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Seismic fragility curves for caisson-type quay walls
Joana Fernandes Chouriço
Department of Civil Engineering and Architecture (DECivil), Instituto Superior Técnico,
University of Lisbon
December 2015
Abstract: Port structures, including quay walls, have been damaged by earthquakes over the past
few years. The derivation of fragility curves is found to be very important for quantifying the
vulnerability of such structures. This study proposes fragility curves derived from two-dimensional
numerical simulations using FLAC 2D software. A set of soil profiles were used that fit the ground
types B, C and D defined by Eurocode 8. The seismic action was introduced using records of
earthquakes with a magnitude greater than 5,5. The quay wall was 10 m high and 10 m wide, while
the foundations were 20 m thick. The lower boundary of the model was absorbent. To evaluate
structural damage, 4 levels were defined based on standard horizontal displacement at the top of
the wall together with tilting.
Keywords: earthquakes, fragility curves, FLAC 2D, quay walls, caissons
1. Introduction
Port structures play an important role in international shipping, including the import and export of
goods and tourism. The consequences of an earthquake in port structures can be devastating, with
not only structural but also socio-economic repercussions. An example is the earthquake that occurred
in Japan in 1995 and which affected the port of Kobe, causing a loss of nearly 50% of the annual
income [1]. In most countries, international trade is predominantly done through seaports. It is
therefore imperative to reduce the vulnerability of quay walls.
This work derives fragility curves for use as a tool for studying the seismic vulnerability of port gravity
type structures, in a broad range of ground types.
2. Calibration of the numerical model
The FLAC 2D software was used to simulate the seismic behavior of a caisson type quay wall. This is
a program based on a finite difference method for simulating soil-structure interaction taking into
account the deformations and nonlinear soil behavior under cyclic loading.
2.1. 1D wave propagation
The propagation of shear waves was simulated using a soil column with linear elastic behavior in
order to evaluate the response of the soil to an action introduced at the outcrop. The vertical
boundaries were assumed to behave as free field boundaries, restricted in the horizontal direction in
order to simulate shear waves and, at the base, quiet boundaries were used to simulate the elastic
half-space. The transfer function between the base of the deposit and the surface was computed and
with the analytical solution for 1D shear wave propagation in a visco-elastic layer.
2
0
5
10
15
20
25
30
0 5 10 15 20
|H (w
)|
f [Hz]
Teórico ξ=2% Strata ξ=2% FLAC ξ=2%
Figure 2.1 - Transfer function of the calibration
model
Table 2.1 - Soil properties adopted for the soil
deposit
[kN/m3]
[MPa]
[MPa]
[m/s]
Table 2.2 - Soil properties adopted for half-space
[kN/m3]
[MPa]
[MPa]
[m/s]
2.2. Simulation of soil cyclic behavior
A one-zone element sample calibration was therefore
performed (Figure 2.2). The cyclic behavior of soils was
simulated using the Mohr-Coulomb non-linear elastic
perfectly plastic constitutive soil model, owing to its
relative simplicity and reduced number of parameters
(Table 2.3). The Mohr-Coulomb linear elastic perfectly
plastic constitutive soil model was also used in order to
assess a comparative analysis of the responses.
The Ishibashi and Zhang curves were chosen as a reference to simulate the strain-dependent
stiffness degradation of soil and damping coefficient curves.
Table 2.3 - Soil properties adopted
For this purpose the Ishibashi and Zhang curves were selected, considering IP=20 and p'=100 kPa
(Figure 2.4). The stress-strain relationship for different load levels is presented in Figure 2.3.
a) b) c)
Figure 2.3 - Stress-strain relationship for different load levels applied to a) b) c)
-20
-15
-10
-5
0
5
10
15
20
-2 -1 0 1 2 3 4 5 6
τ xy
[k
Pa
]
ϒ [%]
-20
-15
-10
-5
0
5
10
15
20
-2 -1 0 1 2 3 4 5 6
τ xy
[kP
a]
ϒ [%]
-20
-15
-10
-5
0
5
10
15
20
-2 -1 0 1 2 3 4 5 6
τ xy
[k
Pa
]
ϒ [%]
Figure 2.2 - Geometry adopted in modeling
3
0
10
20
30
40
50
60
70
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0,0001 0,001 0,01 0,1 1 10
ξ [%]
G/G
0
ϒ [%]
Clays PI=20 G/G0 FLAC FLAC Curve theoretical ξ ξ FLAC
Although the shear stiffness degradation
curve (Figure 2.4) is penalized, both the
damping and the shear stiffness degradation
curves seem to correctly describe the non-
linearity of the soil.
