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SEISMIC RESPONSE OF GROUP OF MICROPILES CONSIDERING PILE-CAP
CONNECTIVITY CONDITIONS
Dahlia Hafez1, Alper Turan2, Hesham El Naggar3, Tony
Sangiuliano4
ABSTRACT Micropiles are widely used in seismically active areas,
where they are expected to resist significant lateral loads. The
pile-cap connectivity condition and the characteristics of the
supported superstructure can have a significant effect on the
lateral response of micropile supported foundations. Evaluating
these factors and their impact on the lateral response should be an
important design consideration. This paper includes the results of
a numerical study investigating the soil-micropile-structure
interaction with an emphasis on the pile-cap connectivity condition
and the dynamic characteristics of superstructure. A 3D non-linear
finite element model is developed using the commercial software
package ABAQUS and is used in the analysis of the seismic
soil-micropile-structure interaction problem. The Ricker Wavelets
were used in the analysis. Non-linear soil behavior was modeled
using a Mohr-Coulomb plasticity model and constant Rayleigh
damping. The results indicated that the dynamic characteristics of
the superstructure have a significant impact on the bending moments
of micropiles. The results also indicated that the use of
hinged-head connectivity resulted in significant reductions in the
maximum bending moments. Such assumption also resulted in a uniform
distribution of bending moments among the micropiles within the
group. 1. INTRODUCTION
Micropiles are bored and grouted small diameter piles used in a
wide range of applications, including foundation rehabilitation,
slope stabilization, retaining structures, vibration reduction,
etc. They are particularly suited for situations with difficult
access, restricted clearance and poor ground conditions, where
minimal disturbance to the existing structure is permissible (FHWA
1997). Micropiles have been used for retrofitting and
rehabilitating existing foundations due to their ease of
installation (e.g. Taylor et al. 1998; Zelenko et al. 1998; and
Misra et al., 1999). Micropiles have also been used to increase the
overall resistance and to reduce deflections of existing
foundations subjected to compression and uplift forces (Mascardi
1982; Laefer, 1999; Bruce et al., 1997; and IWM99 1999).
Micropiles can be advantageous for construction in seismic
areas, mainly due to their flexibility, ductility and ability to
withstand uplift forces. Micropiles are used to support foundations
of both new and existing structures (Pearlman et al., 1993; Juran
et 1 Assistant Professor, Faculty of Engineering, Cairo University,
Giza, Egypt, 01145111166, [email protected] 2 Foundation
Engineer, Material Engineering Research Office, Ontario Ministry of
Transportation, Downsview, Ontario, Canada, 4162354333,
[email protected] 3 Professor, Faculty of Engineering, The
University of Western Ontario, London, Ontario, Canada, 5196614219,
[email protected] 4 Foundation Engineer, Material Engineering
Research Office, Ontario Ministry of Transportation, Downsview,
Ontario, Canada, 4162355267, [email protected]
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al., 2001; and Shahrour and Juran, 2004). Most studies on
dynamic soil-micropile-foundation interaction have been numerical
simulations. Kishishita et al. (2000) performed 2-D finite element
simulations of micropiles considering different input motions and
pile types using a linear elastic model and various nonlinear
models for the soil and pile. Shahrour et al. (2001) conducted a
3-D FEM analysis of a single micropile and a micropile group
supporting a superstructure assuming a square micropile
cross-section and elastic material with Rayleigh damping. Ousta and
Shahrour (2001) analyzed a single micropile and group of micropiles
in saturated soils using a cyclic elastic-plastic constitutive
model. Sadek and Shahrour (2004) investigated the influence of pile
inclination on the seismic behaviour of a micropile group. Wong
(2004) investigated the seismic behaviour of micropiles using
different levels of soil non-linearity, load intensities and
frequency contents and pile inclinations. Lastly, the influence of
pile head and tip connections on the dynamic response of micropile
supported foundations was studied by, Sadek and Shahrour (2006)
using a 3D finite element scheme and considering both vertical and
inclined pile.
A number of reduced scale and full-scale micropile tests have
been reported in the literature. Yamane et al. (2000) conducted
lateral and vertical load tests on various full scale micropiles.
Yang et al. (2000) tested a single reduced scale micropile
installed in dry sand on a shaking table. Juran et al. (2001)
tested a single reduced scale micropile, micropile groups, and
micropile networks in the centrifuge. The lateral performance of
micropile groups and micropile networks was assessed in the field
by Geosystems, L.P. (2002). Each of the preceding studies has
considered various micropile inclinations, pile numbers, and load
types.
Although micropiles have been investigated extensively, there
are some factors that may affect the long-term performance of
micropiles and that warrant further study. In this paper, a series
of 3D time domain dynamic analyses and some pseudo-static analyses
of micropile groups have been performed. A linear elastic material
model has been established for the piles and pile cap along. The
modeling of the soil behaviour is performed using simple
Mohr-Columb plasticity. Verification of the finite element model,
details of numerical model, influence of various aspects such as
the dynamic characteristics of superstructure and influence of
pile-cap connectivity conditions have been investigated considering
soil-pile interface non-linearity. Finally, the results are
discussed and conclusions have been provided. 2. METHODOLOGY 2.1
Problem Geometry
The problem investigated in this study is the seismic response
of a 9-group of micropiles constructed in a 25m deep homogeneous
soil deposit. The 9 micropiles were 15m long and 0.25m in diameter,
and were connected to a 3m 3m 0.3 m thick reinforced concrete pile
cap. A single degree of freedom system was connected to the top of
the pile cap as shown in Figure 1 and discussed below.
