Pile induced filtering of seismic ground motion in homogeneous soil

Abstract

The foundation input motion (FIM) that a structure experiences during an earthquake, is known to be different from the free field ground motion due to soil structure interaction (SSI) effects. Kinematic interaction in a single pile can also introduce a rotational component to the FIM. Conventionally, soil structure interaction is performed by applying the free field ground motion to the structure ignoring the effects of kinematic interaction. Deep foundation elements such as piles are known to suppress certain frequencies of ground motion which in turn induces kinematic bending moments in them. In this study, kinematic soil pile interaction is simulated using 3D numerical models using a coupled finite element-boundary element method. Single pile, group pile and piled raft models in a homogeneous soil profile are analysed for vertically propagating shear waves. Three earthquake time histories with varying frequency content are considered in this study. Transfer functions are then plotted together to analyse the effects of pile induced filtering of ground motion. The ratio of response spectrum at the foundation level and free field ground, for the pile group considered, is found to closely follow the behaviour of a fixed headed single pile. It is found that embedment of the pile cap, as in the case of a piled raft can result in further filtering of ground motion.

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Pile induced filtering of seismic ground motion in homogeneous soil
To cite this article: Ramon Varghese et al 2020 IOP Conf. Ser.: Earth Environ. Sci. 491 012049
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5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
IOP Publishing
doi:10.1088/1755-1315/491/1/012049
1
Pile induced filtering of seismic ground motion in
homogeneous soil
Ramon Varghese1, A Boominathan2 and Subhadeep Banerjee 3
1Research scholar, 2 Professor, 3 Associate Professor,
Indian Institute of Technology Madras, India
Abstract. The foundation input motion (FIM) that a structure experiences during an
earthquake, is known to be different from the free field ground motion due to soil structure
interaction (SSI) effects. Kinematic interaction in a single pile can also introduce a rotational
component to the FIM. Conventionally, soil structure interaction is performed by applying the
free field ground motion to the structure ignoring the effects of kinematic interaction. Deep
foundation elements such as piles are known to suppress certain frequencies of ground motion
which in turn induces kinematic bending moments in them. In this study, kinematic soil pile
interaction is simulated using 3D numerical models using a coupled finite element-boundary
element method. Single pile, group pile and piled raft models in a homogeneous soil profile are
analysed for vertically propagating shear waves. Three earthquake time histories with varying
frequency content are considered in this study. Transfer functions are then plotted together to
analyse the effects of pile induced filtering of ground motion. The ratio of response spectrum at
the foundation level and free field ground, for the pile group considered, is found to closely
follow the behaviour of a fixed headed single pile. It is found that embedment of the pile cap,
as in the case of a piled raft can result in further filtering of ground motion.
Keywords: soil structure interaction, pile foundation, piled raft, response spectrum
1. Introduction
Pile foundations are often employed to support structures when shallow soil layers are incompetent to
carry foundation loads. Vertically propagating shear waves from an earthquake can result in bending
moments are shear forces in pile foundations. Critical structures that are often founded on pile
foundations include highway bride abutments, tall buildings, and heavy storage structures.
Seismic soil structure interaction can be considered to be a combination of a kinematic response
and an inertial response. Kinematic response is fundamentally a result of the contrast in stiffness
between foundation and soil stratum. Kinematic response is more prominent for embedded
foundations than shallow foundations [1]. It has been proven that SSI does not always play a beneficial
role in the seismic response of structures as often assumed [2]. The frequency dependent nature of SSI
needs to be taken into account for any reasonable prediction of seismic response. The importance of
considering SSI in the design of pile foundations has been highlighted by several studies from the past
[3-5]. Kinematic response of pile foundations has been found to be significantly influenced by the pile
soil stiffness contrast, and pile spacing [6].

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
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doi:10.1088/1755-1315/491/1/012049
2
Although a proper and rigorous nonlinear SSI analysis can simulate soil pile systems with a high
degree of accuracy [7, 8], the computational effort and skill required is rather high for routine design.
Simplified methods are therefore used depending on the importance of the structure. Simplified
methods for estimate the FIM for pile foundations includes the use of transfer functions or spectral
reduction factors, both considering the frequency dependent alteration in the free field ground motion
[9, 10].
In the present study, finite element based models are developed for 3D SSI analysis using a
substructuring based numerical method. A hypothetical 3x3 pile group in homogeneous soil layer is
considered for the study. The kinematic response of single pile (SP), pile group (PG) and piled raft
(PR) with an embedded pile cap is analysed for three different earthquake motion records with varying
frequency content. The results are then presented in terms of transfer functions with respect to free
field motion at the surface, as well as spectral ratios.
2. Soil Structure Interaction Analysis
2.1 Kinematic Response of Pile Foundations
It is well known that pile foundations filter out high frequencies from translational response while
introducing a rotational component. Rotational component of foundation input motion can be
detrimental depending on the structure soil system [11]. The rotational component diminishes with an
increase in the number of piles along the direction of motion [10]. A vast majority of previous studies
ignore the effect of an embedded pile cap. The assumption of loss of contact of pile cap and soil can be
justified if the possibility of scouring or soil subsidence exists. However, piled rafts are chosen in
situation where raft-soil contact loss is unlikely. Hence the evaluation of pile soil interaction
considering embedment of pile cap becomes relevant for piled raft foundations.
Kinematic soil-pile interaction, being a frequency dependent phenomenon is often quantified using
transfer functions in translation (Iu) and rotation (I

