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Engineering, Technology & Applied Science Research Vol. 10, No. 3, 2020, 5713-5718 5713

www.etasr.com Nagao: An Experimental Study on the Way Bottom Widening of Pier Foundations Affects Seismic …

An Experimental Study on the Way Bottom Widening

of Pier Foundations Affects Seismic Resistance

Takashi Nagao

Research Center for Urban Safety and Security
Kobe University
Kobe City, Japan

nagao@people.kobe-u.ac.jp

Abstract—The resistance of a pier to horizontal loads, like seismic

loads, is due to the flexural rigidity of its foundations and the

horizontal subgrade reaction. In the event of a massive

earthquake, the latter becomes very small because of the

softening of the ground, while the structure may experience a

large inertia force and lateral spreading pressure. Therefore,
structures with high seismic resistance are required in areas with

high seismicity. When a wide caisson is used as a pier foundation,

a rotational resistance moment caused by the vertical subgrade

reaction acting on the foundation bottom can be expected.

Although this rotational resistance moment increases if the

foundation is widened, in design practice the subgrade reaction

coefficient is evaluated as being low under such circumstances.

Therefore, even if the foundation is widened, the rotational

resistance moment does not increase greatly. Rotational

resistance commensurate with the increased construction cost

due to foundation widening cannot be expected. In the present

study, horizontal loading experiments were performed at one pier

with a normal foundation and at one with widened at the bottom
foundation, and the way that the widening affected the seismic

performance was examined. The results show that compared with

the normal foundation, the bottom-widened one experienced far
less displacement and offered higher earthquake resistance.

Keywords-earthquake resistance; subgrade reaction; pier;

displacement

I. INTRODUCTION

A pier supports vertical loads (e.g. dead weight, cargo) by
means of columnar foundations (e.g. piles) that penetrate to the
bedrock, and resists horizontal loads (e.g. inertia forces during
an earthquake) by means of (i) the flexural rigidity of the
foundations and (ii) the horizontal Subgrade Reaction (SR). As
ships have become bigger, so wharfs have had to be made
deeper, and this increase in water depth results in increased
seismic load. In addition, it has been noted that (i) lateral
spreading pressure may act during a massive earthquake and
(ii) the maximum lateral spreading pressure may exceed the
one specified in seismic design codes [1]. Many damages to
pile foundations during the 1995 Kobe Earthquake have been
reported [2], and a pier in Kobe port buckled at points below
the ground surface, which was caused by the lateral spreading
pressure [3]. Many other cases have been reported of wharfs
being displaced laterally during earthquakes [4-7]. Because a
pier is strongly affected by ground deformation during an

earthquake and experiences residual deformation even when its
structural members are not damaged [8], the deformation
performance of a pier against seismic loads is an important
design criterion. The damage to the pile foundation becomes
even greater when liquefaction occurs [9].

Pier foundations comprise steel-pipe and reinforced-
concrete piles, and large-diameter caissons are also used when
large earthquake loads are considered. When caissons are used
as foundations, a Rotational Resistance Moment (RRM) due to
the vertical SR acting on the foundation base bottom is
expected because of the wide foundations. In the event of a
massive earthquake, the horizontal SR becomes very small
because of the deterioration in ground stiffness [10]. However,
because the foundations are embedded in a strong soil layer,
the effect of lowered ground stiffness at the Foundation Bottom
(FB) is small even during a massive earthquake, and a
sufficient vertical SR can be expected. In addition, when
caisson foundations are used, the area subjected to the vertical
SR can conceivably be increased by widening the FB, thereby
increasing the RRM to enhance the earthquake resistance.
Also, the seismic performance can be expected to increase
because of the soil weight acting on the widened section.
However, it has been noted that although the RRM increases as
the foundations are widened, the SR coefficient used in the
calculation of SR decreases with increasing foundation width
[11-15]. In design practice, formulas for calculating the SR
coefficient are used, which incorporate that effect [16]. When
such formulas are used, the RRM does not increase greatly
even if the foundations are widened, and therefore one cannot
expect a rotational resistance that is commensurate with the
increased construction cost due to the foundation widening.
However, no studies to date have clarified the effect by
experiments on the frame structure, and it is very important in
the earthquake-resistant design of piers to examine how the
foundation width affects the earthquake resistance.

In the present study, experiments involving horizontal
loading were performed on pier models with either a normal
columnar foundation or one with widened FB, and how the
latter affected the seismic performance was examined. Also the
differences in SR and displacement performance due to the
widened FB are discussed.

