill construction


29

Figure 3.4 Transfer functions from the wall response in Configuration No1 – after backfill

construction


30

Figure 3.5 Transfer functions from the backfill response in Configuration No1


31

Figure 3.6 Transfer functions from the wall response in Configuration No3 – wall placed on the

foundation layer before backfill construction (*refers to the soil prism behind the wall)


32

Figure 3.7 Transfer functions from the wall response in Configuration No3 after the construction

of the backfill


33

Figure 3.8 Transfer functions from the backfill response in Configuration No3.


34

Empirical Eqs (3.2) and (3.3) for the foundation layer properties, yield the same stiffness values

(calculated at the middle of the layer) to those recorded, if the vertical confining stress is used

instead of the isotropic stress corresponding to an earth pressure coefficient Κ0~1. This earth

pressure coefficient is much higher than the values 0.445 to 0.46 that have been estimated

experimentally for dense to loose Leighton Buzzard sand 14-25, from triaxial tests (Stroud,

1971). On the other hand, the triaxial tests were conducted at much higher confining stresses p’,

than in the shaking table conditions. Recent experimental findings (Chu & Gan, 2004) indicate

that the earth pressure coefficient Κ0 in loose silicate sands converges to 1 when the confining

stress converges to zero (Figure 3.9). In this light, it is a rational hypohesis to use the vertical

stress in Eqs (3.2) and (3.3) (that is the isotropic p’ for K0 = 1).

Figure 3.9 Variation of earth pressure coefficient K0 at very low confining stress (from Chu &

Gan, 2004)

In the same way, if the calculations from Eqs (3.2) and (3.3) are repeated for the middle of the

backfill, the value of 20GPa is derived for G0, corresponding to the resonant frequency around

47Hz. With the backfill present, the foundation soil underneath becomes stiffer, with G0

calculated at 40GPa. If the frequency of 47Hz, recorded also during white noise testing analysis,

is the dominant frequency of the 0.6m high backfill, the next step is the calculation of the

resonant frequency of the two-layered profile of Figure 3.11, by means of the known

amplification factor of Eq. (3.4) (Kramer, 1996).

2 21 2 1 2

* * * *

1 2 1 1 1 2

1AF =

cos cos sin sins

s s s s s

VH H H H

V V V V V

(3.4)


35

Where * 1 2s sV V i . Indeed, for the given soil properties of each layer and for an

approximate damping ratio β = 0.05, the calculated resonant frequency of 36Hz is exactly the

same as the one measured during white noise testing. The only frequency coming from white

noise testing, remaining to be indentified is that of 52 -55Hz.

Figure 3.10 Increase in soil shear modulus with depth based on empirical relations


36

H1

H2

ρ2, Vs2

ρ1, Vs1

u f f

u (t) = u0 e -iωt

Figure 3.11 Resonant frequency of the two-layered medium with properties: H1 = 0.4m, Vs1 =

157m/s, H2 = 0.6m, Vs2 = 113m/s

It is known that the resonant frequency f1 of a soil layer of finite length, is related to the

corresponding free field frequency f1,ff of an infinite layer through a geometrical coefficient Φ,

as shown in Eq. (3.5), which is a function of Poisson ratio v and the backfill’s height to length

ratio, H/L.

1 1, fff f (3.5)

Analytical expressions for Φ have been proposed by numerous researchers (Matsuo & Ohara,

1960; Wood, 1973; Veletsos et al, 1995; Wu & Finn, 1999), under appropriate simplifications

and approximations during the elastodynamic equations solving, as is the assumption of zero

vertical strain or zero vertical dynamic stress. If these expressions from literature are applied to

the shaking table model, that is for f1ff = 47Hz, H = 0.6m, L = 3m και ν = 0.3, the resonant

frequency of 56 – 58Hz is derived for the soil-wall system. This is slightly higher than the

frequencies actually recorded, but on the other hand, the retaining wall at the experimental

conditions is not rigid, as the analytical solutions assume. Given that the retaining wall can yield

and rotate, the soil-wall system is naturally softer, and from this point of view, the recorded

frequencies of 52 - 55Hz are in total agreement with the theoretical predictions. Summarizing the


37

conclusions of the dynamic tests, the elastic parameters of the model are presented in Figure

3.12. Additionally, the Poisson’s ratio ν can be taken equal to 0.3 for all layers, and the damping

ratios were measured from 2.5% to 5%, as shown in the results of the white noise testing in the

Appendix.

