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Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 9819-9824 9819 
 

www.etasr.com Lemsara et al.: Seismic Fragility of a Single Pillar-Column Under Near and Far Fault Soil Motion with … 

 

Seismic Fragility of a Single Pillar-Column 

Under Near and Far Fault Soil Motion with 

Consideration of Soil-Pile Interaction 
 

Foudhil Lemsara 

LGC-ROI, Department of Civil Engineering, Faculty of Technology, University of Batna 2, Algeria 

f.lemsara@univ-batna2.dz 

(corresponding author)  

 

Tayeb Bouzid 

LGC-ROI, Department of Civil Engineering, Faculty of Technology, University of Batna 2, Algeria 

tayeb.bouzid@univ-batna2.dz 

 

Djarir Yahiaoui 

LGC-ROI, Department of Civil Engineering, Faculty of Technology, University of Batna 2, Algeria 

d.yahiaoui@univ-batna2.dz 

 

Belgacem Mamen  

Department of Civil Engineering, Faculty of Science and Technology, University of Abbès Laghrour 

Khenchela, Algeria 

belgacem.mamen@univ-khenchela.dz 

 

Mohamed Saadi 

LGC-ROI, Department of Civil Engineering, Faculty of Technology, University of Batna 2, Algeria 

m.saadi@univ-batna2.dz 
 

Received: 10 October 2022 | Revised: 30 October 2022 | Accepted: 31 October 2022 

 

ABSTRACT 

The soil-structure interaction is a significant challenge faced by civil engineers due to the complexity 

potential in terms of seismic fragility evaluation. This paper presents a seismic fragility estimation of a 

single pier considering seismic ground motion types. Furthermore, sand type, pile diameter, pier height, 

and mass variation were considered to estimate their effect on the seismic fragility of the concrete pier. 

Incremental dynamic analysis was performed using a beam on a nonlinear Winkler foundation model. The 

analysis model condition compared near- and far-ground motion effects. Dynamic analysis and fragility 

assessment of the single-pier structure showed that low mass center produced less vulnerability of the 

concrete pier in the two cases of the sand type under near- and far-ground motions. The near and far 

earthquake simulations at complete failure probability had a difference of less than 5% when 0.65s<T1<1s 

and 2.4<T1/T2, but the opposite was shown when T1<0.5s and 3<T1/T2 were present together. 

Keywords-soil-pile-structure interaction; incremental dynamic analysis; BNWFmodel; ground motion types; 

seismic fragility 

I. INTRODUCTION  

Under seismic loading, liquefiable soil increases the 
seismic fragility of expansion bearing, piles, and embankment 
soil. The fragility of common components, such as columns, 
depends on the overlying liquefiable sand. The effect of soil 
strength for clay and sandy sites on the seismic performance of 

skewed bridge components and its relation with the skew angle 
was studied in [1, 2]. The seismic fragility of a pile was studied 
with different seismic demands in [3]. The nonlinear Winkler 
foundation model is widely used to study soil-pile and soil-
pile-structure interactions using nonlinear dynamic analysis [4]. 
In [5], a comparison of soil-structure interaction and fix-base 
model effects on a structure's seismic fragility was presented. 



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www.etasr.com Lemsara et al.: Seismic Fragility of a Single Pillar-Column Under Near and Far Fault Soil Motion with … 

 

A near-fault earthquake severely damages structures more 
than a far-fault one. This comparison was investigated in [6] 
through a numerical simulation of the seismic damage of arch 
bridges with three earthquake indicators: area intensity, energy 
rate, and cumulative absolute velocity. The demand/capacity 
ratio of an arch bridge pier is higher under near- than far-fault 
earthquakes [7]. In addition to [4], pushover analysis was used 
to study soil-pile and soil-pile-structure interactions in [8]. In a 
single pile, columns fail before pile foundations [9]. Soil 
permeability can be considered a complex property due to its 
influence on seismic fragility with different soil types [10]. In 
[11], the impact of the soil-pile interaction on the seismic 
fragility of wharf structures was investigated by comparing two 
systems: with and without soil-pile interaction. Most recent 
studies were based on the Winkler foundation model to study 
the seismic fragility of the Soil-Pile-Structure interaction (S-P-
S). This model is a good instrument for investigating the 
seismic fragility of concrete bridge-soil systems using stepwise 
and LASSO regression [12]. In [13], the mitigation of pile 
group spacing on scour and liquefaction effects was studied. 

