seismic response and damage mechanism of underground
TRANSCRIPT
SEISMIC RESPONSE AND DAMAGE MECHANISM OF
UNDERGROUND STRUCTURE OF SUBWAY TRANSFER STATIONS
Zhong-Yang YU1, Hong-Ru ZHANG
2, Chao-Qun HUANG
3, Chun-Sheng QIAO
4
ABSTRACT
Urban rail transit has been considered a significant solution for efficient mass transport in the major cities of
China. On mainland China 57 cities have approval to develop urban rail transit systems, which had totalled 3832
km in operation by the end of 2016. It is predicted that the total planned distance in operation by the year 2020
will be greater than 10,000 km, most of which will be underground. Most urban areas in China are located in
earthquake zones. Therefore, the seismic behaviour of underground structures in the rail transit system is of great
concern, following the collapse of the Daikai station in Kobe, Japan during the 1995 earthquake. To understand
the seismic performance and damage mechanism of the complex underground structures of subway transfer
stations, numerical models have been developed, which include dynamic soil-structure interactions, soil property
variations, structural connection conditions and damage mechanisms. A simplified model for the design and
performance criteria of underground subway transfer stations is proposed.
Keywords: Underground Structure; Seismic Response; Damage Mechanism; Subway Station
1. INTRODUCTION
Underground structures had been considered to have better seismic performance due to the constraints
of the surrounding soil. For this reason seismic research was rarely focused on underground structures,
with the exception of lifeline pipes. However, the destruction of the structure of Dai Kai underground
station during the Hanshin earthquake in 1995, has provided a new understanding of subway station
structure (Tiwatate Y et al. 2000). Metro engineering withstanding seismic events is important in
urban disaster prevention and mitigation.
Existing studies are primarily focused on simple underground structures. Zhuang Haiyang (2006, 2007
and 2008) and Chen Lei (2012) have conducted seismic numerical simulations for symmetrical
underground subway stations, such as double story double span structures, in which the model
boundary effect, soil layer and underground structure acceleration response, earthquake stress and
strain are studied. Liu Jingbo (2006, 2007, 2008 and 2014) analysed problems with the underground
seismic structural design and proposed the static elastic-plastic analysis method, pushover analysis
method and integral response displacement method for underground structures, and the approximate
boundary conditions and earthquake parameters in numerical analyses are presented. Based on the
Beijing and Nanjing subway typical underground station structures, shake table model tests were
carried out by Tao Lianjin (2006) and Chen Guoxing (2007) to measure the dynamic response
characteristics of underground structures. Actual earthquake damage case study, model tests and
numerical simulations in the above literatures have shown that the destruction of the underground
structure is mainly influenced by the deformation of soil layer, while the inertia effect is not
significant. For an underground structure containing an interior column, the central pillar is the weak
1PhD student, School of Civil Engineering, Beijing Jiaotong University, Beijing, China, [email protected]
2Professor, PhD, School of Civil Engineering, Beijing Jiaotong University, Beijing, China, [email protected]
3MSc student, School of Civil Engineering, Beijing Jiaotong University, Beijing, China, [email protected]
4Professor, PhD, School of Civil Engineering, Beijing Jiaotong University, Beijing, China, [email protected]
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point within the main structure, and the damage caused by an earthquake starts with the failure of the
central column.
However, for complex structures, such as cross-transfer subway stations and other large underground
station complexes, there are few studies reported in the literature due to the complex dynamic response
characteristics, which are difficult to test. Dai Kai station, as a simple, single layer, double span
structure, is the only example of underground station earthquake destruction. Its damage can not
represent the seismic behaviour of more complex structures. For complex, large space structures, there
is not rich seismic experience. Therefore, thorough research is urgently needed. The cross structure of
a cross-transfer station can lead to an uneven deformation of the station structures during a seismic
event. Shear deformation caused by seismic waves in one direction, leads to complex forces, such as
tension or torsion in other directions. The dynamic interaction effect of the connected structures is
significant. Therefore, it is difficult to simulate a 3D structure system using a 2D model.