Figure 3.12 Elastic parameters of the soil layers of the problem

3.2 EXPERIMENTAL RESULTS FOR DISPLACEMENTS, SEISMIC LOADS AND

FAILURE MECHANISMS

The measurements of system displacements for all tested configurations are summarized in

Figure 3.13. The total, cumulative settlements and rotations of the wall, for each series of

sequential input motions are presented in Figures 3.13a and 3.13b, and the incremental

displacements for each input motion are presented in Figures 3.13c-3.13e, indicating different

behaviour of the wall models under the same input. The measurements confirm the predictions

for the expected failure modes and the levels of critical acceleration. The sliding failure is clearly

visible in Configuration No1, as is the bearing capacity failure in Configuration No3.

Configuration No2 although designed to be weaker in sliding, also exhibits significant rotational

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

deformations are also observed in Configuration No1 for high acceleration levels, revealing that

walls resting on a compliant base exhibit local bearing capacity failure near the toe, due to high


38

compressive stress concentration. This observation elucidates the importance of properly

designing retaining structures to avoid developing significant rotational response.

Some characteristic experimental measurements are presented in Figures 3.14 to 3.18, relative to

failure mechanisms, accelerations, dynamic and permanent displacements and bending moments,

organized in sets of graphs suitable for direct comparisons. Most of the herein presented results

relate mainly to Configurations No1 and No3, for they exhibit yielding near similar acceleration

conditions but in different modes. Limited results are presented for Configuration No2, which is

significantly weaker compared to the others, failing almost simultaneously in foundation sliding

and rotation (i.e., bearing capacity) mode, thus is less important for comparison reasons.

Typical results from Configurations No1 and No3, for two cases of harmonic loading (0.19g και

0.23g) are presented in Figures 3.14 and 3.17. The following observations can be made: First the

response of each configuration is as expected. A translational response mode is evident in

Configuration No1 and a rocking one in Configuration No3. Sliding discontinuities are obvious

on the acceleration time histories of Configuration No1 (Fig. 3.14a), at a critical acceleration

slightly higher than that of Table 2.3. Note that the translational yield acceleration is not steady,

but always increases after every successive yielding, as even a small rotation causes penetration

of the wall toe into the foundation soil thus increasing passive resistance. On the other hand,

Configuration No3 starts rotating at initiation of yielding, without any evidence of sliding

discontinuities on the recorded accelerogram. Second, in both cases the wall stem appears to

have an amplified response, mainly because of foundation rocking and secondarily of pure

bending of the stem. Naturally, this is more evident in Configuration No3. Third, both models

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

The same results for earthquake loading on Configurations No1 and No3 are presented in Figures

3.15 and 3.18. In this case, the input motion contains higher effective peak accelerations, but the

number of important strong cycles (half cycle pulses) is only three. The sliding failure is again

clearly visible in Configuration No1, as is the bearing capacity failure in Configuration No3

caused by the high eccentricities induced by seismic thrust. An important notice about the failure

modes arising from the combination of the two comparisons, is that the bearing capacity failure

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

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

sliding block theory (Newmark & Rosenblueth, 1971; Kramer, 1996). Accordingly, rotational

mechanisms appear to be more critical under strong earthquakes, even though they are


39

sufficiently resilient against sliding (Fig 3.17d and Fig 3.18d). Moreover, some rotational

deformation is also observed in Configuration 1 for high acceleration levels, revealing that a wall

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

concentration of high compressive stresses. This observation elucidates the importance of

properly designing retaining structures to avoid development of significant rotational response.