The same results with [5] were shown in [14] considering a 
skewed bridge. In [15], the effect of irregular configuration and 
the stiffness of the substructure on the vulnerability of the 
bridge was shown. The soil-pile and soil-pile-structure 
interactions were investigated more comprehensively in [16]. 
The effects of the soil-structure interaction on the seismic 
fragility of a bridge were investigated in [17], considering the 
effects of wave passage. The selection of foundation type is an 
essential key for the construction of a superstructure and 
estimating its seismic fragility. The pile foundation is an 
improvement in superstructure performance compared to the 
shallow foundation [18]. The effects of soil stiffness and pile 
flexibility on the seismic fragility of the pile were assessed in 
[19] using finite element analysis. In addition to the effect of 
infrastructure parameters on the seismic fragility of the 
structure, there is the influence of the pier parameters, such as 
the higher-order mode of the pier bridge column that produces 
overestimated seismic demands of the pile foundation in terms 
of curvature and displacement [20]. The lateral performance of 
an eccentrically braced frame was investigated in [21]. The 
effectiveness of retrofitting a reinforced concrete structure was 
shown in [22]. In [23], the seismic performance of a base-
isolated nuclear power plant structure was investigated taking 
into account near and far-fault earthquake influence.  

This study investigated the effects of near- and far-fault 
earthquakes on the seismic fragility of a single-column pile, 
taking into account the soil-pile spring system's p-y curve using 
the Seismostruct software and incremental dynamic analysis. 

II. NEAR AND FAR GROUND MOTION 
SELECTIONS 

The main benchmark for selecting near- and far-fault 
earthquakes is the closest distance from the fault (Rjb) where 
the near-fault has an Rjb of less than 15Km [24]. This study 
used the records of earthquakes from [25]. The ground motions 
were characterized by a median of PGV/PGA equal to 113 for 
near- and 119 for far-fault. In Figure 1(a, b), the thin lines 
define the individual spectra, and the thick line defines the 
mean spectrum of near (NR) and far (FR) ground motions.  

(a) 

 

(b) 

 

Fig. 1.  Acceleration response spectra of (a) near-fault earthquakes, (b) far-
fault earthquakes. 

III. NUMERICAL MODELING OF SOIL-PILE 
INTERACTION 

The Seismostruct software offers different concrete 
materials and steel reinforcing bars. The nonlinear Mander [26] 
and the Menegetto-Pinto models of steel reinforcing are shown 
in Figures 2 and 3. The modeling of the soil-pile interaction 
was based on the design of the p-y curve relationship: p is the 
soil reaction and y is the lateral deflection. The nonlinear 
Winkler foundation model (BNWF) [4] was employed, defined 
as multilinear curves. The structure was modeled using a 3D 
formulation, whereas the soil was modeled using a 1D 
formulation based on the reference p-y model as [4]: 

p = 0.9p�. tanh�
�
�
�.���

y�   (1) 

where k is the initial modulus of the subgrade reaction in soil 
and pu is the ultimate bearing capacity. 

 

 
Fig. 2.  Stress-strain curve of concrete mander material. 

-0,002 0,000 0,002 0,004
-28,8

-25,6

-22,4

-19,2

-16,0

-12,8

-9,6

-6,4

-3,2

0,0

S
tr

e
ss

 (
M

P
a
)

Strain [-]  



Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 9819-9824 9821 
 

www.etasr.com Lemsara et al.: Seismic Fragility of a Single Pillar-Column Under Near and Far Fault Soil Motion with … 

 

 

Fig. 3.  Stress-strain curve of steel Menegetto-Pinto model. 

The properties of each p-y curve derive from the parameters 
of homogeneous soil layers considering spring spacing of 0.5. 
Two different pile diameter deposits, each with two sand types, 
loose and dense, and three different masses were considered: 
1500, 3000, and 4500kN. For simplification, an abbreviation is 
proposed concerning different models: LS for the loose sand 
model, DS for the dense sand model, and d for pile diameter, 
where d=d1=1.5m and d=d2=2m. Two different heights (H) of 
piers, equal to 5 and 10m, were used. The pile length (L) was 
fixed at 30m as in [27]. The loose and dense sand had a friction 
angle of 30° and 45°, respectively. Figure 4 shows the soil-pile 
interaction model designed in Seismostruct software.  

