# Evaluation of Seismic Fragility of Weir Structures in South Korea

Authors: Bu Seog Ju; WooYoung Jung
Journal: Mathematical Problems in Engineering
 (2015)

---

## Abstract

In order to reduce earthquake damage of multifunctional weir systems similar to a dam structure, this study focused on probabilistic seismic risk assessment of the weir structure using the fragility methodology based on Monte Carlo simulation (MCS), with emphasis on the uncertainties of the seismic ground motions in terms of near field induced pulse-like motions and far field faults. The 2D simple linear elastic plain strain finite element (FE) model including soil structure foundations using tie connection method in ABAQUS was developed to incorporate the uncertainty. In addition, five different limit states as safety criteria were defined for the seismic vulnerability of the weir system. As a consequence, the results obtained from multiple linear time history analyses revealed that the weir structure was more vulnerable to the tensile stress of the mass concrete in both near and far field ground motions specified earthquake hazard levels. In addition, the system subjected to near field motions was primarily more fragile than that under far field ground motions. On the other hand, the probability of failure due to the tensile stress at weir sill and stilling basin showed the similar trend in the overall peak ground acceleration levels.


---

## Body

## 1. Introduction

Recently 16 multifunctional weir structures were constructed on four major rivers in Korea. Weir structures designed to change river flow characteristics have similar functions like dams such as electric power generation, flooding control, and water supply. While there are many advantages associated with weir structures, they also have weaknesses; few weaknesses were reported in the case of weir structures built in the rivers. In another word, the weir structure is one of the infrastructures that have coexisting pros and cons. The general examples of drawbacks include increase of the oxygen content, accumulating garbage and other debris, and fauna changes in the water (http://en.wikipedia.org/wiki/Weir). Furthermore, the weir structures can be exposed to multiple hazards such as earthquakes and flooding caused by serious problems such as flooding due to structural failure, discontinuity between soil foundation and the weir, and strong impulse water wave due to ground motions.According to Chanson [1], over the past decades, several failures in 20 hydraulic structures (dams and weirs) derived from foundation failures, concrete cracks, and flood overflow in the world. In addition, the hydraulic structures as an essential energy supply system like the power plant must remain operational and functional safety without hydrodynamic instabilities during an earthquake. However, on September 21st, 1999, Chi-Chi earthquake (M
w 7.6) struck critical facilities such as Taipei 101 building, Shih-Kang dam as a concrete gravity dam, and Shih-Kang Primary School located at central region of Taiwan. Taipei 101 building did not suffer any significant structural damage even though it was under construction during the earthquake. On the other hand, Kung et al. [2] observed that the damage of Shih-Kang dam was caused by three different types of failures: (1) structural failure due to large ground motion greater than allowable deformation of the concrete gravity dam; (2) the cracks to weir body and the piers due to strong contact impact; (3) the fracture failure (i.e., one of the most complicated failure types) to the spillways and the abutment of the dam due to combination impact between strong ground motion and fault rupture energy. Besides, analytical studies of seismic evaluation in terms of hydraulic structures have been issued in recent years, after the unique failure of Shih-Kang dam as a concrete gravity dam structure.For example, Yao et al. [3] conducted the safety evaluation using seismic fragility of a concrete arch dam located in the southwestern area of China. The seismic fragility was evaluated by nonlinear time history analyses using 18 realistic seismic ground motions. The results from numerical analyses using ABAQUS 3D Finite Element (FE) model noted that the failure criteria such as opening, slipping, and displacement of the dam were affected by seismic ground motions intensity levels. Tekie and Ellingwood [4] used 4 limit states (material failure-concrete, material failure-foundation, sliding at the dam, and deflection of the top of the dam relative to the heel) to develop seismic fragility of concrete gravity dam located on New River in West Virginia in the USA. In particular, the dam-reservoir hydraulic interaction was considered in dynamic equation of motion and spectral accelerations, especially 12 earthquake records which occurred in the USA as intensity measure of ground motions were applied. The numerical results obtained from 2D FE analyses revealed that the sliding at the dam and tensile cracking at the neck of the dam were more critical than other limit states.Consequently, the seismic safety evaluation of infrastructure (i.e., weir structures) with increase of earthquake records in Korea has received more attention as a key area of research. This study focused on evaluating Probabilistic Seismic Risk Assessment (PSRA) of the weir structure. More specifically, the 2D FE model of the weir structure including soil-structure foundation was conducted by ABAQUS Finite Element package, in order to develop the seismic fragility of the weirs. Furthermore, 30 near-field and 30 far-field earthquake records scaled to different peak ground acceleration (PGA) levels were considered as intensity measure and ground motions uncertainty. In this study, multiple linear time history analyses were carried out to generate the fragility based on Monte Carlo Simulation (MCS).


