Influence of diaphragm wall on seismic responses of large unequal-span subway station in liquefiable soils

Tunnelling and Underground Space Technology 91 (2019) 102988

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Influence of diaphragm wall on seismic responses of large unequal-span subway station in liquefiable soils

T

⁎

Jianning Wanga, Guowei Maa, Haiyang Zhuangb, , Yuanming Doua, Jisai Fub a b

School of Civil and Transportation Engineering, Hebei University of Technology, 5340 Xiping Road, Beichen District, Tianjin 300401, China Institute of Geotechnical Engineering, Nanjing Tech University, 200 Zhongshan North Road, Hongqiao District, Nanjing 210009, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Underground structure Diaphragm wall Sand liquefaction Soil-structure interaction Seismic response

Ground liquefaction is one of the severest threats that ensue subsequent damage to the subway underground structure during and after strong earthquakes. However, few studies on the seismic response of large-scale subway underground structures in liquefiable site, especially for complex subway stations, have been reported. Existing researches that consider the diaphragm wall as safety reserve for the seismic design of subway stations are oblivious of the influence of the diaphragm wall on the deformation and uplift of underground structures. Contradictory to the original intention, the diaphragm wall may have adverse effects on the overall deformation behavior and force redistribution of the structure. Thus comprehensive exploration of the interaction between the diaphragm wall and the subway station in liquefiable site during and after earthquake should be carried out to rationalize the design of the underground structure. Numerical simulations of the seismic response of different soil-structure interaction systems are implemented and discussed in the present study. In the numerical simulation, the constitutive model for saturated sand and the Arbitrary Lagrange-Euler (ALE) method to prevent mesh distortion are applied to constitute the static and dynamic coupling finite-element model. Earthquake responses of the soil and the complicated underground subway station are then investigated. Modeling results are analyzed in respect of earthquake responses yielding the liquefaction distribution of the site, the uplift feature of the unequal-span subway station, the dynamic settlement and vector characteristics of the surrounding soil, the lateral deformation and the earthquake-induced damage of the underground structure. It is found that the uplift of the unequal-span subway station is featured by uneven uplift across the spans. When the diaphragm wall is installed, the tension damage degree of the bottom plate of the subway station are intensified, while the components of cantilever span in the upper layer suffer the less. The resulted new findings from this study shed light on the seismic performance and seismic design method for the unequal-span subway stations at a liquefaction site.

1. Introduction Large liquefaction-induced ground deformation, which has been observed in previous severe earthquakes, has devastated various buildings and infrastructures (Zhang and Wang, 2012; Kang et al., 2014). The existing seismic damage data indicate that serious damage to the underground structures by ground liquefaction is not uncommon. For example, extensive liquefaction occurred in Kushiro during the 1993 Kushiro-Oki earthquake. It was reported that the liquefaction phenomenon was the most prominent detrimental factor in the port area to lead to severe damage of a large number of underground pipelines (Suzuki et al., 1995). Extensive liquefaction-induced ground settlement and lateral deformation at the site near the oil storage tank at the dock of Kushiro West Port was also detected during 1994 ⁎

Hokkaido Toho-Oki earthquake in Japan, which ensued uplift damages to the underground pipe network in liquefied foundation (Koseki et al., 2000). In the 1995 Kobe earthquake in particular, some underground structures, such as subway station, section tunnel, comprehensive pipe gallery, and buried pipeline, were severely damaged or completely destroyed. It was believed that extensive ground liquefaction aggravated severely the damage (Wang, 1993; Iida et al., 1996; Hashash et al., 2001; Huo et al., 2005; Senzai et al., 1997). It can be stated that the seismic response of a large underground subway structure should be affected more easily by the saturated sand liquefaction-induced ground deformation. The Daikai station, destroyed in the 1995 Kobe earthquake, was registered as the first case of a complete collapse of an underground structure in the history of the world earthquake engineering. Since

Corresponding author. E-mail address: [email protected] (H. Zhuang).

https://doi.org/10.1016/j.tust.2019.05.018 Received 23 October 2018; Received in revised form 24 April 2019; Accepted 21 May 2019 Available online 03 June 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

Tunnelling and Underground Space Technology 91 (2019) 102988

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Nomenclature

Srectangle

List of notations

ru EPP σ'v E0 ψ σc0 ωc ωt σcu σt0 dt dc p0 np ϕ ϕpt a c1, c2 e1, e2 d1, d2 y1, y2 py ysl i h

