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, [email protected]
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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