## 2. Description of the Weir Structure

The weir structure, Gangjeong-Goryeong weir, designed in 2009 to 2011 is located on the Nakdong River near Daegu Metropolitan City in Korea. This structure was constructed to control the flood and drought, supply the drinking water, and generate the electric power (3000 kW). The overall length of the multifunctional weir system as a concrete gravity structure is 933.5 m. It consists of two different systems: (1) the weir structure (nonoverflow section) with rising sector gates (120 m); (2) another concrete gravity weir system to allow overflow through their tops (833.5 m). The height of each structure is 11 m and the elevation of the two different systems is 9.47 m and 19.50 m, respectively. The storage volume of the system is 92.3 million m3 and the design flood is 13,200 m3/s. Moreover, the structure is designed for the maximum flood elevation at 24.02 m. The maintenance range of upstream and downstream of the structure is 300 m and 700 m, respectively, as shown in Figure 1 (http://www.kwater.or.kr/). The soil foundation at the site is classified by three layers: (1) sand layer; (2) gravel-sand mixture layer; (3) rock layer. Figure 2 shows a general design of weirs and the dimensions of overflow monolith (block number 10) at Gangjeong-Goryeong weir structure which is shown in Figure 3.Figure 1
The maintenance range of upstream and downstream in the Weir (http://www.kwater.or.kr/).Figure 2
Description of the Gangjeong-Goryeong weir.Figure 3
Schematic design of the weir structure (block number 10, unit: mm).


## 3. Finite Element Model of the Weir Structure

### 3.1. FE Modeling Description

To evaluate the performance of the weir structures, the Finite Element (FE) model was generated by ABAQUS [5], as shown in Figure 4, and a 4-node bilinear plane strain quadrilateral element was applied to the weir body, mass concrete, and soil-structure foundation. The dimension of y direction of the weir system was modeled with 58.114 m and x direction was 83.5 m including upstream and downstream side, in consideration of stress transfer. The material properties for the weir system were listed in Table 1. The design strength of the weir body and mass concrete system designed to peak ground acceleration at 0.154 g was 24 MPa and 18 MPa, respectively, and unit weight was 2350 kg/m3. For simplification, the weir body as a master surface and mass concrete as a slave surface were connected by tie condition in ABAQUS.Table 1
Material properties of the weir structure.
Structures
Elastic modulus(MPa)
Poisson’s ratio
Density(t/mm3)
Weir body
26,637
0.167
2.4
E
-
9
Mass concrete
24,579
0.167
2.4
E
-
9
Steel
200,000
0.25
7.85
E
-
9
Soil layer 1
2
0.4
1.7
E
-
9
Soil layer 1
25
0.4
1.9
E
-
9
Soil layer 1
2,000
0.3
2.4
E
-
9Figure 4
FE model of the weir including soil foundations.


