Proceedings of Indian Geotechnical Conference December 15-17, 2011, Kochi (Paper No. G 302)

DYNAMIC ANALYSIS OF A FULLY INSTRUMENTED EMBEDDED RETAINING WALL:

PRELIMINARY INTERPRETATION

A. Dey Assistant Professor, Department of Civil Engineering, IIT Guwahati, arindam.dey@iitg.ernet.in

C. Rainieri, C. Laorenza, G. Lanzano, M. di Tullio, D. Gargaro, D. Brigante, G. Piccolo, G. Fabbrocino, F. Santucci

de Magistris StreGa Lab, SAVA Department, Univ. of Molise, Italy.

ABSTRACT: The present paper reports a full-scale experimental study, subsequent monitoring and interpretation to shed

light on the dynamic analysis of an embedded retaining wall. The wall is a part of the New Student House of the University

of Molise, Campobasso, Italy. The total height of the wall is nearly 18m, sustaining a free height of nearly 6m. It is

composed of two rows of reinforced concrete piles, 800mm in diameter, arranged in a staggered alignment, and connected

by a reinforced concrete (r.c.) top-beam. Two piles, located in the central portion of the wall, have been instrumented with

specially designed embedded piezoelectric accelerometers and conventional inclinometer cases. Geotechnical data,

interpreted from the conventional borehole stratigraphy and down-hole tests, have been used to develop a dynamic Finite

Element model of the system, implemented with the aid of PLAXIS 2D v8.4. Guided by the scatter in the predicted natural

frequencies as compared to that obtained from the in-situ monitoring, subsequent model updating will lead to the

development of more refined model definition with superior representation of the real-time system.

INTRODUCTION

Deep excavations, bridge abutments and harbour-quays are

usually supported by means of rigid or flexible retaining

walls, such as gravity, cantilever and/or embedded walls.

Their behaviour under static conditions has been

investigated in detail over the years; however, their

dynamic behaviour and the soil-structure interaction

mechanisms are not that thoroughly investigated. When

subjected to dynamic excitation, the different components

of the retaining system exhibit complex and interdependent

responses, which are significantly augmented in the

presence of material and/or geometrical nonlinearities [1].

Depending on the expected material behaviour of the

retained soil and the possible mode of wall displacement,

design of retaining walls subjected to dynamic excitations

is generally carried out by the following two approaches (a)

The classical Mononobe-Okabe approach [2]. (b) The

Subgrade-reaction approach [3]. These methods, though

commonly used, fail to provide a satisfactory prediction of

the overall response of the retaining structure subjected to

dynamic excitation. Parameters influencing the behaviour

of the system, such as damping, natural frequencies of the

system, phase differences and amplification effects of the

backfill, remain unaccounted in the above theories.

A pseudo-dynamic approach based on the assumption of a

finite speed of elastic shear-wave propagation, results in an

enhanced prediction of the behaviour of the retaining

system. Such an analysis reveals that the distribution of

earth pressure and the point of application of the dynamic

thrusts are primarily governed by dynamic properties of the

backfill [4]. This approach, although commonly used for

gravity walls, may be unreliable for flexible retaining walls.

As a solution, dynamic analyses, taking into account soil-

structure interaction represent the most effective techniques

to predict the response of a flexible retaining wall [5, 6].

Depending on the intensity of the input excitation at the

base of the domain relative to the elastic limit, the structure

is modelled as linear or nonlinear. The soil is idealised by

either an equivalent linear or an effective stress model,

depending on the expected strain level in the soil deposit

during the induced motion. However, to achieve a reliable

prediction of the wall behaviour, an extensive soil

characterisation through in-situ and laboratory

investigations, a proper constitutive model for soil and a

precise definition of the dynamic excitation are required.

Information provided by Structural Health Monitoring

(SHM) systems can enhance the level knowledge about

retaining systems, and useful hints for their accurate

numerical modelling can be obtained. Both operational and

earthquake data are relevant to enhance numerical models.

This paper reports the dynamic response of a full-scale

fully-instrumented embedded retaining wall. Pertinent

issues referring to the main uncertainties and steps in the

development of the finite element model, and its

progressive refinement based n the monitoring data is

discussed. Attention is also focussed on the soil-structure

interaction mechanisms, the flexible retaining wall being

acting as the boundary between non-uniform geometry

sections. The key role for the enhancement of the numerical

model played by ambient vibrations measurements is

described in detail, leading to the development of an

updated model, representative of the behaviour of the

system in operation and ready to be further enhanced to

explore the response of embedded retaining walls during

and after an earthquake.

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STRUCTURAL CHARACTERISTICS OF THE

WALL

The reinforced concrete embedded retaining wall is a part

of the new Student House at the University of Molise in

Campobasso, approximately 200 km SE of Rome. It is an

embedded sheet pile wall, composed by two alignments of

adjacent staggered piles. Figures 1a and 1b provides the

basic geometric data of the wall in discussion. A complete

description of the wall is reported in [7]. Figure 2 shows the

staggered arrangement of the piles.