Based on a typical cross-transfer station used in practical engineering, which is the cross structure of
the three-story-three-span structure and two-story-three-span structure, detailed dynamic finite element
simulation analysis were carried out in this study. The results were compared with the 2D analysis to
determine the area most vulnerable to forces in the cross structure. In addition, the pushover method
was used to analyse the failure characteristics of the three-story-three-span and two-story-three-span
structures, and the damage mechanism of the underground structure was discussed.
2. SESMIC RESPONSES OF UNDERGROUND SUBWAY STATION
2.1 Dynamic Finite Elements Models
The underground structure considered in this study was an underground cross-transfer station for two
subway lines, constructed using a cut and cover method. It was composed of a three-story-three-span
structure for one line crossing, and a two-story-three-span structure for the other line. The plan and
cross section of the structure is shown in Figure 1.
(b) Cross section 1 of the underground structure
(a) Plan section of the underground structure (c) Cross section 2 of the underground structure
Figure 1. Plan and cross section of the structure (Unit: mm)
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The dimension of the three-story structure was 22.8 m in width, 21.85 m in height, 0.8 m-thick top
plates, 0.4 m-thick medium plates, 0.9 m-thick bottom plates, 0.8 m-thick side walls, 1.2 m-wide
longitudinal beams, and 0.8×1.0 m interior columns. The dimensions of the two-story structure was
22.8 m in width, 13.85 m in height, and the same dimensions for the remainder of the three-story
station structure. In addition, the longitudinal space of the interior columns was 9.0 m in both
directions and the burial depth of roof of the structure was 3.0 m.
An equivalent 2D dynamic analysis model was proposed: a standard three-story-three-span station
structure. The remainder of the parameters of the 2D model were selected to be the same as the 3D
model.
Concrete material used in the station structure was C40, with the basic properties shown in Table 1.
The main reinforcement of the structure was HRB 400 reinforced steel bars, composed of C28@150
for side walls, C25@150 for plates, and 32C28 for interior columns.
Table 1. Damage parameters of C40.
(From Code for Design of Concrete Structures GB 50010-2010)
Density (Kg/m3) Elastic Modulus (GPa) Poisson ratio Damping ratio
2500 32.5 0.25 0.05
The elastoplastic model with Mohr-Coulomb failure criteria was applied as the constructive law of the
soil. The parameters of the soils are shown in Table 2, and the depth division of the soil layer with the
cross section of the structure is shown in Figure 2.
Table 2. Soil parameters.
(From Geological Survey Report of Beijing Metro Line 7)
Soil Depth
(m)
Density
(kg/m3)
Shear Wave
Velocity(m/s)
Dynamic
Modulus Of
Shear(MPa)
Cohesion
(kPa)
Friction
Angle(º)
Poisson
Ratio
① 3 1750 170.0 50.6 5 10 0.35
② 5 1960 223.3 97.7 31 17 0.36
③ 16 1980 238.6 112.7 33 19 0.36
④ 36 2020 317.8 204.0 28 30 0.33
⑤ 20 2120 462.7 453.8 0 45 0.26
Figure 2. Soil layer distribution and structure embedment (Unit:mm)
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In order to test the possibility of using the plain strain model to analyse the 3D underground cross
structure, a 3D finite element model of the full structure and a 2D model corresponding to standard
cross section were constructed.
The size of the 3D finite element model was 239×239×80 m, which included the soil surrounding the
structure of the underground station. Figure 3 shows the total finite element model and the structure
model. The finite element model includes two typical elements: eight-node hexahedral elements for
the soil medium, and four-node shell elements for the station structure. Viscoelastic boundary
conditions were introduced to eliminate the wave reflection in the lateral boundary, by horizontal
dampening springs and vertical restraints on the four lateral boundaries of the soil. The surface of the
bedrock served as the seismic input interface. In this numerical simulation, the input had horizontal
seismic excitations, perpendicular to the two-story-three-span cross section.
(a) Full mesh model (b) Mesh of structure only
Figure 3. 3D mesh of cross transfer underground subway station
The size of the 2D finite element model was 239×80 m, which included the soil surrounding the
underground station structure. Figure 4 shows the total finite element model and the structure model.