Ρ density of soil φ angle of internal friction ν Poisson’s ratio hmax maximal height of element Vs shear and compression motion velocity fmax maximal vibration frequency of input earthquake motion D center-to-center space of columns EeqIeq equivalent stiffness of unit width of the equivalent wall EcIc stiffness of single column τcrit maximum friction force or the shear stress limit μ friction coefficient of the contact surface P normal contact stress on the contact surface fr reversed yield surface fi active yield surface F damaged surface M increment of model hardening parameter Mmax model parameter for the damaged surface α increment of model hardening parameter H elastoplastic tangent modulus H' plastic modulus r radii of the active yield surface rmax corresponding damage surface in deviatoric stress plane G initial shear modulus G0 reference shear modulus n material parameter measured by experiment Sunequal-span peak seismic subsidence of the lateral foundation of a unequal-span subway station

l

peak seismic subsidence of the lateral foundation of a typical two-story and three-span subway station excess pore water pressure ratio excessive pore pressure of soil initial effective vertical stress of soil elastic modulus dilation angle initial compressive yield stress compression stiffness recovery parameter tensile stiffness recovery parameter limited compressive yield stress initial tensile yield stress tensile damage factor compress damage factor reference mean pressure pressure dependence exponent friction angle phase transformation angle residual strength pressure contraction parameters hardening parameters dilation parameters locking strain parameters locking release pressure slip strain parameter slope of land subsidence difference between the surface measurement point and the lateral wall of the structure in the vertical direction of land subsidence horizontal distance between the surface measurement point and the structural side wall

one of the factors affecting the overall deformation behavior and force redistribution of the structure. Deployment of the diaphragm wall could play an adverse role in the seismic response for the complex crossstation structure in the liquefiable ground (Liu and Song, 2006; Orense et al., 2003; Zhuang et al., 2019). Therefore, it is imperative to comprehensively explore the failure mechanism of the unequal-span underground structure in liquefiable soils as well as the influence of diaphragm wall on the dynamic response of the SSI system during strong ground motions. This paper presents numerical investigation into the seismic behaviors of a large unequal-span underground subway station in liquefiable soils and the influence of diaphragm wall on seismic responses. An existing constitutive model for saturated sand is adapted and integrated into the commercial FEM software. The Arbitrary Lagrange-Euler (ALE) adaptive method that prevents the mesh distortion has been adopted to maintain high-quality of the mesh. An advanced finite-element model is then established to simulate the nonlinear static and dynamic coupling interactions between the liquefiable foundation, the diaphragm wall, and the complex subway station. The effects of the diaphragm wall on earthquake responses of the modeled system are investigated. The liquefaction and deformation characteristics of the site, the uplift, and damage characteristics of the station structure are analyzed. The revelations in this study are expected to provide insight understanding of the seismic response mechanism for the underground structure subject to soil liquefaction so as to rationalize appropriate seismic design of underground structures.

then, the seismic researches on underground structures have attracted extensive attention all over the world and have achieved many development (Chen et al., 2016b; Tsinidis, 2017; Ma et al., 2018; Miao et al., 2018). In recent years, physical and numerical studies have been conducted to estimate the seismic response of the soil-underground structure interaction (SSI) system subject to liquefaction. The dynamic responses of the site and the failure mechanism of the underground structure subject to ground liquefaction have been profoundly reported (Tamari and Towahata, 2003; Azadi and Hosseini, 2010a, b; Chian and Madabhushi, 2012; Chian et al., 2014; Hu et al., 2018). However, efforts have been biased on the analyses of simple and regular underground structures, such as circular tunnels and rectangular stations (Unutmaz, 2014; Watanabe et al., 2016). On the other hand, the seismic performance of the underground structure, which is dominated by the deformation of surrounding soils, is substantially affected by the changes in overall tectonic dimensions. Therefore, the seismic behavior of large complex cross-section underground structures remains to be further explored. With the continuous advancement of urbanization and the rapid development of rail transit system in China, a large crosssection station structure type with wide upper layer and narrow lower layer has been widely used as the typical subway station form in the development of urban underground space. Nevertheless, previous researches on this new complex station structure type are very limited. It has been derived that large unequal-span underground structures are at greater risk than traditional rectangular ones during an earthquake in soft soil (Zhuang et al., 2015; Chen et al., 2016a; Chen et al., 2018). Large deformation of soil layer and the uplift of station induced by site liquefaction will also pose a substantial threat to the seismic safety of the structure. In addition, in the design of the diaphragm wall, as the safety reserve for the seismic design of underground structures, the influence of the wall on the deformation and uplift of underground structures is ignored. It should be understood that the diaphragm wall is