From the acceleration distributions of Figs 3.17c and 3.18c, it can be observed that the

earthquake loading results to conditions closer to the assumptions of pseudostatic analysis, as a

soil mass moving in phase with the wall is evident, especially for the rotational mode of

Configuration No3. Contrary to the case of earthquake excitation, wall and soil under harmonic

loading appear to respond in a quite different way. Finally, the peak seismic increment of

bending moments is compared in Figs 3.17e and 3.18e. A noteworthy observation is that the

earth pressure on the wall stem increases when the system moves towards the backfill, that is for

an acceleration not critical for overall stability. On the other hand, at yielding acceleration, earth

pressure on the stem is minimum. This is in agreement with the findings of the analysis

presented by Green et al (2008) on a full scale numerical model and the experimental and

numerical results of Al Atik & Sitar (2010). By comparing Configurations No1 and No3, it can

be clearly identified that rotational modes induce lower earth pressures on the wall (due to

rotational flexibility of the foundation) but different distributions leading to a higher point of

application of the thrust.

Finally, the response of Configuration No2 to harmonic and earthquake excitation with PGA =

0.17g presented in Figure 3.16, exhibits a similar behaviour to both Configurations No1 and

No3, resulting to simultaneous sliding and rotational failure. As seen from both the acceleration

time histories (3.16a) and the failure mechanisms (Figure 3.16d) the sliding failure mode

prevails, which is consistent to the critical accelerations estimated in Table 2.3.

In Figure 3.19, measured settlement profiles at the state of failure are plotted together with the

assumed failure mechanisms for Configurations No2 and No3. The following are worthy of note:

First, these failure mechanisms were observed only for transient earthquake loading, whereas in

the case of harmonic excitation, the settlement profile could not clearly reveal the emergence of

the main failure planes, as it had more-or-less a smooth parabolic shape. This can be explained in

view of a non-uniform settlement and deformation mechanism and stronger dynamic effects

imposed by earthquake loading. Second, the progressive, cumulative development of plastic

deformation strongly affected the clear emergence of the failure mechanism. For example, in


40

Configuration No1, deformation took place in small increments for sequential strong shaking. In

Configuration No3, the deformation progress was also incremental – the failure mechanism

presented in Figure 3.19 was observed at a very high deformation level, not reached in

Configuration No1. Only in the case of Configuration No2, when important plastic deformation

was instantly developed, a clear failure mechanism was noticed on the soil surface. Although

there is actually not a “rigid block” response in the retained soil mass, the experimental findings

show that the earthquake excitation induces a more uniform acceleration distribution within the

retained soil mass, which corresponds to a more uniform Rankine stress field, as assumed in the

pseudo-static analyses. Third, the assumed failure mechanisms confirm the estimations based on

the material properties, the stability analysis and the yield accelerations presented in Tables 2.2

and 2.3 respectively. This comparison is only indicative, as these are velocity characteristics, not

exactly coinciding with the corresponding stress characteristics.


41

Figure 3.13. 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 No1, No2 and No3, respectively


42

Figure 3.14. Comparison of typical experimental results for Configurations No1 and No3 under

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

displacements, (c) positive acceleration distribution (maximum inertial forces towards the

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


43

Figure 3.15. Comparison of typical experimental results for Configurations No1 and No3 under

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

positive acceleration distribution (maximum inertial forces towards the backfill), (d) negative

acceleration distribution (maximum inertial forces towards the wall)


44

Figure 3.16. Typical experimental results for Configuration No2: (a) measured wall

accelerations for harmonic sinusoidal and seismic excitation, (b) corresponding wall

displacement, (c) positive acceleration distribution (maximum inertial forces towards the

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


45

Figure 3.17 Comparison of typical experimental results for Configurations No1 and No3 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.