Each micropile was assumed to comprise a 0.09m diameter
concentric steel reinforcement bar extending from the pile head to
toe, and pressure grouted. A series of dynamic analyses were
carried out to study the effect of pile to cap connectivity
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condition on the bending moments on the micropiles with various
superstructure considerations. In addition, the influence of the
micropile location within the group on its seismic response was
studied.
Figure 1. Schematic of problem geometry.
2.2 Numerical Modeling
A finite element model was used to investigate the behavior of
the soil-pile-structure system depicted in Figure 1. The micropile
supported foundation and soil layer were modeled using mainly
8-noded linear hexahedron elements with three degrees of freedom
per node (see Figure 2). Since the higher frequency components of
input motion are difficult to transmit if the element size is too
large, the maximum element size used was between 1/6th and 1/8th of
the minimum Rayleigh wavelength in accordance with Kramer (1996).
The problem boundaries are modeled using infinite elements (Lysmer
and Kuhlemeyer, 1969). A mesh sensitivity analysis was performed to
verify the validity of mesh density.
The initial step in each analysis involved a geostatic analysis,
which was carried out to establish the initial geostatic
equilibrium. The seismic loading was simulated by applying
acceleration time histories at the base of the model. Two
simplified superstructures were investigated which were modeled as
single degree of freedom oscillators comprising a concentrated mass
and a column. The superstructure was composed of a concentrated
mass of 40 tons. The fixed base fundamental frequency of short and
tall structures (SDOF-S and SDOF-T) system were calculated as 1.36
Hz and 0.4Hz. 2.3 Validation of Numerical Model
The 3D finite element model used in the analysis was verified
using field load test
data presented by Richard and Rothbauer (2004). Their load
testing program involved lateral load tests conducted on 20
micropiles with length to diameter (L/D) ratio greater
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than 20 and had a steel casing along the entire micropile
length. The micropile considered in the verification of the
numerical model was micropile C1, which was 244mm in diameter with
bending stiffness, EI, equal to 1.914 E+10 KNmm2 (see Richard and
Rothbauer, 2004). The pile length was not specified, thus it was
taken as 8 m long which satisfies the length to diameter ratio
criterion.
The micropile was embedded in a soil layer classified as sandy
or silty clay with shear strength, cu = 86 kPa and unit weight, =
18.9kN/m3. The soil was modeled using the Mohr-Columb Plasticity
model. The elastic modulus and Poissons ratio where not given.
Therefore, they were back calculated using typical values to match
the field results. The elastic modulus, E, was taken as 23.7 MPa
while Poissons ratio was taken as 0.3, which gave the best fit to
the measured field results. The lateral boundaries were rigid
boundaries placed at a distance 100m from the center of the pile.
The model base was constrained using rough-rigid boundary
conditions. Due to the symmetry of the problem, only half of the
problem was modeled. A good agreement was achieved with the lateral
load test results and finite element simulations. Thus, the same
micropile and soil characteristics are utilized for other analyses
performed in this study. 2.4 Applied Seismic Load
The seismic load was applied in the form of a Ricker wavelet
(Gazetas, 2001). The horizontal accelerations with peak amplitude
of 0.3g with a predominant period of 0.16s was applied to the model
base. The duration of the Ricker wavelet was two seconds. The
analyses, however, were continued for four seconds. The Ricker
wavelet input time history used is given as:
])].(..exp[[)].(..[21
.)( 20
20
ttdtfttdtf
Ata
[1]
where, a(t) is the acceleration time history, t is the time, dt
is the sampling interval, t0 is the duration of interest, A is the
maximum acceleration, and f is the predominant frequency of the
motion. 3. RESULTS
The results for three cases were studied. The first case was a
foundation supporting no structure (No-STR case), which reflected
the kinematic behaviour of the micropile group. The second and
third cases were for the foundations supporting a short (SDOF-S
case) and a tall (SDOF-T case) superstructure, respectively. For
each of the three cases, a hinged and a fixed micropile head fixity
conditions between the micropile group and the cap were
considered.
3.1. Effect of Dynamic Characteristics of Superstructure and
Pile Head Fixity
The distribution of the maximum bending moment along the central
pile P5 considering a superstructure with different characteristics
are presented in Figures 3 and 4 for the fixed-head and hinged-head
conditions, respectively.
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For fixed-head conditions, it was observed that the
superstructure had a significant influence on the bending moments.
SDOF-T case resulted in higher bending moments relative to SDOF-S
case and No-STR cases. Maximum values of bending moments were near
the pile-cap connection. For hinged-head conditions, the maximum
value of bending moments occured at around 10 m depth (see Fig 4).