The elements applied include two typical elements: the four-node bilinear tetragonal elements in a
plane-strain condition for the soil medium, and two-node planar linear beam elements for the station
structure. The viscoelastic boundary conditions were also introduced, modeled using vertical restraints
and horizontal dampening springs on the lateral boundaries of the soil. The surface of the bedrock
served as the seismic input interface. The input was horizontal in-plane excitations.
Figure 4. 2D mesh of standard cross section of underground station
In this simulation, the first 30 seconds data of N-W horizontal component of El-Centro Seismic Wave
was inputted at the bottom of the model. In the analysis, additional 5 seconds zero data was added to
end to dissipate the seismic response. The peak acceleration of the record was adjusted to 0.1g for
simulating Level 7 seismic intensity. The original 30 seconds waveform is shown in Figure 5.
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5 10 15 20 25 30
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Time(s)
Accele
rati
on
(g)
Figure 5. Original El-Centro seismic waves
(The data from https://strongmotioncenter.org/, Imperial Valley Earthquake, May 18, 1940, Station No. 117,
Comp S00E, Peak Acceleration = 341.69531 cm/sec/sec)
2.2 Dynamic Seismic Response of the Cross Transfer Underground Station Structure
3D and 2D dynamic simulations were carried out, based on the corresponding finite element models.
The internal forces of the side walls and interior columns are shown in Figure 6 for both models,
where the vertical coordinate represents the buried structural depth, and the horizontal axis presents
the internal forces of the structure. In these figures, “1CS”, “2CS”, “3CS” and “4CS”, respectively,
stand for the 3D results from the cross structure with a distance of one, two, three and four times
column space away from the cross structure, as is shown in Figure 1; while “2D” stands for the
corresponding results from the 2D model.
0 300 600 900 1200
24
21
18
15
12
9
6
3
Sidewall Moment (kN-m/m)
Str
uct
ure
Bu
ried
Dep
th (
m)
2D
1CS
2CS
3CS
4CS
0 200 400 600 800 1000
24
21
18
15
12
9
6
3
Sidewall Shear Force (kN/m)
Str
uct
ure
Bu
ried
Dep
th (
m)
2D
1CS
2CS
3CS
4CS
0 3000 6000 9000 12000
24
21
18
15
12
9
6
3
Interoir Column Axial Force (kN)
Str
uct
ure
Bu
ried
Dep
th (
m)
2D
1CS
2CS
3CS
4CS
(a) Sidewall moment (b) Sidewall shear force (c) Interior column axial force
Figure 6. The maximum internal forces of the side walls and interior columns
Some differences between the 2D and 3D internal forces were observed. The two-story structure can
be regarded as a shear wall for the three-story structure, which may explain the lateral wall bending
moment being smaller and the shear force larger in comparison with the 2D results.
This effect gradually decreases as the distance increases and at a distance greater than three times of
the column space from the cross section, the bending moment and shear forces of the side wall were
similar as those in the 2D standard structure along the depth direction. Therefore, the internal forces of
the side wall were not influenced by the cross structure at distances three times the column space.
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The axial forces of the interior column were primarily determined by the static loading and there is no
obvious distinction between the 3D and 2D standard structures.
Overall, it was demonstrated that the range of influence on the cross structure was about 3 times the
column space, and the internal forces of the structure beyond this range are not affected by the
intersection. A standard structure seismic design method could be adopted when the distance is
beyond the influence range and the enhanced design method could be used for the intersection.
3. DAMAGE MECHANISM OF UNDERGROUND SUBWAY STATION
3.1 Pushover Models
To investigate the damage mechanism, pushover simulations were performed on 2D models of a two-
story-three-span station structure and a three-story-three-span station structure, with the same size
cross structure.
C50 concrete was used in the interior columns and C35 concrete was used in all other station
structures. The reinforcement configuration with HRB 400 is shown in Table 3. When the moment of
bent dominant members reached their ultimate bending moments, hinges occurred. The failure forces
for the interior columns were the ultimate axial forces.
To simplify the analysis in the simulation, the structures were elastically linear before yield, and full
plastic after yield. The site soil was assumed to be elastic and saturated. The shear wave velocity was
160 m/s (soft soil), with a density ρg= 2.0 g/cm3, and Poisson's ratio μd = 0.47.