46

Figure 3.18 Comparison of typical experimental results for Configurations No1 and No3 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.


47

Figure 3.19 Backfill surface settlement distribution at failure: (a) initial grid geometry -

dimensions in mm, (b), (c) settlement distributions for Configurations No2 and No3,

respectively.

4 Interpretation of displacements in light of

sliding block theory predictions

A key issue related to the performance based design of retaining walls is the control of the

allowable displacements, involving sliding and tilting, to ensure the safety and good performance

of retaining systems and nearby structures. Various simplified methods are available in the

literature following the pioneering work of Newmark (1965), for the prediction of permanent soil

deformation under a given base excitation motion. These include the simplified Richards & Elms

(1979) method for sliding displacement prediction and the Zeng & Steedman (2000) method for

the corresponding tilting mode. These methods are schematically presented in Figure 4.1. Their

predictions are compared to the experimental results, for validation and better understanding of

the retaining wall behaviour and the corresponding failure mechanisms.

In order to apply the sliding block methodology in the case of the cantilever wall, the soil mass

above the foundation slab shall be considered as part of the “rigid block”. In addition, the

retaining walls of Figure 4.1 are founded on a rigid base so the rotational displacement estimated

by the Zeng & Steedman (2000) methodology, arises from the tendency of the wall to rotate


48

about the toe (point O). As mentioned in the introduction, this is not the critical failure

mechanism when the wall is founded on a compliant base. In this case, the tilting deformation is

mainly an effect of bearing capacity failure at the toe area, something that is not taken into

consideration by Zeng & Steedman (2000), nor by any other simplified method in the literature.

Figure 4.1. Gravity retaining wall on rigid base examined against (a) sliding according Richards

& Elms, (1979) and (b) rotation about the toe (point O) according to Zeng & Steedman, (2000)

The permanent deformation of the wall according to the sliding/rotating block theory, is

calculated by double time integration, of the relative wall-base linear acceleration or the relative

radial acceleration, for which a good estimation of the corresponding “critical accelerations” is

necessary. Apart from performing the time integration, Richards & Elms (1979) proposed the

simple formula given in Eq. (4.1), which provides an upper-bound estimation of permanent

displacement based on true records (Franklin & Chang, 1977)

2 3

max max

40.087perm

y

a

a

vd (4.1)

In Eq. (4.1) amax and vmax is the maximum base acceleration and velocity and ay is the sliding

critical acceleration. The prediction of the above equation has to be multiplied with the number

of cycles for the case of a harmonic excitation.

The results of the theoretical methods are compared to the corresponding experimental data of


49

Configurations No1 and No3, in Figures 4.2 to 4.6, separately for harmonic and seismic loading.

In the first graph of each figure, the permanent displacements (increments) recorded along the

wall by the 3 LVDTs D1-D3, are presented as functions of the motion PGA. On the graph the

critical acceleration values against sliding and tilting (bearing capacity) are also noted. It has to

be mentioned at this point, that the critical acceleration that can cause uplift and overturning of

the wall (provided the existence of a rigid base) are much higher (about 0.62g for Configuration

Νο1 and 0.43g for Configuration Νο3). In the next two graphs, the experimental data are

compared to the predictions of the theoretical methods, both for wall sliding (LVDT - D1) and

wall rotation, calculated from the measurements of LVDTs D1 and D2. In Figures 4.7 and 4.8,

theoretical and experimental time histories for sliding and tilting are compared, for

Configurations No1 and No3 under harmonic loading of 0.19g and 0.23g and under seismic

loading with PGA of 0.35g and 0.55g, respectively.