) defined as
where d is the diameter of pile, u represents displacement, and subscripts p, and ff represent the pile
foundation and free field soil respectively. A dimensionless frequency parameter, ao defined as in Eq.
3, is used in this study.
In addition to transfer functions, the ratio of response spectrum ordinates of the foundation and free
field soil has also been used to represent kinematic response of pile foundations [9]. The spectral ratio,
is defined as
where represents the response spectrum ordinate and subscripts p and ff represent the pile and free
field respectively.
The spectral ratio has the advantage of direct and easier applicability for structural analysis. In the
present study, both transfer functions and spectral ratio are extracted for the cases of single pile, pile
group and piled raft.

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
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doi:10.1088/1755-1315/491/1/012049
3
Total soil structure system
Excavated soil
volume
Structure
Free field site
2.2 Flexible volume substructuring method
The substructuring method in frequency domain that involves partitioning the soil foundation system
into sub systems and then using the principle of superposition forms one of the most computationally
efficient techniques for SSI analysis. In the present study, three dimensional SSI analysis is carried out
using the FEM-BEM based program ACS SASSI program [12,13]. The soil-foundation system is
partitioned into three subsystems namely free field site, excavated soil, and structure or foundation as
presented in Fig. 1. The foundation and near field soil are modelled using 3D finite elements whereas
the far field soil is taken into account using the Thin Layer Method [14]. The free field soil is
represented in terms of impedances defined at each interaction nodes. The equation of motion in
frequency domain can be expressed as
[]{} = {} (5)
where C is the total stiffness matrix which can be expressed as a function of the complex stiffness
matrix [K], mass matrix [M} and frequency ω as
[] = [] − 2[] (6)
The equations of motion for the Flexible Volume Sub-structuring Method (FVSM) method are
formed by combining the equation of motion of the structure and those of soil in the frequency
domain.
In equation (7) the subscripts s, i and f refer to degrees of freedom at the superstructure, basement
and excavated soil nodes respectively. In the FVSM technique, all finite element nodes of the
excavated soil volume are treated as interaction nodes, which leads to a rigorous and computationally
expensive analysis. The soil profile consists of viscoelastic horizontal layers. Material damping is
introduced by complex moduli which includes an effective damping ratio. Evaluation of the
methodology against published centrifuge shaking table test results as well as analytical results have
been reported by different authors [15-18] and is not repeated for brevity.
Figure 1. Partitioning of the total system into substructures in the Flexible Volume Method
2.3 Pile soil system
The problem of kinematic foundation soil interaction is often studied by analysing massless
foundations subjected to vertically propagating shear or compressional waves [2, 19]. The assumption
of massless shallow foundation can be compensated by considering foundation mass in the inertial
interaction stage of SSI analyses. In the present study, kinematic response of a fixed head single pile, a
9 pile group and a corresponding piled raft foundation in a homogeneous viscoelastic soil stratum with
elastic modulus of 30 MPa, and damping ratio of 5% overlying rigid stratum were analysed. The piles

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
IOP Publishing
doi:10.1088/1755-1315/491/1/012049
4
t
10 m
0.5 m
(a)
(
(c)
b)
1 m
4 m
4
1 m
y
x
1 m
2
2 m
(d)
1 m
were of diameter of 0.5 m and length of 10 m spaced at 8 pile diameters in the longitudinal direction
and 4 pile diameters in the transverse direction as presented. A homogeneous soil layer of thickness 20
m overlying rigid stratum is considered in the analysis. Three-dimensional finite element models of a
single pile (SP), pile group (PG) and piled raft (PR) were created with vertical mesh size restricted to
one fifth of the shortest wavelength to satisfy the wave passage criteria. Figure 2(a)-(c) presents
schematic diagrams of the three cases considered. The fixity of the single pile was ensured by applying
rotational restraint at the pile head nodes. The pile group model presented in Fig. 2 (b) was adopted
from the hypothetical model considered in Poulos [20]. The model with a ground contacting pile cap
or raft, will be referred to as piled raft (PR) in the following sections. The piled raft model with raft
thickness (t) of 0.5 m corresponding to one pile diameter was considered in this study. The raft was
assigned close to zero mass to avoid inertial interaction effects in the PG and PR models.
In order to rigorously capture pile-soil-pile and raft-soil-pile interactions, near field soil elements
are defined between the piles. The analysis in frequency domain is essentially linear. In the present
study soil is modelled as a viscoelastic solid and the foundation elements are assigned linear elastic
properties. Nonlinear response such as pile soil slip and strain dependent shear modulus and damping
of soil are not considered in this study. Eight noded brick elements were used to model the pile, raft
and near field soil respectively.
Figure 2. Schematic diagram showing (a) the single pile (b) pile group, (c) piled raft and (d) pile
layout in PG and PR models