Fig. 1 Basic geometry of the embedded sheet pile wall

Fig. 2 Staggered arrangement of piles

GEOTECHNICAL CHARACTERIZATION OF THE

WALL SITE

The wall site is characterised by a medium-to-high seismic

hazard. From a geophysical point of view, the site is

characterised by deposits of varicoloured scaly stiff clays,

with alternate beds of limestone, calcareous marls and

sandy materials, with supplementary presence of calcernite

and fragments of San Bartolomeo’s flysch.

The geotechnical characterisation of the site is primarily

based on the two borehole investigations (S5 and S6)

carried out on either side of the retaining wall site.

Stratigraphic column extractions, Standard Penetration

Tests (SPT) and Down-hole tests (DH) have been executed.

The extracted samples have been subjected to laboratory

investigations to determine the physical characteristics. The

strength parameters of the soil samples were determined by

triaxial and direct shear tests. Figure 3 typically shows the

different soil layers as identified based on the

stratigraphical characteristics and SPT blow counts. DH

tests carried out in the two boreholes allowed the evaluation

of the primary and shear wave velocities (Vp, Vs) of the

different strata. This information leads to the estimates of

the Poisson’s ratio, modulus of elasticity and shear modulus

under dynamic conditions according to the standard

expressions.

20.5 1 1 1 22; .

2 11

2 1

V Vp sE Vp

gV Vp s

EG (1)

Fig. 3 Stratigraphy investigation in borehole S6

Since the boreholes S5 and S6 are located along the general

contour of the area, there is a grade difference of about 8m

at the ground level between the two. The excavation of the

borehole S6 started from an absolute height of about 676m,

while that of Borehole S5 commenced from about 668m.

The boreholes were separated by a longitudinal distance of

about 35m. Examination of the boreholes by setting up a

grade difference of 8m, identical to the difference in the

ground level during the beginning of their excavation, and

inferences from the stratigraphic column tests, SPT blow-

counts and shear wave profiles led to the recognition of the

presence of soil layers with nearly identical characteristics

but at a certain level difference, which is identified to be

nearly 3m. Hence, a slope of 1V:10H has been adopted for

the geometry of the numerical model.

Based on the above interpretations, a simplified

geotechnical model was adopted for further numerical

investigations. The details of the monitoring techniques and

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Dynamic monitoring and analysis of a fully instrumented embedded retaining wall

investigations can be obtained in [8].

PRELIMINARY NUMERICAL MODEL FOR

MEAUREMENT INTERPRETATION

A finite element (FE) model of the embedded retaining wall

has been set using PLAXIS 2D v8.4: Dynamics Module [9]

in order to evaluate its dynamic properties I linear elastic

conditions, which can be referred to be the representative of

the system in operation (i.e. when it is subjected to ambient

vibrations). Figure 4 depicts the adopted numerical model

for the embedded retaining wall system, and the

corresponding FE mesh.

Fig. 4 Preliminary FE model and the adopted meshing

The dynamic behaviour of the system under operational

conditions has been investigated by modelling the soil as

linear elastic (LE) material in compliance to the observed

low amplitude of ambient vibrations. The elastic modulus

adopted for each stratum has been evaluated on the basis of

the velocity profiles resulting from the DH tests. Average

values of the elastic parameters E and as obtained from S5

ands S6 boreholes have been used for setting the model.

The embedded retaining wall has been modelled by a plate

element of finite thickness. The stiffness of the piles-beam

system has been evaluated by considering a 1m large strip

of the wall, including two piles (Figure 2). Since, the in-situ

sheet pile wall is comprised of two alignments of non-

contiguous piles, the axial and bending stiffness of the

overall system lies in between the stiffness of a single and

the aggregated value of the two contiguous piles connected

by a top beam. The scaled down values adopted are: Axial

stiffness (EA) = 3.08x107 kN/m, and Bending stiffness (EI)

= 4.76x106 kNm2/m. The equivalent thickness of the plate

element (deq) is evaluated by the following expression:

deq= (12*EI/EA), and a value of 1.362 m had been adopted

for the same in the model. A no-slip debonding condition

has been assumed at the soil-wall interface. In compliance

with the high depth of the water table resulting from the

geotechnical investigations, no interaction with the water

has been considered. Table 1 summarizes the adopted soil

and wall parameters for the basic model.

Before starting the model calibration, an optimization of the

model parameters has been achieved in order to obtain its

best functionality. This provides the basic guidance to

choose the appropriate numerical parameters without

jeopardizing the reliability and accuracy of the predictions.

Suggestion about analysis parameter settings is provided in

[9].