2.3. 2D numerical model
In this section, the 2D numerical model to simulate soil-quay wall interaction is analyzed.
2.3.1. Geometry and material properties
The numerical modeling was performed assuming that the quay wall has 10 m high and 10 m wide.
The quay wall foundation soil has 20 m thick. The boundary conditions included free field boundaries
laterally applied together with absorbent boundaries applied at the base (Figure 2.5).
Figure 2.5 – Geometry and boundary conditions
The soil behavior was assumed to behave like the Mohr Coulomb non-linear elastic perfectly plastic
model, while the quay wall behavior was assumed to be linear elastic (Table 2.4).
Table 2.4 – Soil properties
Parameters Quay Wall Supported Soil Foundations Half-Space
1920
- 45
Figure 2.4 - Stiffness degradation and damping coefficient curves for clays with PI=20 and p´=100kPa
4
2.3.2. Gravity action
To simulate the tensions existing
in the model before the seismic
action, a static analysis
considering only the effect of
gravity was carried out. Figure
2.6 shows the initial in-situ
vertical total distribution stresses
generated.
2.3.3. Input seismic loading
A seismic action (Figure 2.7), recorded in the
Friuli earthquake, Italy, scaled to obtain PGAs of
0,05g, 0,4g and 0,8g, was then introduced. These
three levels of seismic intensity were chosen to
exhibit the behavior of the soil in three possible
behavior ranges: from very small to small
deformations, small to medium deformations and
large deformations, respectively.
2.3.4. Results
It can be clearly observed that the structure
suffers horizontal displacement as well as rotation
(Figure 2.8). The evolution in horizontal and
vertical displacements as well as the rotation
during the seismic action is shown in Figure 2.9
and Figure 2.10.
a) b) c)
Figure 2.9 - Displacement evolution during seismic action at point A of the quay wall for a) PGA = 0.05g; b) PGA
= 0.4g c) PGA = 0.8g
Figure 2.6 –initial in-situ vertical total distribution stresses
FLAC (Version 7.00)
LEGEND
12-Oct-15 10:43
step 50064
-5.556E+00 <x< 1.056E+02
-6.056E+01 <y< 5.056E+01
Grid plot
0 2E 1
YY-stress contours
-5.40E+05
-4.80E+05
-4.20E+05
-3.60E+05
-3.00E+05
-2.40E+05
-1.80E+05
-1.20E+05
-6.00E+04
0.00E+00
Contour interval= 6.00E+04
Extrap. by averaging -5.000
-3.000
-1.000
1.000
3.000
(*10 1̂)
0.100 0.300 0.500 0.700 0.900
(*10 2̂)
JOB TITLE : Campo de tensoes verticais [Pa]
FLAC (Version 7.00)
LEGEND
12-Oct-15 10:43
step 50064
-5.556E+00 <x< 1.056E+02
-6.056E+01 <y< 5.056E+01
Grid plot
0 2E 1
YY-stress contours
-5.40E+05
-4.80E+05
-4.20E+05
-3.60E+05
-3.00E+05
-2.40E+05
-1.80E+05
-1.20E+05
-6.00E+04
0.00E+00
Contour interval= 6.00E+04
Extrap. by averaging -5.000
-3.000
-1.000
1.000
3.000
(*10 1̂)
0.100 0.300 0.500 0.700 0.900
(*10 2̂)
JOB TITLE : Campo de tensoes verticais [Pa]
Figure 2.7 – Input seismic action
-0,3
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0 1 2 3 4 5 6
Dis
pla
ce
me
nt
[m]
t [s]Horizontal Vertical
-0,3
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0 1 2 3 4 5 6
Dis
pla
ce
me
nt
[m]
t [s]Horizontal Vertical
-0,3
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0 1 2 3 4 5 6
Dis
pla
ce
me
nt
[m]
t [s]Horizontal Vertical
Figure 2.8 - Deformed mesh at the end of the analysis for PGA=0,4g
5
a) b) c)
Figure 2.10 – Quay wall rotation for a) ; b) ; c)
There is a clear increase in both horizontal and vertical displacement (Figure 2.9) and rotation (Figure
2.10) of the quay wall with an increasingly stronger seismic action.