### 3.2. Loading Conditions

In general, the system weight (gravity-weight) was determined by the combination of concrete unit weight and the system volume and 5 different loading conditions (hydrostatic pressure, hydrodynamic pressure, uplift pressure, silt pressure, and earthquake) were considered in this study. The hydrostatic pressure is typically proportional to the depth of water and the equation of hydrostatic pressure can be expressed as(1)
P
w
=
γ
w
h
,where γ
w = unit weight of water and h is the depth of water. Therefore, the total water pressure in the horizontal direction and vertical water pressure by the unit length are 1
/
2
γ
w
h
2 and γ
w
h
A, respectively.Next, the weir-reservoir interaction as a hydrodynamic effect was obtained from Westergaard [6] hydrodynamic approach. The mathematical description of hydrodynamic governing equation in two-dimensional system can be derived as follows [6, 7]:(2)
∂
2
P
∂
x
2
+
∂
2
P
∂
y
2
=
1
C
2
∂
2
P
∂
t
2
.In this equation, the velocity of sound in water C
=
K
/
ρ
w and P
(
x
,
y
,
t
) is the hydrodynamic pressure. ρ
w is the water density and K is the water bulk modulus. In particular, for the structure subjected to an earthquake, the Westergaard hydrodynamic pressure based on added mass method is given as follows:(3)
P
d
=
7
8
ρ
w
g
k
H
×
h
,where k is 2
/
3
P
G
A
/
g. H is the total depth of the water and h is the depth from the water surface to the point of hydrodynamic pressure [8].The uplift pressure of the weir structure is characterized by upward pressure of water as it flows through opening cracks of the foundation or the body connection parts due to the seepage or penetration path [8]. The equation of uplift pressure associated with the hydrostatic pressure may be written as [9](4)
U
=
γ
w
×
C
×
A
×
H
2
+
1
2
(
H
1
-
H
2
)
×
τ
,where C is the ratio of area with respect to hydrostatic pressure and A is the bottom area due to uplift pressure. H
1 is the depth of upstream of the system and H
2 is the depth of downstream of the weir. Also, τ means the ratio of H
1
-
H
2 in terms of cut-off grouting and drainage curtain.Besides, earth pressure due to backfill placed against the structure in foundation excavation and silt (horizontal and vertical) pressure due to deposit of silt must be taken into account in the dam or weir design [10]. With dam design criteria in Korea (2011), silt pressure can be calculated by the following:(5)
P
s
=
γ
s
u
b
K
a
H
,in which γ
s
u
b is the submerged unit weight; K
a defines the coefficient of earth pressure, and H is the depth of silt deposit in the structure.Lastly, in order to consider the dynamic interaction among the structure, reservoir, and soil-foundation, the dynamic equation of motion of the system subjected to a seismic ground motion can be obtained(6)
m
u
¨
(
t
)
+
c
u
˙
(
t
)
+
k
u
(
t
)
=
-
m
u
¨
g
t
+
R
,where u
¨
(
t
), u
˙
(
t
), and u
(
t
) are the acceleration, velocity, and displacement, u
¨
g
(
t
) is the ground motion, and R is the hydropressure and earth pressure mentioned above. In addition, [m], [c], and [k] are the mass, damping, and stiffness matrices of the system. Details of seismic ground motions for analytical fragility functions of the weir structure are described in the next section.


## 3.1. FE Modeling Description

To evaluate the performance of the weir structures, the Finite Element (FE) model was generated by ABAQUS [5], as shown in Figure 4, and a 4-node bilinear plane strain quadrilateral element was applied to the weir body, mass concrete, and soil-structure foundation. The dimension of y direction of the weir system was modeled with 58.114 m and x direction was 83.5 m including upstream and downstream side, in consideration of stress transfer. The material properties for the weir system were listed in Table 1. The design strength of the weir body and mass concrete system designed to peak ground acceleration at 0.154 g was 24 MPa and 18 MPa, respectively, and unit weight was 2350 kg/m3. For simplification, the weir body as a master surface and mass concrete as a slave surface were connected by tie condition in ABAQUS.Table 1
Material properties of the weir structure.
Structures
Elastic modulus(MPa)
Poisson’s ratio
Density(t/mm3)
Weir body
26,637
0.167
2.4
E
-
9
Mass concrete
24,579
0.167
2.4
E
-
9
Steel
200,000
0.25
7.85
E
-
9
Soil layer 1
2
0.4
1.7
E
-
9
Soil layer 1
25
0.4
1.9
E
-
9
Soil layer 1
2,000
0.3
2.4
E
-
9Figure 4
FE model of the weir including soil foundations.