Considering a series of dynamic analyses of vertical

propagation of S-waves in a homogeneous layer using

Plaxis 2D v. 8.4 Dynamic module, a suitable calibration

technique is suggested in [8]. It takes into account the

influence of boundary conditions, mesh distributions and

damping parameters on the response of the system. The

width of the model domain significantly affects the quality

of the computed response. A domain having low width-to-

height ratio does not fulfill the modeling assumption of

semi-infinite soil and, as a consequence, the reflection of

the propagating waves from the boundaries adulterate the

response in the region of interest. Hence, to minimize such

effects, a domain aspect ratio (ratio of total domain width to

the average height) greater than 40 is chosen.

Table 1 Material properties of soil adopted in basic FE model

Soil Layer A B C D

Material Type LE LE LE LE E0 (105 kPa) 3.188 4.086 14.51 26.49 G0 (105 kPa) 1.113 1.433 5.045 9.243 0.432 0.426 0.438 0.438 (kN/m3) 18.00 19.03 19.47 19.98

Vs (m/sec) 246.2 271.6 503.9 673.3 HL (m) (Left of wall) 8 3 5 10 HR (m) (Right of wall) 3 3 5 10

In order to facilitate wave absorption at the vertical

boundaries of the model, absorbent boundaries have been

used. Their effect is maximized by setting the relaxation

coefficients as follows: C1=1 and C2=0.25. Meshing also

has a significant effect on the accuracy of the computed

response. The criteria reported in [9] have been adopted in

the present study to determine the mesh size and a suitable

refined meshing scheme has been accordingly set. Figure 4

portrays the adopted meshing for the mentioned numerical

model.

Numerical damping parameters [9] affect the amplification

of the response at resonances but the shape of the

amplification function is not essentially modified. An

implicit Newmark scheme governs the numerical time-

integration and numerical damping is specified by

Newmark damping parameters. An Undamped Newmark

Scheme, also known as average acceleration scheme, has

been considered (so that the predicted frequency spectra

suffer minimal effect from numerical damping) with the

following parameters: N =0.25 and N =0.5.

Rayleigh damping is used to simulate material damping

under plane-strain conditions. Rayleigh parameters have

been determined as per [9]. Considering a 1% damping on

the overall system, Rayleigh damping parameters have been

set as follows: R =0.293 and R =3.032x10-4, both for the

soil and the structure. For the present study a Gaussian

white noise of duration 1 hour and an impulse load 0.01 sec

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long have been applied as input, both having a sampling

frequency of 100 Hz. These types of excitation have been

selected for convenience in compliance with the main

purpose of the dynamic analyses, namely the extraction of

the fundamental dynamic properties of the system from the

simulated model responses. In fact, the selected input

signals are characterized by a flat spectrum over the

bandwidth of interest and, as such, allow an effective and

reliable extraction of the dynamic properties of the system

even with output-only modal identification techniques.

Such techniques can be, therefore, conveniently used if the

purpose of the analysis is a comparison in terms of dynamic

properties only, neglecting the aspect of the frequency

response function. The excitation is applied as propagating

shear waves generated by base shaking.

Dynamic analysis of the basic model is carried out to

determine the acceleration response of the retaining wall at

different locations. It has been subsequently analyzed in

order to extract the dynamic properties of the modeled

system and to compare them with the corresponding

experimental estimates obtained from dynamic

measurements provided by the SHM system installed on the

wall [7]. The values of the first two resonant frequencies of

the preliminary numerical model, as calculated by

Frequency Domain Analysis (FDD) from the acceleration-

time response of the wall were equal to 4.7 Hz and 6.7 Hz,

respectively. Figure 5 presents the frequency spectra of the

same.

Fig. 5 Frequency spectra obtained by FDD on acceleration-

time history of the wall

Table 2 enumerates the results obtained from experimental

and numerical investigation, and computes the degree of

scatter between the two. It can be observed that in terms of

the frequencies of vibration, the degree of scatter is more

than 20% for the first mode. This can be attributed due to

the uncertainties related to the determined soil properties

especially at the top and bottom layers, and the inadequate

knowledge about the depth and profile of the bedrock. Such

uncertainties can be effectively handled by model

refinement through uncertainty reduction and model

optimization. However, this subject is beyond the scope of

this paper and will be discussed in future articles on this

project.

Table 2 Scatter between experimental and preliminary numerical investigation.

Mode fexp (Hz) fFEM (Hz) Scatter (%)

I 3.68 4.7 21.7 II 7.23 6.7 -7.33

CONCLUSIONS

This paper reports the determination of the dynamic

response of embedded retaining wall system under

operational conditions subjected to ambient vibrations. In

this article, the development of a numerical dynamic FE

model of the same has been reported. Based on the

extensive geotechnical investigation, a basic model has

been set and its dynamic response is investigated. Plaxis 2D v8.4: Dynamics Module have been aptly utilised to develop

the numerical model of the same. Calibration of the model

has been done to choose the optimal set of parameters

which would provide the best results from the preliminary

numerical model. The fundamental frequencies of vibration

have been identified and compared to those obtained from

SHM investigations. Although significant scatter have been

reported between the two results, uncertainties related to the

models have been identified and the procedure to develop a

refined model would be described in a subsequent article.

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