Table 3. Structural reinforcement and ultimate forces.
Side Wall Top Plate Medium
Plate Bottom Plate
Interior
Column
Reinforcement
(mm) C28@150 C25@150 C18@150 C28@150 32C28
Ultimate forces 919 kN·m 732 kN·m 197 kN·m 1228 kN·m 2326 kN
The total size of the 2D soil-structure system model was 200×50 m, with the soil medium represented
using four-node bilinear tetragonal elements in a plane-strain condition, and the station structure was
represented using two-node planar linear beam elements. The mesh is shown in Figures 7 and 8.
The lateral boundary was vertically constrained, while the horizontal boundary was free and the
bottom boundary fixed. Lateral push loading with an inverted triangle vertical distribution was used.
Figure 7. Mesh of two-story-three-span subway station model
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Figure 8. Mesh of three-story-three-span subway station model
3.2 Damage Mechanism of the Underground Station
In the seismic design for structures, the elastic limit and plastic limit are usually used as parameters to
estimate the performance of the structures in a seismic event. The elastic limit was marked by the
appearance of the first plastic hinge in structure members; while the plastic limit was presented by the
appearance of sufficient hinges to form a plastic mechanism.
3.2.1 Development of Underground Structure Damage
With the increase of seismic loading, plastic hinges in the underground structure appeared gradually
and the damage increased until the structure completely collapsed.
In the two-story underground structure, the first plastic hinge appeared at the intersection of the
interior column and the middle plate (Figure 9(a)). This was followed by the plastic region of the
structure developing rapidly. The joints of the middle plates with the side wall and the interior
columns subsequently turned into the plastic phase. The left and right joints of the side walls and the
bottom also entered into the plastic phase later (Figure 9(c)).With the load increasing, the bottom ends
of the interior columns and the top end of the side wall entered into the plastic stage, as is shown in
Figure 9(e). Finally, the plastic hinges appeared at the top ends of the interior columns (Figure 9(f)).
(a) (b) (c)
(d) (e) (f)
Figure 9. Plastic development of two-story underground structure
In the three-story underground structure, the plastic development sequence was similar to the two-
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story underground structure, with the first plastic zone appearing at the intersection of the side wall
and the middle plate (Figure 10(a)). The joints of the middle plates with the side wall and the interior
columns subsequently turned into the plastic phase. The left and right joints of the side walls and the
bottom also entered the plastic phase later (Figure 10(c)). With the load increasing, the bottom ends of
the interior columns and the top end of side wall entered into the plastic phase, as is shown in Figure
10(e). The top ends of the interior columns finally entered into the plastic stage (Figure 10(f)).
(a) (b) (c)
(d) (e) (f)
Figure 10. Plastic development of three-story underground structure
Therefore, it can be considered that the damage mechanism of cut and cover structures start with the
destruction of the middle plate.
3.2.2 Design Limit for Design Earthquake and High Level Earthquake
The performance of a structure is often determined in a design using the inter-story drift angle of the
underground structure, enabling the structure working conditions to be measured. The inter-story drift
angle is calculated by:
/R H (1)
Where: R is inter-story drift angle, Δ is the relative horizontal displacement of adjacent story and H is
the height of story.
Based on the definition of the inter-story drift angle, the elastic limit of the two-story underground
structure was 1/835 and the plastic limit was 1/225. The elastic limit of the three-story underground
structure was 1/1191 and the plastic limit was 1/296.
In the two-story structure, the inter-story drift angle exceeded 1/250, the limit of current design code
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for a high level earthquake.
In the seismic design of the ground structure, the structural working condition can be estimated based
on the inter-story drift angle. Underground structures may perform differently at the same inter-story
drift angle. Therefore, the inter-story drift angle might not be the best parameter to determine the
underground structure working conditions during a seismic event.
4. CONCLUSIONS
In order to investigate seismic behaviour of complex underground urban rail transit station precisely,
3D and 2D dynamic numerical model were used to simulate the seismic response characteristics of a
cross-transfer subway structure. The comparison between the distribution of the internal force and
displacement of both models shows that the cross structure has significant influence on the cross-
transfer subway structure. The bending moments and shear forces of the side wall are influenced by
the cross structure in a distance about 3 times of the column space, while the internal forces of the
interior columns are mainly determined by the static loading.