3. Fragility curves
Since the most common deformation modes found in rigid support structures are sliding, tilting and
settlement, the parameters used to define the minimum requirements for each level of damage (EDP's
- Engineering Demand Parameters) are linked to these modes. This study adopted the methodology
proposed in SYNER-G [1] to obtain fragility curves.
The International Navigation Association (PIANC 2001) [2] defines four damage levels (Degrees I-IV)
based on the degree of normalized residual horizontal displacement (d/H) together with any residual
tilting towards the sea (ϴ) (Table 3.1).
Table 3.1 – Definition of damage states for gravity quay walls (PIANC, 2001)
Damage levels, Degree I Degree II Degree III Degree IV
EDPs d/H <1,5%** 1,5% a 5% 5% a 10% > 10%
ϴ [ᵒ] < 3ᵒ 3ᵒ a 5ᵒ 5ᵒ a 8ᵒ > 8ᵒ
The lognormal cumulative probability distribution is used to define the fragility curves (1). These
curves demonstrate the probability of exceedance of a certain level of damage, previously established,
and are defined by:
(1)
Where: is the probability of exceeding a certain level of damage, dsi; Φ is the lognormal cumulative
distribution function; IM is the seismic motion intensity measurement; is the limit median value of
necessary to cause a certain level of damage, dsi; and
(2) is the total lognormal standard
deviation describing the overall uncertainty associated with each fragility curve, modeled by the
combination of the following sources of uncertainty: level of damage,
, response and bearing
capacity of the structure, and seismic movement,
.
(2)
-0,9
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0 1 2 3 4 5 6
Ro
taç
ão
[ᵒ]
t [s]
-0,9
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0 1 2 3 4 5 6
Ro
taç
ão
[ᵒ]
t [s]
-0,9
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0 1 2 3 4 5 6
Ro
taç
ão
[ᵒ]
t [s]
6
The uncertainty associated with the definition of
damage states,
, is set equal to 0,4 while the
uncertainty due to the capacity , , is assigned equal to
0,3 [1].
A linear regression analysis was used to estimate the
parameters (lognormal standard deviation) and
(Figure 3.1).
3.1. Numerical model adopted
The geometry of the gravity quay wall was identical to the configuration adopted for the calibration 2D
model (Figure 2.5 in section 2.3.1) with the addition of a load to simulate the hydrostatic behavior.
The estimated horizontal displacements of the quay wall are strongly influenced not only by the type of
soil involved in the analysis, but also by the stiffness profile variation according to depth. Ignoring the
increase in stiffness variation with depth would thus translate into an inaccurate estimation of soil
displacements. The model was therefore divided into 5m thickness layers (Figure 3.2).
Figure 3.2 - Geometry and mesh of the model adopted in FLAC
To cover a broad range of ground types, defined in Eurocode 8, the Vs and Cu combination profiles
shown in Figure 3.3, which cover Eurocode 8 ground types B to D, were modeled.
a) b)
Figure 3.3 – Combinations of clay soils adopted a) S wave velocity profiles b) Cu profiles
Figure 3.1 – Example of a simple linear regression
to estimate the parameters and [4]
-20
-15
-10
-5
0
5
10
0 200 400 600 800
Pro
f. [m
]
Vs [m/s]
B-B C-B D-B C-C D-C D-D
-20
-15
-10
-5
0
5
10
0 200 400 600 800 1000
Pro
f. [m
]
Cu [kPa]
B-B C-B D-B C-C D-C D-D
7
40 records were applied to each Vs profile [3], where the value of the peak horizontal acceleration,
PHA, recorded corresponded to the respective type of foundation soil. These records were obtained at
different stations with different epicenters, hypocenters, magnitudes, duration, tectonic environment
and frequency content. The online European data seismic action platform, ESD, was used and
seismic records with a PHA varying between 0,9 to 7,85 m/s2 and magnitudes above 5,5 were
selected, aiming to include the variability inherent to seismic motion.