Corresponding author: Takashi Nagao

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www.etasr.com Nagao: An Experimental Study on the Way Bottom Widening of Pier Foundations Affects Seismic …

II. METHOD

A. Experiments Outline

In the experiments, a soil tank of 900mm (width) × 500mm
(depth) was used as shown in Figure 1, and a steel rigid frame
model simulating a pier was installed in the ground as shown in
Figure 2. This pier model was loaded horizontally using a
mega-torque motor. To avoid effects due to the soil being
restrained by the side walls of the soil tank, the 150mm-deep
pier model was installed in the central part of the 500mm-deep
soil tank. Steady braces were installed so that the horizontally
elongated model would not tilt in the depth direction of the soil
tank because of loading. Figure 3 shows the specifications of
the model. The normal type involves a rigid frame that has a
columnar foundation with a circular cross section of 60mm
diameter whereas the widened type involves a column that has
the same diameter but whose base has been widened to
115mm. The dimensions of these models are based on a scaling
factor (prototype/model) of 100 for the length considering the
recent increases in wharf water depth. The normal and widened
model weights are 0.142kN and 0.150kN respectively, the
latter being heavier because it has a wider base.

Fig. 1. Experimental soil tank

Fig. 2. Model installation status

The ground was prepared by air pluviation, using Tohoku
silica sand No. 6 in the dry state. Although pier foundations
penetrate solid ground, the ground shallower than the bearing
stratum is usually soft. Thus the model ground comprised an
upper layer and a lower layer with relative densities of 42%

and 77% respectively, corresponding to standard penetration
test N-values of 5 and 33, respectively. The upper layer was
100mm thick and the lower layer was 135mm thick, thereby
ensuring that the deformation in the lower soil layer was not
constrained because of the rigid bottom plate of the soil tank.
As shown in Figure 1, the model foundation was embedded by
45 mm into the stronger lower layer.

(a)

(b)

Fig. 3. Model specifications. (a) widened, (b) normal (unit: mm)

By similitude [17], the horizontal loading rate on the model
was determined to be 1/31.6 of the actual scale, in which the
horizontal loading rate was 20cm/s as in [1]. The maximum
displacement under loading was 10mm, which by similitude
corresponds to an actual displacement of 10m.

B. Measured Quantities

The quantities measured in these experiments were the SR
on the pier bottom, the horizontal and vertical displacements of
the pier, and the horizontal load. Time history data were
recorded by a data logger. The SR on the FB was measured by
installing earth pressure gauges on the model FB, two per leg in
the widened type and one per leg in the normal type, on the
basis of the relationship between the diameter of the earth
pressure gauge and that of the model foundations. The
horizontal and vertical displacements were measured by
attaching a displacement gauge to the model as shown in
Figure 3. In the following, the loading side is referred to as the
rear side, and the side where displacement occurs by loading is
referred to as the front side. The measured data were subjected
to (i) a Fast Fourier Transform, (ii) low-pass filtering at 1Hz,
and then (iii) an inverse Fast Fourier Transform to obtain
smooth time history data as in [1].

pressure gauge

5
0
0

3
0

4
7
0

900

1
5
0

mega torque
motor

steady brace

model

(unit: mm)

100

135

Plan view

Side view
mega torque

motor

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www.etasr.com Nagao: An Experimental Study on the Way Bottom Widening of Pier Foundations Affects Seismic …

III. RESULTS

A. Load–Displacement Relationship

Figure 4 shows the time history of horizontal load (red) and
horizontal displacement (blue). Because the loading was
carried out at constant displacement speed, the horizontal
displacement increased linearly with time at the same rate for
each type. The load increased over time, but the degree of
increase was not constant. In both types, the load increase with
time was large until around 1s when it became gradual. This
was due to the change in the displacement mode of the pier
around 1s: at first the rigid frame tilted because of the
horizontal load, then, as the tilt increased, the horizontal
resistance was reduced by the rear side leg floating up,
whereupon sliding occurred. The final horizontal displacement
was 10mm for both types, but the loads required to produce the
final displacement differed, with the maximum load being
0.40kN for the widened type and 0.34kN for the normal type.
The widened type was less likely to deform than was the
normal type.