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
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5
Figure 3. The finite element mesh of the pile group half model
Table 1. Transient ground motion considered in the study
Earthquake
Year
Recording Station
PHA (g)
Mw
Central Mexico
2017
UNAM
0.054
7.1
Ferndale
2014
Ferndale Fire Station
0.062
6.8
Valparaiso
2017
Curacavi
0.083
6.9
Taking advantage of symmetry in the PG and PR models, half models were defined with symmetry
plane parallel to the x axis. For nodes along the symmetry plane, the translational degrees of freedom
perpendicular to the plane were restrained. The finite element mesh of the half model of the pile group
is presented in Fig. 3.
2.4 Seismic SSI analysis
The response of the soil foundation system is evaluated for vertically propagating shear waves. The
ground motion is defined at the ground level. Response to harmonic loads, or transfer functions are
evaluated at the bottom of the pile cap and raft for PG and PR models respectively. Transient response
of the system is evaluated for three different earthquake time histories with varying frequency content.
The earthquake motion is defined by a time history of acceleration and is introduced at the first layer
i.e., ground level. Details of the three input time histories are presented in Table 1. The analyses were
carried out for a total of 34 frequencies covering a frequency range of 0.01 Hz to 22 Hz considering
the frequency content of the input motion. Fig. 4 (a)-(f) presents the acceleration time history and
Fourier spectra of the input motions.
3. Results and Discussion
3.1 Harmonic response
The harmonic response of the three cases are often presented in terms of transfer functions in
translation and rotation [21]. Fig. 5 presents the transfer function in translation for single fixed headed
pile, pile group and piled raft cases. The responses of pile group and piled raft models are found to
deviate from that of a single pile, and the deviation is found to vary with frequency. It is evident that
an embedded pile cap plays an important role in the translational response of the system. For the pile
group-soil system studied, the embedment effect is found to cause up to 25% decrease in translational
response at a dimensionless frequency value of 0.28. However, at ao values above 0.4, the trend is
Pile cap
Near field soil
elements

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
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6
found to reverse, with an embedded pile cap resulting in a higher response in comparison with the case
of pile group.
Figure 4. Acceleration time history and Fourier spectra of (a)-(b) Central Mexico 2017, (c)-(d)
Ferndale 2014, and (e)-(f) Valparaiso 2017 ground motions
Figure 5. Transfer function in translation for the three foundation cases.

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
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doi:10.1088/1755-1315/491/1/012049
7
3.2 Transient response
The transient responses of the three foundation systems were evaluated for three different earthquake
input motions described in Table 1. The input motions were defined at the ground level. The kinematic
SSI effects are quantified using the spectral ratio, as defined in equation (4). The spectral ratios for the
three input motions, obtained from the analyses are presented in Fig. 6. It was found that the spectral
ratio for pile group closely follows the fixed head single pile behaviour. The piled raft model however
was found to exhibit a considerable deviation from the behaviour of the pile group.
Figure 6. Spectral ratio for (a) Central Mexico 2017, (b) Ferndale 2014, and (c) Valparaiso 2017
ground motions
The peak acceleration observed at the top of the piled raft was observed between 8-9% lower than
that of the pile group, for Central Mexico 2017 and Ferndale 2014 input motion with low and
intermediate frequency content respectively. Another significant effect of pile cap embedment is the
characteristic period at which the spectral ratio reaches unity. Available empirical relationship for
spectral ratio such as those proposed by Di Laora and de Sanctis [9] do not consider this effect.
Findings from this study point to the necessity of developing improved spectral ratio functions for

5th International Conference on MODELING AND SIMULATION IN CIVIL ENGINEERING
IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049
IOP Publishing
doi:10.1088/1755-1315/491/1/012049
8
piled raft foundations.
4. Conclusions
The kinematic response characteristics of a single pile, pile group and piled raft models are studied by
carrying out three-dimensional soil structure interaction analyses employing a finite element based
numerical method. Harmonic and transient response of the foundation models are evaluated for
vertically propagating shear waves. The foundation input motion is characterized by plotting transfer
function in translation as well as spectral ratios with respect to free field ground motion. The variation
in transfer functions of pile group and piled raft is found to be frequency dependent. Embedment of
the pile cap is found to result in a reduction of translational response by up to 25% at certain
frequencies. From the spectral ratios evaluated for the three foundation types, it was found that
embedment of pile cap results in a decrease in low period amplitude as well as an increase in the
characteristic period at which the filtering effect can be ignored.
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