## 3.2. Loading Conditions

In general, the system weight (gravity-weight) was determined by the combination of concrete unit weight and the system volume and 5 different loading conditions (hydrostatic pressure, hydrodynamic pressure, uplift pressure, silt pressure, and earthquake) were considered in this study. The hydrostatic pressure is typically proportional to the depth of water and the equation of hydrostatic pressure can be expressed as(1)
P
w
=
γ
w
h
,where γ
w = unit weight of water and h is the depth of water. Therefore, the total water pressure in the horizontal direction and vertical water pressure by the unit length are 1
/
2
γ
w
h
2 and γ
w
h
A, respectively.Next, the weir-reservoir interaction as a hydrodynamic effect was obtained from Westergaard [6] hydrodynamic approach. The mathematical description of hydrodynamic governing equation in two-dimensional system can be derived as follows [6, 7]:(2)
∂
2
P
∂
x
2
+
∂
2
P
∂
y
2
=
1
C
2
∂
2
P
∂
t
2
.In this equation, the velocity of sound in water C
=
K
/
ρ
w and P
(
x
,
y
,
t
) is the hydrodynamic pressure. ρ
w is the water density and K is the water bulk modulus. In particular, for the structure subjected to an earthquake, the Westergaard hydrodynamic pressure based on added mass method is given as follows:(3)
P
d
=
7
8
ρ
w
g
k
H
×
h
,where k is 2
/
3
P
G
A
/
g. H is the total depth of the water and h is the depth from the water surface to the point of hydrodynamic pressure [8].The uplift pressure of the weir structure is characterized by upward pressure of water as it flows through opening cracks of the foundation or the body connection parts due to the seepage or penetration path [8]. The equation of uplift pressure associated with the hydrostatic pressure may be written as [9](4)
U
=
γ
w
×
C
×
A
×
H
2
+
1
2
(
H
1
-
H
2
)
×
τ
,where C is the ratio of area with respect to hydrostatic pressure and A is the bottom area due to uplift pressure. H
1 is the depth of upstream of the system and H
2 is the depth of downstream of the weir. Also, τ means the ratio of H
1
-
H
2 in terms of cut-off grouting and drainage curtain.Besides, earth pressure due to backfill placed against the structure in foundation excavation and silt (horizontal and vertical) pressure due to deposit of silt must be taken into account in the dam or weir design [10]. With dam design criteria in Korea (2011), silt pressure can be calculated by the following:(5)
P
s
=
γ
s
u
b
K
a
H
,in which γ
s
u
b is the submerged unit weight; K
a defines the coefficient of earth pressure, and H is the depth of silt deposit in the structure.Lastly, in order to consider the dynamic interaction among the structure, reservoir, and soil-foundation, the dynamic equation of motion of the system subjected to a seismic ground motion can be obtained(6)
m
u
¨
(
t
)
+
c
u
˙
(
t
)
+
k
u
(
t
)
=
-
m
u
¨
g
t
+
R
,where u
¨
(
t
), u
˙
(
t
), and u
(
t
) are the acceleration, velocity, and displacement, u
¨
g
(
t
) is the ground motion, and R is the hydropressure and earth pressure mentioned above. In addition, [m], [c], and [k] are the mass, damping, and stiffness matrices of the system. Details of seismic ground motions for analytical fragility functions of the weir structure are described in the next section.