(a)

(b)

Fig. 4. Time history of horizontal load and horizontal displacement

The relationship between the horizontal displacement (dx)
and the vertical displacement (dy) is shown in Figure 5. The
red line indicates the widened type and the blue line denotes
the normal type. The vertical displacement is positive upward,
and when the tilting occurs by horizontal loading, the model is
displaced upward by rotation. A large vertical displacement
occurred with horizontal displacement for the normal type, but
the vertical displacement of the widened type was small. This
occurred because it was difficult for the widened type to tilt
because the RRM due to the vertical SR acting on the FB was
large.

Fig. 5. Relationship between horizontal and vertical displacement

B. Vertical Subgrade Reaction

Figure 6 shows the time history of the vertical SR on the
FB. As described above, the widened type had two earth
pressure gauges per leg, namely p1–p4 from front to rear. The
normal type had one earth pressure gauge per leg, namely p1 in
the front and p2 in the rear. In both types, the SR at the rear leg
decreased sharply with increasing load: it became zero and the
rear leg floated upon application of a horizontal load of
0.113kN in the widened type and 0.091kN in the normal type.

(a)

(b)

Fig. 6. Time history of SR

As a ratio to the dead weight, this load was 0.75 for the
widened type and 0.64 for the normal type. The SR for p2 of
the widened type, which was the rear side SR in the front leg,
became zero when a horizontal load of 0.252kN was applied,
which corresponded to 1.80 as a ratio to the dead weight. The
front SR for p1 of the normal type did not increase significantly
even if the load or displacement increased after the rear SR for
p2 became zero. This was because the displacement mode
changed from tilting to sliding. The widened type exhibited a
similar tendency.

0.5 1 1.5 2 2.5
0

0.1

0.2

0.3

0.4

widened

time(s)

lo
a
d
(k
N
)

d
x
(m
m
)

0.5 1 1.5 2 2.5
0

0.1

0.2

0.3

0.4

normal

time(s)

lo
a
d
(k
N
)

d
x
(m
m
)

0 2 4 6
0

0.2

0.4

0.6

dx(mm)

d
y
(m
m
)

0.5 1 1.5 2
20−

100

0.1

0.2

0.3

0.4

widened

time(s)

p
re
ss
u
re
(k
P
a
)

lo
a
d
(k
N
)

0.5 1 1.5 2
20−

100

0.1

0.2

0.3

0.4

normal

time(s)

p
re
ss
u
re
(k
P
a
)

lo
a
d
(k
N
)

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IV. DISCUSSION

A. Vertical Subgrade Reaction Characteristics

When a rigid frame is subjected to horizontal loading, tilted
displacement occurs first. We discuss how the tilted
displacement characteristics differ between the normal type and
the widened type. Figure 7 shows the change in the distribution
of the SR with the change in the applied load. The horizontal
axis is the distance from the front end, and the stars mark the
installation positions of the earth pressure gauges. The values
in the legend are those of the horizontal load. When the load is
small (0.02kN), the SR (p2, p4) at the rear side of each leg is
larger than that at the front side (p1, p3) for both the front and
rear side legs of the widened type. This occurs because in the
widened type, the column is installed on the rear side rather
than in the center of the base bottom, and the loading
distribution of its dead weight is not uniform. Although the
front side SR (p1) increases with increasing horizontal load,
there is no change in the rear side SR (p2) on the front side leg
in the range of horizontal load up to 0.10kN. By contrast, the
SR decreases on both rear sides (p3 and p4).

(a)

(b)

Fig. 7. Distribution of SR

In the normal type, the SR (p1) at the front increases with
increasing loading and the SR (p2) at the rear decreases, but the
p2 decrease is larger than the p1 increase. This is because the
rigid frame does not rotate at the center of the span of the
superstructure but does rotate at a point closer to the front than
the center. By contrast, in the widened type, it is difficult to
evaluate the rotational center in this state because the initial
distribution of the dead weight is not uniform. Therefore, we
first averaged the initial values of the four SRs from p1 to p4
and then subtracted their initial average values from the values
of each SR. In addition, the values of the SRs on the front and
back side of each leg were averaged, and were plotted against

the center of the earth pressure gauge installation position for
each leg. The results are shown in Figure 8, where the legend is
the same as in Figure 7. These results indicate that the
rotational center is unchanged and constant regardless of the
magnitude of the load, and that the rotational center position
differs between the normal type and the widened type. In the
widened type, the rotational center is close to the center of the
superstructure span, namely at 0.47 times the span length from
the front end, while in the normal type, the rotational center is
at 0.37 times the span length from the front end. The arm
length of the RRM is larger for the widened type than for the
normal type, and therefore the RRM of the widened type is
larger than that of the normal type. This is the effect of bottom
widening.