 

 
Fig. 4.  Soil-pile spring interaction. 

The calculation of the probability exceedance of a structure 
at a limit state is defined in (2), which is given by [15, 28-29]: 

p� ����� = �
��������μ

σ
�   (2) 

where μ and σ are the mean and the standard deviation of the 
logarithmic of the peak ground acceleration when the pier 
reaches the threshold of performance level D at each limit state, 
and Φ is the standard normal cumulative distribution function. 
To estimate the probability of pier damage, the analysis 
procedure was (Figure 5): 

1. Modeling of soil-pile interaction and vertical load value 
using Seismostruct software. 

2. Define the drift value at each limit state of different 
models using nonlinear static analysis. 

3. Select ground motion records (near- and far-fault 
earthquakes). 

4. Generate the incremental dynamic analysis and find the 
median and standard deviation of the incremental 

dynamic analysis. 

5. Drawing of seismic fragility curve. 
 

 

Fig. 5.  Analysis procedure. 

IV. RESULTS AND DISCUSSION 

A. Limit States and Incremental Dynamic Analysis 

Figure 6(a) shows the form of the incremental dynamic 
analysis example. The 20 thin lines define the individual 
incremental dynamic analysis and the thick red line defines its 
mean response. Figure 6(b) shows the comparison of the mean 
response. The mean response of the incremental dynamic 
analysis increases with mass center under the two ground 
motion types. After realizing the incremental dynamic analysis 
series for each model, their mean and standard deviation were 
calculated. The mean and standard deviation of incremental 
dynamic analysis in the case of pile diameter of 1.5 and 2.0 m, 
and H=5m are shown in Tables I and II, respectively, and the 
mean value decreases with mass increase. 

TABLE I.  MEDIAN AND STANDARD DEVIATION VALUES 
OF IDA WITH PILE DIAMETER EQUAL TO 1.5 M 

Mass (KN) 1500 3000 4500 

Earthquake type Near Far Near Far Near Far 

Mean (μ) 

Loose 

sand 
0.94 1.03 0.38 0.37 0.23 0.22 

Dense 

sand 
0.90 1.00 0.40 0.38 0.25 0.23 

Standard 

deviation 

(σ) 

Loose 

sand 
0.36 0.37 0.32 0.35 0.28 0.31 

Dense 

sand 
0.28 0.36 0.26 0.26 0.23 0.22 

-0,006 -0,003 0,000 0,003 0,006 0,009
-614,4

-512,0

-409,6

-307,2

-204,8

-102,4

0,0

102,4

204,8

307,2

409,6

512,0

614,4

S
tr

e
ss

 (
M

P
a

)

Strain [-] 



Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 9819-9824 9822 
 

www.etasr.com Lemsara et al.: Seismic Fragility of a Single Pillar-Column Under Near and Far Fault Soil Motion with … 

 

TABLE II.  MEDIAN AND STANDARD DEVIATION VALUES 
OF IDA WITH PILE DIAMETER EQUAL TO 2M. 

Mass (KN) 1500 3000 4500 

Earthquake type Near Far Near Far Near Far 

Mean (μ) 

Loose 

sand 
1.73 1.70 0.82 0.76 0.50 0.47 

Dense 

sand 
1.98 2.01 0.80 0.55 0.42 0.48 

Standard 

deviation 

(σ) 

Loose 

sand 
0.36 0.32 0.32 0.32 0.30 0.32 

Dense 

sand 
0.24 0.32 0.23 0.49 0.17 0.24 

 

(a) 

 

(b) 

 

Fig. 6.  (a) Incremental dynamic analysis under NR ground motion, (b) 
Example of mean response comparison of IDA. 

B. Fragility Curves 

Utilizing parameters from the mean and standard deviation 
of incremental dynamic analysis, and the standard normal 
cumulative distribution function (2), the fragility curves are 
expected and generated in the design figures for the collapse 
prevention state. 