## 4. Seismic Ground Motions

In order to develop the seismic vulnerability of the system, the uncertainties of the ground motions with respect to frequency range, ground motion intensity, and earthquake fault mechanism were taken into account. According to Billah et al. [11], the ground motion fault mechanisms as an uncertainty characteristic have a significant effect on the seismic fragility of the bridge. In case of near fault mechanisms, a long period velocity pulse (pulse-like motion) and higher input energy on the system were discharged [11, 12]. Hence, 30-near-field set with epicentral distance less than 10 km and 30-far-field set with epicentral distance over 10 km were carried out to generate the seismic fragility for the weir structure. The details of the ground motions selected from PEER-NGA [13] were listed in Tables 2 and 3.Table 2
Selected ground motions: near field.
Number
Events
Year
Station
Mag.
Fault
Epicentral distance (km)
PGA(g)
1
Parkfield
June 28th,1966
Cholame-Shand on Array number 5
6.19
Strike-slip
9.6
0.1381
2
San Fernando
Feb. 9th,1971
Pacoimadam
6.61
Reverse
0
1.2259
3
Tabas,Iran
Sep. 16th,1978
Dayhook
7.35
Reverse
0
0.3279
4
Tabas,Iran
Sep. 16th,1978
Tabas
7.35
Reverse
1.8
0.8358
5
ImperialValley
Oct. 15th,1979
AeropuertoMexicali
6.53
Strike-slip
0
0.3267
6
ImperialValley
Oct. 15th,1979
El CentroArray number 10
6.53
Strike-slip
6.2
0.1053
7
ImperialValley
Oct. 15th,1979
El CentroArray number 4
6.53
Strike-slip
4.9
0.2478
8
ImperialValley
Oct. 15th,1979
Sahop CasaFlores
6.53
Strike-slip
9.6
0.2874
9
Victoria,Mexico
June 9th,1980
VictoriaHospital
6.33
Strike-slip
6.1
0.0446
10
Irpinia,Italy
Nov. 23rd,1980
Auletta
6.9
Normal
9.5
0.0576
11
Irpinia,Italy
Nov. 23rd,1980
BagnoliIrpino
6.9
Normal
8.1
0.1394
12
IrpiniaItaly
Nov. 23rd,1980
Sturno
6.9
Normal
6.8
0.2506
13
Irpinia,Italy
Nov. 23rd,1980
Calitri
6.9
Normal
8.8
0.1774
14
MorganHill
Apr. 24th,1984
AndersonDam
6.19
Strike-slip
3.2
0.4230
15
MorganHill
Apr. 24th,1984
CoyoteLake Dam
6.19
Strike-slip
0.2
0.7109
16
Nahanni,Canada
Dec. 23rd,1985
Site 2
6.76
Reverse
0
0.4890
17
Nahanni,Canada
Dec. 23rd,1985
Site 3
6.76
Reverse
4.9
0.1404
18
N. PalmSprings
July 08th,1986
Desert HotSprings
6.06
Reverse
1.0
0.3313
19
N. PalmSprings
July 08th,1986
MorongoValley
6.06
Reverse
3.7
0.2182
20
N. PalmSprings
July 08th,1986
North PalmSprings
6.06
Reverse
0
0.5941
21
SuperstitionHills
Nov. 24th,1987
ParachuteTest Site
6.54
Strike-slip
0.9
0.4550
22
Loma Prieta
Oct. 18th,1989
Capitola
6.93
Reverse
8.7
0.5285
23
Loma Prieta
Oct. 18th,1989
GilroyGavilan Coll.
6.93
Reverse
9.2
0.3570
24
Loma Prieta
Oct. 18th,1989
GilroyArray number 1
6.93
Reverse
8.8
0.2088
25