The following can be concluded from the graphs: First, yielding accelerations estimated

in Table 2.3 are confirmed judging from the behaviour of the experimental curves. Second, the

predictions of Richards & Elms (1979) method for the wall sliding are in relatively good

agreement with the experimental measurements. In the case of Configuration No1, which is a

mainly sliding mechanism, Richards & Elms (1979) method significantly overestimates the

permanent deformation, with increasing seismic excitation. In the case of Configuration No3,

there is a better agreement than in Configuration No1. For accelerations lower than critical the

permanent deformation is underestimated and it is overestimated for higher acceleration values.

These deviations can be explained from the point of view that Equation 4.1 is an upper bound of

the permanent deformation and considers the critical acceleration as a constant value. In reality,

the critical acceleration always increases, as the wall toe penetrates the underlying soil layer,

resulting to increasing sliding resistance. This has been already observed at the experimental

results (see Figures 3.14 and 3.16), as well as in numerical simulations (Green et al, 2008).

Additionally, the sliding block technique neglects any possible wall sliding back towards the

backfill, which in the case of strong shaking may not be negligible. Finally, the sliding block

technique initially underestimates permanent displacement in the case of Configuration No3, as

this deformation is mainly a product of the tilting mode of failure mobilized first.

Third, the Zeng & Steedman (2000) method fails to predict the experimentally measured

permanent rotation of the wall at low accelerations, whereas at higher accelerations, a notable

overestimation is observed. This can be explained taking under consideration the compliance of


50

the foundation, and the corresponding bearing capacity failure mechanism, which is the

predominant rotational failure mode. It appears that the compliance of the base and the

development of plastic deformation under the wall toe absorbs energy and is rather helpful for

the stability of the wall during strong earthquakes, not allowing wall uplift and overturning. On

the other hand, comparisons of the two experimental Configurations show that the rotational

mechanism of Configuration No3 systematically yields greater deformation at strong earthquake

loading, whereas the sliding mechanism of Configuration No1 is more affected from harmonic

loading. This may indicate that the bearing capacity failure happens more rapidly, compared to

the sliding block mechanism mobilization, that is purely a time integration effect, depending on

the time interval within which the critical accelerations is been exceeded. Generally the

behaviour of sliding mechanisms is more stable and predictable, plus the fact that the wall can

sustain important sliding without damage, contrary to tilting structures.


51

Figure 4.2 Comparisons of experimental permanent displacement and rotation with the

predictions of sliding/rotating block theory – Configuration No1 under harmonic loading


52




53


predictions of sliding/rotating block theory – Configuration No1 under seismic loading


54




55

Figure 4.6 Comparisons of time histories for experimental permanent displacement and rotation

with the predictions of sliding/rotating block theory – Configuration No1 under harmonic

loading 0.19g and 0.23g and under seismic loading 0.35g and 0.55g


56

Figure 4.7 Comparisons of time histories for experimental permanent displacement and rotation

with the predictions of sliding/rotating block theory – Configuration No3 under harmonic

loading 0.19g and 0.23g and under seismic loading 0.35g and 0.55g


57

5 Interpretation of dynamic bending moments

Given that no direct measurements of earth pressures were made, some estimates of earthquake

loading on the retaining wall can only be inferred from the bending moment measurements on

the wall stem. In fact, the strain gauges performed adequately in recording the dynamic variation

of the dynamic component of bending moment, but not its static counterpart due to gravitational

action. The only available information arises from the seismic component of the bending

moment, ΔΜ. As has already been mentioned, an increase in the wall bending moment (positive

ΔΜ) is observed when the wall moves towards the backfill and a corresponding decrease when

the wall is in an active failure condition. The same remarks have been based on numerical

simulations of a full scale cantilever retaining wall by Green et al (2008).