2. Numerical model 2.1. Station structure and soil site Rapid development of urbanization and subway transportation have 2

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thickness of the top, middle, cantilever and bottom slab is 0.8, 0.4, 0.65 and 1.0 m, respectively. The thickness of the upper and lower sidewalls of the station is 0.6 and 0.8 m, respectively. According to the actual situation of the project, the soil mixing wall (SMW) construction method is adopted on the upper side of the structure, and a superimposed diaphragm wall is arranged on the lower side with a thickness of 0.8 m and a elevation of −30 m at the bottom. In addition, the enclosure system of the SMW construction method on the upper and lateral sides of the station is limited to the material strength, which can only exist as a temporary structure, while the diaphragm wall on the lower part of the station can exist as a permanent structure. Therefore, the seismic response of station structures with and without diaphragm walls in the liquefaction site is compared and analyzed in this paper.

raised major concerns in China since it is related to the convenience of daily life of billion’s people. In addition to meeting basic traffic operation functions, some subway stations have additional requirements, such as commercial shopping and integrated layout of underground space. The mode of combining subway station and commerce is one of the trendy development for future underground space planning. Thus, in the pursuit of continuous change of station structure section form, the subway station structure with upper width and lower narrow crosssection is increasing. In this study, a typical unequal-span subway station in Suzhou Metro Line 1 with five spans on the upper floor and three on the lower is selected as the research object. The complex subway station is made of steel reinforced concrete. The details of the concrete structure and rebar are shown in Fig. 1. The

31500 6800

5250

5250

7100

800

7100

AL1(800*1600) KZ1(700*1000)

5950

600

(300*900)

TL1(900*1900) KZ2(600*1000)

AL3(600*1500)

800

1100

1000

800

KZ3(600*1000) TL3(1000*2100) 800

-30.0m

TL2(800*1000)

6030

RC ring beam (1000*1200)

300

650

400

AL2(800*650)

AL: Angle beam TL: T-shaped beam KZ: Frame column (800*1600): The cross sectional width of the component is 800mm and the height is 1600mm. Unit: mm

(a) Details of subway station

D28@150

D25@200

D25@150 D28@150

D28@150

D32@150

D28@150

D28@150: The cross sectional diameter of the rebar is 28mm and the separation distance is 150mm.

-30.0m

(b) Details of steel reinforcement Fig. 1. Cross sectional dimensions of unequal-span subway station. 3

D28@150

D25@200

D22@150

D22@200

D25@150

D22@150

D32@150

D28@200

D28@150

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this step. Ideally, the loads and initial stresses should exactly equilibrate and produce zero deformations. However, in complex problems it may be difficult to specify initial stresses and loads that equilibrate exactly. Accordingly, the geostatic procedure only requires that the initial stresses are close to the equilibrium state or the displacements corresponding to the equilibrium state might be small enough (less than 10−5 m in this study). The static analysis results are subsequently applied to counteract the geostatic loading. Due to the short duration of an earthquake, the ground settlement should be very little during a horizontal earthquake, in that the excess pore water pressure has hardly dissipated before the end of the earthquake. However, the large ground settlement should mainly take place in a long time after a horizontal earthquake. Due to above fact, the lateral boundary of soil foundation has been approximately looked as having no vertical displacement during a horizontal earthquake. For the following dynamic analysis, the boundary conditions are modified to remove the horizontal constraint of the lateral boundary of the site while restraining the vertical displacement. The horizontal constraint of the bedrock surface is replaced by the seismic motions, shown as Fig. 3. It should be mentioned that 20 kPa extra distribution loads on the ground surface, representing the potential live load, are taken into account in both static and dynamic calculations. To reduce the effect of lateral boundary, the damping ratio of the soil elements on the lateral boundaries have been magnified to 10 times of the real damping ratio. For the dynamic contact between the soil and concrete structures, the normal direction of the contact surface is assigned as “hard” contact, which implies that the contact surface will be separated immediately when there is tension between the soil and the concrete structures. The tangential direction of contact surface obeys Coulomb’s Friction Law, so that