Fig. 8. Distribution of SR

The RRM calculation is based on the SR distribution and
the rotational center. The RRM values are plotted against the
load in Figure 9. The red line indicates the widened type and
the blue line expresses the normal type. For a load of 0.1kN,
the RRM is 0.045kN·m in the widened type and 0.035kN·m in
the normal type, with the former being 1.28 times the latter. In
design practice, SR distributions are calculated assuming that
the foundation center of each leg is the rotational center when
evaluating the seismic resistance of a pier. The SR distributions
in such a conventional design differ greatly from the SR
distributions revealed by this study, and the conventional
design underestimates RRM of a pier as a frame structure
because the arm length of RRM is evaluated as being short.

Fig. 9. Rotational resistance moment

B. Displacement Characteristics

Figure 10 compares the relationship between the loads and
the horizontal displacement of the two types. The red line

0 100 200 300 400 500
0

widened

distance(mm)

su
b
g
ra
d
e
r
e
a
c
ti
o
n
(k
P
a
) 0 100 200 300 400 500

widened

distance(mm)

su
b
g
ra
d
e
r
e
a
c
ti
o
n
(k
P
a
)

0 0.05 0.1 0.15 0.2
0

0.02

0.04

0.06

load(kN)

m
o
m
e
n
t(
k
N
m
)

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indicates the widened type and the blue line the normal type.
For a given load, the widened type exhibits smaller horizontal
displacement than the normal type. Because the model weights
differ between the normal and the widened type, as described
above, the results of comparing the displacement characteristics
in seismic coefficient form by dividing the horizontal load by
the model weight are converted into values on the real scale
according to the similitude [17] as shown in Figure 10(b). The
red line denotes the widened type and the blue line indicates
the normal type. In the range of seismic coefficient of 0.4–0.6,
the range of displacement ratio is 0.19–0.38, and the larger the
seismic coefficient, the higher the seismic resistance of the
widened type. In comparison with the RRM ratio, the
difference between the two types is large for the horizontal
displacement. Therefore, the widened type can be said to have
especially high horizontal displacement resistance. For vertical
displacement, as shown in Figure 11, the widened type (red)
produces very little displacement in comparison with the
normal type (blue). In the range of seismic coefficient up to
0.6, the displacement ratio is less than 2%.

(a)

(b)

Fig. 10. Relationship between seismic coefficient and horizontal

displacement

Fig. 11. Relationship between seismic coefficient and vertical displacement

V. CONCLUSIONS

In this study, in order to discuss how widening the bottom
of pier foundations affects the seismic resistance, horizontal
loading experiments were performed by installing two types of
pier models in the ground, namely (i) a normal type with a leg
diameter of 60mm and (ii) a widened type with a width of
115mm. The main conclusions drawn are outlined below.

In a rigid frame subjected to horizontal load, tilted
displacement occurs first, the vertical SR on the front side leg
increases with increasing horizontal load, and the vertical SR
on the back side leg decreases. The rotational center as a rigid
frame is not at the center of the span but at a point closer to the
front than the center of the span. The rotational center position
differs between the normal type and the widened type. The
widened type has a larger RRM arm length than the normal
type because the rotational center is closer to the center of the
span compared with that of the normal type. Therefore,
compared to the normal type, the widened type has a larger
RRM which at maximum is 1.28 times the RRM of the normal
type. In design practice, such vertical SR distributions cannot
be reproduced, and the RRM is underestimated.

When the amount of horizontal displacement with respect
to the seismic coefficient is compared in terms of real scale, the
widened type has 0.19–0.38 times the horizontal displacement
in the range of seismic coefficient from 0.4 to 0.6 compared
with the normal type. Compared with the normal type, the
widened type experiences less horizontal displacement,
especially in the range of large seismic coefficient, and the
widened type has remarkably high seismic resistance against
the action of a massive earthquake. For vertical displacement,
the widened type produces only 2% or less of the displacement
of the normal type.

ACKNOWLEDGMENTS

The experiments were conducted with the help of Rie
Yamaoka and Daisuke Shibata. This research was supported
financially by JSPS KAKENHI Grant No. JP18K04324 and
Oriental Shiraishi Co., Ltd.