C. Effect of Mass 

Depending on the variation of pier height (H), the results of 
the numerical simulation are classified into two parts: Figures 7 
and 8 for H=5m and Figures 9 and 10 for H=10m. Figure 7(a) 
presents the seismic fragility of the concrete pier in case the 
pile is embedded in dense sand under a near-fault ground 
motion. This figure shows that when placing a different mass 
of 1500, 3000, and 4500kN, the pier structure needs a peak 
ground acceleration equal to 0.90, 0.40, and 0.25g, 
respectively, to exceed 50% of failure probability. These results 
show that the high mass needs a low Peak Ground Acceleration 
(PGA) to exceed 50% of failure probability under near-fault 
ground motion. The seismic fragility curves under far-fault 
ground motion show the same trend. All figures show similar 
trending results with a mass variation. 

(a) 

 

(b) 

 

Fig. 7.  Seismic fragility of pier with dense sand condition and H=5m: (a) 
Near (NR) ground motions, (b) Far (FR) ground motions. 

(a) 

 

(b) 

 

Fig. 8.  Seismic fragility of a pier with loose sand conditions and H=5m: 
(a) Near (NR) ground motions, (b) Far (FR) ground motions. 

D. Near and Far Fault Ground Motion Comparison 

These results show that high mass needs a low PGA to 
exceed 50% of failure probability under near-fault ground 
motion. A comparison of seismic fragility curves under far-
fault ground motion shows the same trend. Additionally, all 
Figures show similar trending results with mass variation. 
Figures 7 and 8 showed that the lower difference between PGA 
of near- and far-ground motion at 50% of failure probability in 
the case of H=5m are: LS-d1-3000, DS-d1-3000, LS-d1-4500, 
LS-d1-4500, LS-d2-4500. These models keep this most 
negligible difference value at complete failure probability 
(100%). The fundamental periods of the different models are 
0.81, 0.69, 0.98, 0.85, and 0.56s, and their T1/T2 ratios were 
2.89, 2.46, 2.88, 2.5, and 2.94, respectively. 

On the other hand, some models have a slight difference at 
only 50% failure probability. The last figures show that in 
models presenting R<5%, the far-fault produced a higher 
failure probability than the near-fault ground motion due to its 
higher value of PGV/PGA. These models were LS-d2-1500 
and LS-d2-3000 in the case of H=5m and DS-d2-1500 in the 
case of H=10m. The fundamental periods of these models were 



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www.etasr.com Lemsara et al.: Seismic Fragility of a Single Pillar-Column Under Near and Far Fault Soil Motion with … 

 

0.41, 0.56, and 0.64s, and their T1/T2 ratios were 3.72, 3.5, and 
1.82, respectively. These Figures showed a higher probability 
of failure of the pier structure in far-fault earthquakes than in 
near-ground motions, as observed in [31], while a higher 
probability of failure was presented in [23] in near-fault 
earthquakes in all events. 

 

(a) 

 

(b) 

 

Fig. 9.  Seismic fragility of pier with dense sand condition and H=10m: (a) 
Near (NR) ground motions, (b) Far (FR) ground motions. 

(a) 

 

(b) 

 

Fig. 10.  Seismic fragility of pier with loose sand condition and H=10m: (a) 
Near (NR) ground motions, (b) Far (FR) ground motions. 

V. CONCLUSIONS 

This study compared the seismic fragility of a single 
concrete pier under near- and far-fault earthquakes. The effects 
of mass variation, closest ground motion type, and pile 
diameter were considered with two sand models, loose and 
dense. The seismic fragility of a concrete pier exceeded 50% 
and 100% of failure probability when placing a higher mass 
value at the pier end in all cases of pile section. The difference 
between the peak ground acceleration of near- and far-fault 
earthquakes at complete failure probability was less than 5% 
when the analysis modal conditions (0.65s<T1<1s and 
2.4<T1/T2) were verified. The pier structure was highly affected 
by a higher value of PGV/PGA regardless of the near and far 
ground motions if one of two conditions was given: 

1<T1<0.65s or T1/T2 < 2. The higher difference between the 
peak ground acceleration of near and far earthquakes at 
complete failure probability was concluded if the two following 
conditions are presented together: T1<0.5s and 3< T1/T2. 

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