2D quasi-static pushover analyses for two-story-three-span and three-story-three-span underground
structures were carried out to study their failure mechanisms. The results indicate the first plastic zone
appeared in the middle plate for both structures, then the joints of side wall and the bottom entered the
plastic stage. The bottom ends of interior columns and the top end of side wall entered into the plastic
phase later. Finally, the top ends of the interior columns turned into the plastic stage and the structures
became unstable. However, there is a slight difference in the initial plastic development stage that the
location of the first plastic hinge is different for two structures. It has to be mentioned that this failure
characteristics may result from the real engineering designed structures, where the members subjecting
to vertical loads and joints had been strengthened to prevent integral structural collapse, and the soft
soil assumption.
5. ACKNOWLEDGMENTS
This project was supported by the National Natural Science Foundation of China (51678042).
6. REFERENCES
Chen Guoxing, Zhuang Haiyan, Du Xiuli (2007). Analysis of large-scale shaking table test of dynamic soil-
subway station interaction. Journal of Earthquake Engineering and Engineering Vibration, 27(2):62-67.
Chen Lei, Chen Guoxing, Mao Kungming (2012). 3D refined nonlinear analysis of seismic response
characteristics of frame metro station under near-field strong ground motion of large earthquake. Chinese
Journal of Geotechnical Engineering, 03:490-496.
Chen Lei, Chen Guoxing et al (2012). 3D Refined Nonlinear Analysis on Seismic Responses of Three-arch and
Two-column Subway Station Structure. Journal of the China Railway Society, 11:100-107.
Li Lin, Liu Jingbo, Liu Xiangqing (2008). Study on seismic responses of a subway station and design parameters
of ground motions. Journal of Earthquake Engineering and Engineering Vibration, 01:17-23.
Liu Jingbo, Gu Yin, Du Yixin (2006). Consistent viscous-spring artificial boundaries and viscous-spring
boundary elements. Chinese Journal of Geotechnical Engineering, 28(9):1070-1075.
Liu Jingbo, Li Bin, Liu Xianqiang (2007). A static elasto-plastic analysis method in seismic design of
underground structures. China Civil Engineering Journal, 07:68-76.
Liu Jingbo, Wang Wenhui, Dasgupta Gautam (2014). Pushover analysis of underground structures: Method and
application. Science China Technological Sciences, 57(2):423-437.
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Liu Jingbo, Wang Wenhui et al (2014). Integral response deformation method in seismic analysis of complex
section underground structures. China Civil Engineering Journal, 01:134-142.
MCC & GAQSIQC (The Ministry of Construction of China, General Administration of Quality Supervision,
Inspection and Quarantine of China) (2011). Code for Design of Concrete Structure GB50010-2010, 2011
edition. China Construction Industry Press. Beijing, China.
Tao Linjin, Wang Peilin, Bian Jin (2006). Shaking table test of typical subway station structure. Journal of
Beijing University of Technology, 32(9):798-801.
Tiwatate Y, kobayashi H, Kusu et al (2000). Investigation and shaking table tests of subway structures of the
Hyogoken-Nanbu earthquake. Proc. 12th WCEE, New Zealand. 1-6.
Zhuang Haiyang, Chen Guoxing (2006). Analysis of nonlinear earthquake response of two-story double-column
subway station structure. Chinese Journal of Rock Mechanics and Engineering, 25(S1):3074-3079.
Zhuang Haiyang, Chen Guoxing, Zuo Xi (2007). Analysis of Dynamic Deformation Characteristics of Two-
story Subway Station Structure under Horizontal Earthquakes. Journal of Earthquake Engineering and
Engineering Vibration, 27(6):140-147.
Zhuang Haiyang, Chen Guoxing, Wang Xiuxin (2008). Study on the earthquake responses of subway station
built with different thicknesses of soft soil layers in the foundation. Journal of Earthquake Engineering and
Engineering Vibration, 28(6):245-253.