3.2. Sensitivity analysis
Most of the fragility curves available in the literature define the IM as the PHA. This parameter can be
obtained almost immediately from an accelerogram and for this reason it is often used in evaluating
the damage induced in a structure. In this analysis, the PGA recorded at the ground surface was used
as IM as well as Ia.
3.2.1. Variation effect of the supported soil
This section assesses the effect of supported soil, while keeping the soil foundation characteristics, in
the fragility curve behavior. Figure 3.4 compares the effect of supported soil types C and D, with
foundation soil type C, using as IM parameter PGA and Ia.
a) b)
Figure 3.4 - Comparison of fragility curves considering EDP's HRND (d/H) for seismic combination SScSFc and SSdSFc as a function of a) PGA b) Ia
The decrease in the supported soil strength parameters, which causes an increase in displacements
at the top of the wall, is reflected in the curves, with an increasing likelihood of a certain level of
damage being exceeded.
3.2.2. Variation effect of the foundation soil
The deformation at the base of the quay wall is directly related to the stiffness of the foundation soil. In
this respect, Figure 3.5 presents the effect of the variability of the properties of the foundation layer
while maintaining the features of the supported soil.
0
0,2
0,4
0,6
0,8
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Pf(
ds≥d
si|IM
)
PGA (g)
Degree I SScSFc Degree II SScSFc Degree III SScSFc
Degree I SSdSFc Degree II SSdSFc Degree III SSdSFc
0
0,2
0,4
0,6
0,8
1
0 1 2 3 4 5 6
Pf(
ds≥d
si|IM
)
Ia (m/s)
Degree I SScSFc Degree II SScSFc Degree III SScSFc
Degree I SSdSFc Degree II SSdSFc Degree III SSdSFc
8
a) b)
Figure 3.5 - Comparison of fragility curves considering EDP's HRND (d/H) for seismic combination SSdSFb, SSdSFc and SSdSFd as a function of a) PGA b) Ia
It can be noted that the foundation soil has a greater influence on the seismic response of the quay
wall than the supported soil. Comparing the combination in both figures (Figure 3.4 and Figure 3.5), it
can be seen that a decrease in the strength of foundation soil has a higher impact on the fragility
curves, with an increased probability of damage.
3.2.3. Comparison between displacement and rotation found
The comparison between the HRND and the rotation of the quay wall is illustrated in Figure 3.6.
a) b)
Figure 3.6 - Comparison of fragility curves considering EDP's HRND (d/H) and rotation (ϴ) for seismic combination SSdSFd as a function of a) PGA b) Ia
It can be seen that slipping prevails over quay wall rotation. The slip resistance is provided by soil
deformation at the wall base. Consequently, by reducing the strength parameters of the layer on which
the wall is based on, an increase in displacements can be expected.
3.3. Fragility curves
To validate the fragility curves obtained, the fragility curves found in SYNER-G [1] (Figure 3.7), namely
the curves obtained by Kakderi & Pitilaki (2010) [4] for H ≤10m and Vs = 500m/s (Type B) and Vs =
250m/s (Type C), were used. The combinations used to obtain the fragility curves for soil type C have
Vs,30 of 263 m/s, 265 m/s and 195 m/s.