Chi-ChiTaiwan
Sep. 20th,1999
CHY006
7.62
Reverse
9.8
0.1301
26
Chi-ChiTaiwan
Sep. 20th,1999
TCU076
7.62
Reverse
2.8
0.3029
27
Kobe,Japan
Jan. 16th,1995
NishiAkashi
6.9
Strike-slip
7.1
0.5093
28
Kobe,Japan
Jan. 16th,1995
Takatori
6.9
Strike-slip
1.5
0.6114
29
North Ridge
Jan. 17th,1994
Newhall
6.69
Reverse
3.2
0.5830
30
North Ridge
Jan. 17th,1994
PacoimaKagelCanyon
6.69
Reverse
5.3
0.3011Table 3
Selected ground motions: far field.
Number
Events
Year
Station
Mag.
Fault
Epicentral distance (km)
PGA(g)
1
Kocaeli,Turkey
June 28th,1999
Ambarli
7.51
Strike-slip
68.1
0.2487
2
San Fernando
Feb. 9th,1971
CarbonCanyon Dam
6.61
Reverse
61.8
0.0695
3
San Fernando
Feb. 9th,1971
CedarSpring
6.61
Reverse
92.2
0.0267
4
San Fernando
Feb. 9th, 1971
Colton
6.61
Reverse
96.8
0.0321
5
San Fernando
Feb. 9th, 1971
FairmontDam
6.61
Reverse
25.6
0.0712
6
Friuli,Italy
May 6th, 1976
Barcis
6.5
Reverse
49.1
0.0289
7
Friuli,Italy
May 6th, 1976
Conegliano
6.5
Reverse
80.4
0.0491
8
IrpiniaItaly-01
Nov. 23rd,1980
Rionero inVulture
6.9
Normal
29.8
0.1059
9
ImperialValley
Oct 15th,1979
CalipatriaFire STA
6.53
Strike-slip
23.2
0.1282
10
ImperialValley
Oct. 15th,1979
CerroPrieto
6.53
Strike-slip
15.2
0.1691
11
IrpiniaItaly-02
Nov. 23rd,1980
MercatoSan Severino
6.2
Normal
43.5
0.0417
12
ImperialValley
Oct. 15th,1979
Compuertas
6.53
Strike-slip
13.5
0.1862
13
ImperialValley
Oct. 15th1979
Delta
6.53
Strike-slip
22
0.2378
14
ImperialValley
Oct. 15th,1979
ParachuteTest Site
6.53
Strike-slip
12.7
0.1113
15
ImperialValley
Oct. 15th,1979
SuperstitionMTN Camera
6.53
Strike-slip
24.6
0.1092
16
IrpiniaItaly-02
Nov. 23rd,1980
Rionero inVulture
6.2
Normal
22.7
0.0988
17
Chi-ChiTaiwan
Sep. 20th,1999
CHY019
7.62
Reverse
50
0.0637
18
Chi-ChiTaiwan
Sep. 20th,1999
CHY022
7.62
Reverse
63.2
0.0443
19
Chi-ChiTaiwan
Sep. 20th,1999
CHY023
7.62
Reverse
81.1
0.0584
20
Chi-ChiTaiwan
Sep. 20th,1999
CHY025
7.62
Reverse
19.1
0.1592
21
Kocaeli,Turkey
June 28th,1999
Arcelik
7.51
Strike-slip
10.6
0.2188
22
Kocaeli,Turkey
June 28th,1999
Atakoy
7.51
Strike-slip
56.5
0.1048
23
Kocaeli,Turkey
June 28th,1999
Bursa
7.51
Strike-slip
65.5
0.0453
24
New Zealand02
Mar. 2nd,1987
MatahinaDam
6.6
Normal
16.1
0.2553
25
ImperialValley
Oct. 15th,1979
El CentroArray number 12
6.53
Strike-slip
17.9
0.0658
26
ImperialValley
Oct. 15th,1979
El CentroArray number 13
6.53
Strike-slip
22
0.0456
27
ImperialValley
Oct. 15th,1979
El CentroArray number 3
6.53
Strike-slip
10.8
0.1267
28
ImperialValley
Oct. 15th,1979
El CentroArray number 1
6.53
Strike-slip
21.7
0.0564
29
ImperialValley
Oct. 15th,1979
El CentroArray number 11
6.53
Strike-slip
12.4
0.1403
30
Parkfield
June 28th,1966
TemblorPre-1969
6.19
Strike-slip
17.6
0.3574