REFERENCES

[1] T. Nagao, D. Shibata, “Experimental study of the lateral spreading

pressure acting on a pile foundation during earthquakes”, Engineering,
Technology & Applied Science Research, Vol. 9, No. 6, pp. 5021-5028,

2019

[2] K. Tokimatsu, Y. Asaka, “Effects of liquefaction-induced ground
displacements on pile performance in the 1995 Hyogoken-Nambu

Earthquake”, Soils and Foundations, Vol. 38, No. Special, pp. 163-177,
1998

[3] PIANC, Seismic design guidelines for port structures, A.A. Balkema

Publishers, 2001

[4] G. Mondal, D. C. Rai, “Performance of harbour structures in Andaman

Islands during 2004 Sumatra earthquake”, Engineering Structures, Vol.
30, pp. 174–182, 2008

[5] R. A. Green, S. M. Olson, R. Brady, B. R. Cox, G. J. Rix, E. Rathje, J.

Bachhuber, J. French, S. Lasley, N. Martin, “Geotechnical aspects of
failures at Port-au-Prince seaport during the 12 January 2010 Haiti

earthquake”, Earthquake Spectra, Vol. 27, No. Suppl. 1, pp. S43–S65,
2011

[6] T. Sugano, A. Nozu, E. Kohama, K. Shimosako, Y. Kikuchi, “Damage

to coastal structures”, Soils and Foundations, Vol. 54, No. 4, pp. 883–
901, 2014

0 2 4 6
0

0.1

0.2

0.3

0.4

Experiment

horizontal displacement(mm)

lo
a
d
(k
N
)

0 0.5 1 1.5 2
0

0.3

0.6

0.9

1.2

1.5

Prototype

horizontal displacement(m)

se
is
m
ic
c
o
e
ff
ic
ie
n
t

0 0.1 0.2 0.3 0.4
0

0.3

0.6

0.9

1.2

1.5

Prototype

vertical displacement(m)

se
is
m
ic
c
o
e
ff
ic
ie
n
t

Engineering, Technology & Applied Science Research Vol. 10, No. 3, 2020, 5713-5718 5718

www.etasr.com Nagao: An Experimental Study on the Way Bottom Widening of Pier Foundations Affects Seismic …

[7] G. A. Athanasopoulos, G. C. Kechagias, D. Zekkos, A. Batilas, X.
Karatzia, F. Lyrantzaki, A. Platis, “Lateral spreading of ports in the 2014

Cephalonia, Greece, earthquakes”, Soil Dynamics and Earthquake
Engineering, Vol. 128, Article ID 105874, 2020

[8] T. Nagao, P. Lu, “A simplified reliability estimation method for pile-

supported wharf on the residual displacement by earthquake”, Soil
Dynamics and Earthquake Engineering, Vol. 129, Article ID 105904,

2020

[9] G. Li, R. Motamed, “Finite element modeling of soil-pile response
subjected to liquefaction induced lateral spreading in a large-scale shake

table experiment”, Soil Dynamics and Earthquake Engineering, Vol. 92,
pp. 573-584, 2017

[10] I. Towhata, Geotechnical earthquake engineering, Springer-Verlag, 2008

[11] M. A. Biot, “Bending of infinite beams on an elastic foundation”,
Journal of Applied Mechanics, Vol. 59, pp. A1–A7, 1937

[12] K. V. Terzaghi, “Evaluation of coefficient of subgrade reaction”,

Geotechnique, Vol. 5, No. 4, pp.297–326, 1955

[13] T. Yoshinaka, “Subgrade reaction coefficient and its correction based on
the loading width”, PWRI Report, Vol. 299, pp. 1-49, 1967 (in Japanese)

[14] R. Ziaie-Moayed, M. Janbaz, “Effective parameters on modulus of

subgrade reaction in clayey soils”, Journal of Applied Sciences, Vol. 9,
pp. 4006-4012, 2009

[15] J. Lee, S. Jeong, “Experimental study of estimating the subgrade

reaction modulus on jointed rock foundations”, Rock Mechanics and
Rock Engineering, Vol. 49, No. 6, pp. 2055–2064, 2016

[16] Japan Road Association, Specifications for highway bridges, Part 4,
Substructures, Japan Road Association, 2016

[17] S. Iai, “Similitude for shaking table test on soil-structure-fluid model in

1g gravitational field”, Soil and Foundations, Vol. 29, No. 1, pp. 105-
118, 1989