0
0,2
0,4
0,6
0,8
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Pf(
ds≥d
si|IM
)
PGA (g)
Grau I SSdSFb
Grau II SSdSFb
Grau III SSdSFb
Grau I SSdSFc
Grau II SSdSFc
Grau III SSdSFc
Grau I SSdSFd
Grau II SSdSFd
Grau III SSdSFd
0
0,2
0,4
0,6
0,8
1
0 1 2 3 4 5 6
Pf(
ds≥d
si|I
M)
Ia(m/s)
Grau I SSdSFb
Grau II SSdSFb
Grau III SSdSFb
Grau I SSdSFc
Grau II SSdSFc
Grau I SSdSFd
Grau II SSdSFd
0
0,2
0,4
0,6
0,8
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Pf(
ds≥d
si|IM
)
PGA (g)
Degree I (d/H) Degree II (d/H) Degree III (d/H)
Degree I ϴ Degree II ϴ Degree III ϴ
0
0,2
0,4
0,6
0,8
1
0 1 2 3 4 5 6
Pf(
ds≥d
si|I
M)
Ia (m/s)
Degree I (d/H) Degree II (d/H) Degree III (d/H)
Degree I ϴ Degree II ϴ Degree III ϴ
9
a) b)
Figure 3.7 - Comparison of proposed fragility curves with those of Kakderi & Pitilakis (2010) [4] for soil type a) B
b) C
A large difference between the curves can be observed. There could be several reasons behind the
differences observed. To highlight a few: in addition to different geotechnical characteristics, the
seismic actions of Kakderi & Pitilakis (2010) [4] were scaled up, so that in the assessment of the
variability of magnitude there was lower scatter. The author also uses quay wall geometric
relationships B/H<1, resulting in higher horizontal displacements as a result of the walls rotation,
reflected in a higher probability of damage.
4. Conclusions and future perspectives
This study is dedicated to a seismic response analysis of a caisson-type quay wall based on two-
dimensional numerical simulation using the FLAC 2D program.
40 seismic records for different ground types were used as the input motion and residual horizontal
normalized displacement and rotation were computed to be used as EDPs for deriving fragility curves.
The damage levels proposed by PIANC were adopted. In the sensitivity study, it was concluded that:
the decrease in the strength of the supported soil, while maintaining the same type of foundation soil,
caused an increase in displacement and rotation, reflected in an increased likelihood of damage; the
foundation soil, while maintaining the same supported soil, had a greater influence on the dynamic
behavior of the quay wall than the supported soil; horizontal displacements generated higher levels of
damage than rotation; the rotation of the wall was negligible for soil foundations with soil types B and
C, while a higher likelihood of damage for soil type D was found.
From the fragility curves obtained for soil profiles B, C and D it can be concluded that the seismic
performance of the quay wall with clay soil types B and C is associated with lower damage, while clay
soil type D has a higher probability of damage.
Based on this work, it is proposed that future research should concentrate on: an analysis of sandy
soils including the generation of pore pressures in order to assess the behavior of a quay wall during
the possible occurrence of liquefaction; given the high dependence of the progress of fragility curves
on variability, more seismic actions should be used in the analysis; incorporation of hydrodynamic
behavior.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Pf(
ds≥d
si|IM
si)
PGA (g)
Degree I
Degree II
Degree III
Degree I Kakderi&Pitilakis
Degree II Kakderi&Pitilakis
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Pf(d
s≥d
si|IM
si)
PGA (g)
Degree I
Degree II
Degree III
Degree I Kakderi&Pitilakis
Degree II Kakderi&Pitilakis
Degree III Kakderi&Pitilakis
10
Acknowledgements
This work was undertaken as a thesis to obtain a Masters degree in Civil Engineering at the Instituto
Superior Técnico, University of Lisbon, under the guidance of Professor Rui Pedro Carrilho Gomes.
References
[1] “Guidelines for deriving seismic fragility functions of elements at risk: Buildings, lifelines,
transportation networks and critical facilities - SYNER-G Reference Report 4,” European Union,
Luxembourg, 2013.
[2] PIANC, Seismic Design Guidelines for Port Structures, International Navigation Association, 2000.
[3] “European Soil Database (ESDB),” [Online]. Available: http://esdac.jrc.ec.europa.eu/.
[4] K. Kakderi e K. Pitilakis, “Seismic Analysis And Fragility Curves Of Gravity Waterfront Structures,”
em Fifth International Conference on Recent Advances in Geotechnical Earthquake Engineering
and Soil Dynamics, San Diego, California, 2010.
[5] S. Argyroudis, A. M. Kaynia e K. Pitilakis, “Development of fragility functions for geotechnical
constructions: Application to cantilever retaining walls,” Soil Dynamics and Earthquake
Engineering, vol. 50, pp. 106-116, 2013.