In the present section, an interpretation of the measured dynamic bending moments is presented,

based on simplified assumptions for the variation of inertial forces and earth pressures behind the

wall. This assumptions are presented in Figures 5.1 and 5.2. First, it is a rational hypothesis to

assume that the inertial force acting on the soil mass moving with the wall (hatched gray area in

Figure 5.1), exerts no earth pressure to the wall stem, as indicated by the AASHTO - NCHRP

Report 611 (2008). As a result, the actions that have to be taken under consideration are the

variation of earth pressures ΔPE on the vertical virtual back and the inertial force Fw acting on the

cantilever itself, at the time of minimum and maximum bending moments on the wall, as

recorded from the strain gauges. The first action is calculated by means of the acceleration

recordings at backfill accelerometers A13 and Α16 and the second from the relative top to base

acceleration of the cantilever beam Α6 - Α5, under the assumption of linear with depth

accelerations distribution (Al Atik & Sitar, 2007).

The calculations of earth pressure variations follow a kinematically mobilized assumption shown

in Figure 5.2, suggesting that when the inertial action drives the system towards to the backfill,

stress condition moves from K0 to passive, so contact stresses increase by an amount (ah/g)γz.


58

Respectively, when the inertial forces drive the system towards active failure, there is a

corresponding decrease in contact stresses. If the seismic action is strong enough to cause active

failure, the contact stresses are described by an active stress field (see paragraph 2) and the

variation of stresses is equal to (ΚΑΕ – Κο)γz. A value of Κο~1 can be used in the calculations as

previously.

A5

A6

A13

A16

Wall inertial forces(A6A5) γw τw

Dynamic earth pressures

a(z) γs z ή (Κ0 ΚΑ) γs z

acceleration distribution

a(z)

A13

A16Fw

ΔPE

Figure 5.1 Inertial and contact forces contributing dynamic bending moment on the cantilever

wall

γz

10

KAE γz K0 γz

(ah/g) γz (ah/g) γz

ahah

( ) ( )kh kh

Figure 5.2 Stress variation in the backfill during dynamic loading


59

In Figures 5.3 to 5.6, comparisons of the experimentally measured bending moments with the

predictions of the simplified theoretical approach are presented, for various cases of harmonic

and seismic loading and Configurations No1 and No3. Specifically, the cases of strong harmonic

(0.19g and 0.23g) and seismic (0.35g and 0.55g) loading, as well as two cases of weaker

excitation causing negligible yielding to the system (harmonic 0.15g and seismic 0.17g), are

presented. The experimental time history records for these cases are provided in the Appendix.

In all the above cases the experimental recordings show an increasing variation of the dynamic

bending moment, with increasing excitation level. The predictions of the simplified theoretical

model consistently fit to the experimental data, with higher deviations observed in the case of

Configuration No3, probably due to the characteristic rocking response of the later. The fitting

could be better, if a non-linear earth pressure distribution, suitable for rotational yielding modes

is applied (Kloukinas, 2012).

With respect to the wall stem inertial force effect on the dynamic bending moment, the

theoretical model estimates range between 2.5% and 10% of the total dynamic moment. This is

in agreement with the findings of Al Atik & Sitar (2007), who estimated that the contribution of

the inertial force of the wall stem to the bending moment ranges between 5 to 26 percent of total.

The contribution is minor at the point of the active failure and maximum at the opposite

direction.

Finally, it must be noted that for a safer interpretation of the dynamic loads on the system, more

information is needed through rigorous numerical simulations of the experimental model.


60

\


Configuration No1 under harmonic loading of amplitude 0.15g, 0.19g and 0.23g


61


Configuration No1 under seismic loading of PGA 0.17g, 0.35g and 0.55g


62


Configuration No3 under harmonic loading of amplitude 0.15g, 0.19g and 0.23g


63


Configuration No3 under seismic loading of PGA 0.17g, 0.35g and 0.55g


64

6 Conclusions

In the present report, the results of a suite of shaking table tests on model cantilever retaining

walls conducted in the BLADE laboratory at the University of Bristol, were presented. The

initial motivation of this experimental study was the validation of recent stress limit analysis

solutions for the seismic design of this type of retaining structures (Evangelista et al, 2009, 2010;

Kloukinas and Mylonakis, 2011) in conjunction with the absence of any specific, relative

regulations in established seismic codes, including EC-8. Special issues related to stability design

and response of walls founded on compliant base, were also studied. The experimental design

and procedure, as well as the main outcomes were described in detail and can be summarised to

the following conclusions:

1) The experimental results confirm the predictions of the theoretical stress limit analysis,

with reference to the failure mechanisms and the critical yield accelerations of the system.