The difference in the magnitudes of maximum bending moments
remained insignificant for No-STR, SDOF-S and SDOF-T cases. Thus,
influence of superstructure on the bending moments of hinged-head
micropiles were negligable.
It can be seen from Figures 3 and 4 that the kinematic
interaction influences the seismically induced bending moments in
micropiles where hinged-head conditions are assumed. However, the
maximum bending moments increase drastically with the consideration
of inertial effect of the superstructure when fixed-head conditions
are assumed. It was observed that the assumption of hinged-head
connectivity resulted in significant reduction in the maximum
bending moments. Such reductions were more pronounced for SDOF-T.
For N0-STR, the fixity of the pile-cap connection has almost no
influence on maximum bending moment. Table 1 summarizes the maximum
lateral pile head deflections. The results shown in Table 1
indicate that the maximum lateral deformations were between 3.5 mm
and 4 mm. Thus, the lateral pile head deflections were almost
insensitive to both pile-cap connectivity and supported
superstructure.
Figure 2. Model mesh composed of hexahedron and wedge
element.
Table 1. Maximum lateral pile head deflections. Lateral
Deflection of Pile Head (m) Hinged-Head Fixed-Head No structure
0.00374 0.00369 Short 0.00364 0.00399 tall 0.00378 0.00363
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3.2. Effect of Pile Location within Group
Figures 5 and 6 depict the variation of maximum bending moments
for a corner pile (P1), an edge pile (P4) and a center pile (P5)
for fixed-head and hinged-head conditions (SDOF-T). The results
show that the connectivity condition between the micropile and the
pile cap has a significant impact on the distribution of bending
moments. Results in Figure 5 showed that the maximum bending moment
occurred at the center pile (P5) for fixed-head condition. The edge
pile (P4) and corner pile (P1) experienced smaller bending moments.
The maximum bending moment at the center pile (P5) was calculated
to be five times larger than that of corner pile (P1).
The results shown in Figure 6 indicate that the hinged-head pile
cap connectivity assumption had two important effects: significant
reduction in the maximum bending moments and uniform distribution
of bending moments among the piles located at different locations
within the group. The reduction of maximum bending moment due to
hinged-head assumption were 94% for P5, 87% for P4 and 70% for P1.
The bending moment distribution in P1, P4 and P5 were almost
identical, when hinged-head assumption was adopted.
Figure 3. Maximum bending moment for centre pile
(fixed-head)
Figure 4. Maximum bending moment for centre pile
(hinged-head)
202468
10121416
0 10 20 30
Dep
th(m
)
BM(kNm)
P5fixedtall
50
5
10
15
20
0 0.5 1 1.5 2
Dep
th(m
)
BM(kNm)
P5hingedtall
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Figure 5. The variation of bending moments for P1, P4 and P5
(fixed-head conditions).
Figure 6. The variation of bending moments for P1, P4 and P5
(hinged-head conditions).
4. SUMMARY AND CONCLUSIONS This paper has presented the results
of a series of seismic analyses of a micropile group. The primary
objectives of the analyses were to investigate the effect of the
pile-cap connectivity conditions on the seismic system response. In
addition, the influence of the superstructure characteristics and
location of pile within the group were investigated. The following
is the summary of the results and conclusions arising from this
study.
The results showed that the existance and characteristics of
superstructure had a significant influence on the pile bending
moments for fixed pile-cap connection. SDOF-T case resulted in
higher bending moments relative to SDOF-S and No-STR cases. Maximum
bending moments occured near the pile-cap connection for fixed-head
cases.
20
2
4
6
8
10
12
14
16
0 10 20 30
Dep
th(m
)
BM(kNm)
P5fixedtallP1fixedtall
5
0
5
10
15
20
0 0.5 1 1.5 2
Dep
th(m
)
BM(kNm)
P5hingedtall
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The assumption of hinged-head conditions resulted in significant
reductions in maximum bending moments relative to fixed-head
assumption. The maximum value of bending moments occured at around
10 m depth when hinged-head condition was assumed. The difference
in the magnitudes of maximum bending moments remained insignificant
among No-STR, SDOF-S and SDOF-T cases. Thus, the influence of the
superstructure on the bending moments were negligible when
hinged-pile assumption was made.
The connectivity condition between the micropile and the pile
cap was observed to have a significant impact on the distribution
of bending moments of the piles of different locations within the
group. The maximum bending moment from the highest to lowest
occured at the center pile (P5), edge pile (P4) and corner pile
(P1) for fixed-head condition. The maximum bending moment at the
center pile (P5) was calculated to be five times larger than that
of corner pile (P1).
Hinged-head assumption had two important effects; the
significant reduction in the maximum bending moments and a
uniformizing effect on the bending moments distribution among the
piles located at different locations within the group. The
reduction of maximum bending moment due to hinged-head assumption
were 94% for the center pile (P5), 87% for the edge pile (P4) and
70% for the corner pile (P1). The bending moment distribution in
P1, P4 and P5 were almost identical, when hinged-head assumption
was adopted.
5. ACKNOWLEDGEMENTS The research reported in this paper has been
partially supported by the Ontario Ministry of Transportation and
by the Natural Sciences and Engineering Research Council of Canada
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