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Pile induced filtering of seismic ground motion in homogeneous soil

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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

IOP Publishing

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

IOP Publishing

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

IOP Publishing

doi:10.1088/1755-1315/491/1/012049

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

IOP Publishing

doi:10.1088/1755-1315/491/1/012049

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

IOP Publishing

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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IOP Conf. Series: Earth and Environmental Science 491 (2020) 012049

IOP Publishing

doi:10.1088/1755-1315/491/1/012049

9

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