## 5. Probabilistic Risk Assessment Methodology: Fragility Function

In recent years, seismic probabilistic risk assessment (SPRA) has been applied to identify the performance and limit/damage state of the systems (nuclear power plants (NPP), bridges, buildings, dams, etc.) in hazard and risk management. Kennedy et al. [14] came out with the seismic fragility as a factor of safe method for NPP and the Electric Power Research Institute (EPRI) [15] developed the assessment of NPP seismic margin using conservative deterministic failure margin methodology to provide in-depth recommendation for the seismic fragility analysis. Moreover, in order to estimate the seismic vulnerability of a bridge structure, various analytical fragility methodologies such as nonlinear time history analyses [16], nonlinear static analyses [17], and Bayesian approach [18] were used. Ellingwood and Tekie [19] and Tekie and Ellingwood [4] presented the safety evaluation of existing concrete gravity dams by reservoir inflow, pool elevation, and spectral acceleration of seismic ground motions. Additionally, Ju et al. [20], Ju and Jung [21], and Ju and Jung [22] carried out Monte Carlo Simulation (MCS) to generate the seismic fragility of piping systems as a nonstructural component in critical facilities. Based on MCS methodology, the conditional probability of failure of the weir structure can be defined as follows: (7)
P
f
P
G
A
=
P
E
D
P
s
>
L
S
∣
P
G
A
,in which P
f
(
P
G
A
) denotes the conditional probability in terms of peak ground acceleration (PGA) as the ground intensity measure. In this study, the displacement and stresses are considered as engineering demand parameters (EDPs) and limit state (LS) is associated with EDPs to construct the fragility. Then, the empirical fragility of the weir structure corresponding to LS given in (8) was obtained from multiple linear time-history analyses using MCS accounting for ground motion uncertainties:(8)
P
f
λ
=
∑
i
=
1
N
E
D
P
s
≥
L
S
∣
P
G
A
=
λ
#
E
Q
s
,where EDPs are the maximum stress or displacement from ith linear earthquake time-history analysis at a given PGA level. Therefore, the analytical fragility based on MCS for the weir structure in this study can be derived by log-normal cumulative distribution function (CDF) [23]:(9)
P
f
(
λ
)
=
Φ
l
n
(
λ
/
m
c
)
β
s
d
.Also, the analytical fragility of the weir structure corresponding to damage states is conducted by a correlation between the median capacity (m
c) and the logarithmic standard deviation (β
s
d) of the structural system. Therefore, the damage states or limit states must be achieved prior to evaluation of the probability of failure of the system. This study defined the limit states of the weir structure based on Concrete Design Criteria 2003 [24] and Dam Design Criteria 2011 [9] in Korea and five different limit states for the system were presented in Table 4.Table 4
Limit states of the weir structure.
Limit states
Details
Design criteria
LS-1
Compressive stress at the weir body and stilling basin
0.25
f
c
k
=
6 MPa
LS-2
Tensile stress at the weir body and stilling basin
0.42
f
c
k
=
2.058 MPa
LS-3
Compressive stress at the mass concrete
0.25
f
c
k
=
4.5 MPa
LS-4
Tensile stress at the mass concrete
0.42
f
c
k
=
1.782 MPa
LS-5
The displacement of the weir structure
10 mm