Pseudo-static stability analysis proves to behave adequately for both harmonic and seismic

excitation, although important dynamic effects are evident in the first case, with reference to the

response of the backfill and the wall stem. On the other hand, earthquake loading results to

conditions closer to the assumptions of the pseudo-static analysis, namely the uniform

distribution of the acceleration and the “rigid block” response of the backfill.

2) The response of the various experimental configurations confirm the predictions of the

stability analysis of the retaining wall in terms of an equivalent footing and the relationship

between wall tilting and bearing capacity failure. Wall tilting is commonly observed at the vast

majority of retaining walls founded on compliant base, related to bearing capacity failure due to

high eccentricities and inclination of the reaction transferred to the wall foundation. This remark

highlights the importance of a proper design of walls founded on compliant base with respect to

sliding and rocking.


65

3) The experimental measurements of permanent plastic deformation of the soil-wall

system fit quite well to the predictions of the simplified sliding block technique of Richards &

Elms (1979), but not to the predictions of the corresponding rotating block model of Zeng &

Steedman (2000). The significant deviations observed are explained in terms of tilting failure

related to wall foundation settlement and bearing capacity failure, instead of uplift and

overturning mechanism adopted in Zeng & Steedman (2000) analysis.

4) With respect to the effect of seismic loads on the structure, it is proved that the soil

thrust maximizing the bending moment of the stem, do not coincide to the critical earth pressure

for overall stability, but they appear in opposite phase. This indicates that different load

combinations have to be used for the static design of the wall and for the stability analysis of the

system against sliding and bearing capacity. This is in agreement with numerical analysis results

by Green et al (2008). Moreover, the dynamic bending moments interpretation is in agreement

with the findings of centrifuge testing by Al Atik & Sitar (2007), relative to the effect of the

inertial force on the wall stem.

5) Finally, the suitability of modern codes and specifications (ΕC7, AASHTO) in design

of retaining walls compliant to sliding is confirmed. The specific behaviour appears to be less

sensitive to seismic excitations compared to rotationally sensitive mechanisms. The rotational

compliance of wall foundations result in smaller bending loads on the cantilever beam, but also

on greater permanent rotational deformations, that can cause induce failure on the structure.


66

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Zeng, X. and Steedman, R.S. (2000). "Rotating Block Method for Seismic Displacement of Gravity Walls", Journal

of Geotechnical and Geoenviromental Engineering, ASCE, 126, 709-717.


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Appendix


70

Appendix A.1 – Resonant frequencies and damping ratios from white noise testing

Configuration No1 – Wall on foundation layer – without backfill


71

Configuration No1 – After placement of the backfill


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Configuration No2 – After placement of the backfill (before harmonic loading)


74

Configuration No2 – After placement of the backfill (before seismic loading)


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Configuration No3 – After placement of the backfill (before harmonic loading)


77

Configuration No3 – After placement of the backfill (before seismic loading)


78

Appendix A.2 – Resonant frequencies and damping ratios from white noise testing

In the following set of figures, time histories of strain gauges measurements interpreted into

bending moments (Nm) are presented, for the same cases presented in Section 5 of the report.

The measurements correspond to the strain gauges arrays being situated on central line of the

wall stem. The internal array SG1-SG5 is plotted with black line and the external array SG8-

SG12 with red. As it can be seen from the graphs, the internal instruments work properly only at

Configuration No1. As a result, the bending moments estimation is mainly based on the external

array of strain gauges.


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