## 6. Seismic Fragility of the Weir Structure

A straightforward elastic FE model of the weir structure including the soil-structure foundation was dealt with for the fragility analyses. Before the evaluation, the analysis of eigenvalues and eigenvectors was conducted, in order to determine the dynamic properties of the weir structure with 5% damping ratio. The damping matrix in this study was determined by Rayleigh damping method in form of [25](10)
C
=
α
M
+
β
K
,where α = the mass constant value and β = the stiffness constant value. Then, the fundamental, second, and third frequencies from the eigenvalues were 0.8911, 1.1223, and 1.2622 Hz, respectively, and about 26% effective mass participation was observed at the third mode. It revealed that the third mode was the largest proportion of the total mass in horizontal direction. Consequently, in the estimation of the fragility of the weir structure, 30-near-field and 30-far-field ground motions normalized to the same PGA levels (0.1 g, 0.2 g, 0.4 g, 0.6 g, 0.8 g, 1.0 g, and 1.5 g) were applied to the simple linear elastic FE model, respectively. In addition, the seismic fragilities were implemented at each PGA using (8) as the empirical method and the analytical seismic fragilities were established by (9) for the Gangjeong-Goryeong weir system. With the multiple time-history analyses accounting for ground motion uncertainties, seismic fragilities corresponding to the limit states were described in Figures 5 and 6. The fragilities noted that the system subjected to ground motions was more vulnerable to the tensile stress of the mass concrete structure than other damages. The similar manner is also observed in the weir system subjected to near field and far field ground motions. The probability of failure due to tensile stress (LS-2) of the weir body was not significantly different from LS-3 (i.e., compressive stress of the mass concrete) in overall PGA levels, as shown in Figure 5. On the other hand, in case of the far field ground motions (Figure 6), the failure difference between LS-2 and LS-3 gradually increased as the seismic hazard level increased. Particularly, it showed that the fragility difference between tensile stress of the weir body and compressive stress of the mass concrete was about 27% at PGA 1.0 g. Also, the relative displacement (LS-5) showed the lowest probability of failure in comparison to other damage states on both ground motions. The fragility comparison for the weir structure subjected to near field and far field ground motion intensity was described in Figures 7 to 11. In comparison to the fragility at limit state 2, the probability of failure of the system presented the similar trend between near field and far field ground motions. In addition, the system subjected to near field ground motions was more vulnerable than the weir structure subjected to far field ground motions. However, the probability of failure of the system at LS-1 due to far field ground motions was higher than that of the system under near field ground motion intensity up to PGA 0.78 g. Therefore, the investigations depicted that the weir structure was sensitive to the ground motion intensity, which was the acceleration-sensitivity structural system.Figure 5
The seismic fragility of the weir subjected to near field ground motions.Figure 6
The seismic fragility of the weir subjected to far field ground motions.Figure 7
Comparison of the fragility corresponding to LS-1.Figure 8
Comparison of the fragility corresponding to LS-2.Figure 9
Comparison of the fragility corresponding to LS-3.Figure 10
Comparison of the fragility corresponding to LS-4.Figure 11
Comparison of the fragility corresponding to LS-5.


## 7. Conclusions

The seismic probabilistic risk assessment, which is the seismic fragility, can be commonly used to identify the performance or characteristic strength of the system at a given seismic hazard level in civil engineering structures. In order to develop the safety assessment for the weir structure as a critical structure in Korea, the fragility analysis was carried out in this study. More specifically, this study developed the simple linear elastic FE model including the soil-structure foundation of Gangjeong-Goryeong weir located on the Nakdong River near Daegu Metropolitan City in Korea. To describe the uncertainty in ground motions of the seismic fragility analyses, near field (30 earthquake records) and far field (30 earthquake records) earthquakes were accounted for as intensity measures. With the particular emphasis on incorporating uncertainty into the 2D plain FE model, multiple linear time history analyses based on MCS were carried out. Through this preprocess, the vulnerability of the weir structure was estimated. As a result, from the eigenvalue analysis, the effective mass participation of the third mode in the weir structure was significantly larger than that of the first mode and the second mode in horizontal direction. It was noted that the mode shape and mass participation were very different from the typical building type. The empirical and analytical fragility results in particular revealed that the weir structure was more conservative to the near field fault mechanism in comparison to the far field fault. Furthermore, the weir system including mass concrete and soil foundations was relatively susceptible to limit state 4 (tensile stress at the mass concrete) as compared to other damage states, during an earthquake.Finally, the seismic fragility accounting for the nonlinearity with respect to the interaction between the weir body and soil-structure foundation must be achieved and for a future safety assessment of the weir system the effect of flooding condition must be also considered.



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*Source: 391569-2015-06-03.xml*