Large amounts of loose sands have been deposited downstream of the Yangtze river near Suzhou year after year. According to the typical geological conditions in the area, the soil layer distribution and parameters selected for the calculation model in this paper are shown in Table 1. The overburden thickness of the subway station is 3 m, and shear modulus of the fine-silty sand layer changes from 39.3 MPa to 118.2 MPa along with its increasing buried depth. 2.2. 2D modeling of soil-underground structure interaction system The commercial software Abaqus is applied for the simulation. A 2D FEM nonlinear static and dynamic coupling model with the size of 231.5 m × 60 m is developed for the soil-diaphragm wall-underground structure interaction (SWSI) system and the soil-underground structure interaction (SSI) system. In order to minimize the computing intensity, four-node plane strain-reduced integration elements are selected to model the soil foundation, the diaphragm wall, and the underground subway station. The beam elements are embedded into the model for structural concrete to simulate the rebar in it without consideration of the detachment of the bar from the concrete for simplicity. However, the internal forces of the structure have not studied in this study instead of analyzing on the dynamic stress responses of the underground structure. It is because that the local failure of the bondage between the concrete and the steel bars give rise to local stress concentration, which is not a concern for the current study, whereas it doesn’t contribute to the overall redistribution of the loads. The Arbitrary Lagrange-Euler (ALE) adaptive method is applied to prevent the mesh from excessive distortion (Nomura and Hughes, 1992; Kjellgren and Hyvärinen, 1998). According to Zhuang et al. (2015), the maximal height of element hmax in the direction of shear motion propagating in the soil is defined as

τcrip = μ·P

1 1 ⎞ Vs / fmax hmax = ⎛ − 160 ⎠ ⎝ 75

(1)

where τcrit is the maximum friction force or the shear stress limit; μ denotes the friction coefficient of the contact surface between the soil and the concrete, which is specified as 0.4 in the present study; and P represents the normal contact stress on the contact surface. When the shear stress of contact surface is greater than the maximum friction between them, tangential slippage of soil mass will occur.

where Vs is the shear and compression motion velocity, which can be calculated from G0 = ρVs2; ρ denotes the density of the soil; and fmax represents the maximal vibration frequency of the earthquake excitation. As a result, the maximum height of element hmax of the soil ranges from 1 m to 3 m. To ensure the efficiency of the numerical calculation, the soil meshes at the bottom and both sides of the underground structure are constructed with deliberation to be integrated appropriately with the mesh for the structures. The mesh size of soil in nearfield and far-field foundation is divided into 1 m × 1 m, 1 m × 2 m, 2 m × 1 m, and 2 m × 2 m, respectively, as shown in Fig. 2. The stiffness contribution of the columns inside the structure are treated as continuous walls along the longitudinal direction of the subway station. The equivalent lateral deformation stiffness EeqIeq of the continuous wall can be expressed as

Eeq Ieq = Ec Ic / D

(3)

2.3. Constitutive model for soil Some numerous constitutive models have been developed aiming to simulate the stress–strain behavior of saturated sands during cyclic loading, including generalized plasticity models (Pastor et al., 1990; Wang et al., 2014). In this study, according to Zhuang and Chen (2011), the liquefaction dynamic constitutive model of sandy soil which is developed on the basis of the constitutive model of large liquefactioninduced deformation of sand proposed by Yang and Elgamal (2002) is selected to simulate the process of soil liquefaction. In the original soil model, it is not convenient for users to yield a quadratic equation to compute the amount of translation parameter for defining the coordinates of the yield surface center in deviatoric stress subspace. Meanwhile, the internal yield surfaces were not updated persistently with each strain increment. To improve the above problems, based on the hardening rule in the memory-type nested surface constitutive model of the large soft soil deformation (Zhuang et al., 2008), the new increment calculation formula for the hardening parameters and the

(2)

where EcIc is the stiffness of a column and D stands for the column space in the longitudinal direction of the subway station (7.8 m in the present simulation). Accordingly, the equivalent elastic modulus of the concrete for the middle columns is about 3.85 × 103 MPa. In the static analysis, the bedrock surface is fixed and the lateral boundary of ground is restrained from motion except for the vertical displacement. The geostatic procedure is normally used as the first step of a geotechnical analysis, in such cases gravity loads are applied during Table 1 Distributions and parameters of the site. Soil type

Thickness/m

ρ/(kN·m−3)

G0/MPa

Elastic modulus/MPa

φ/(°)

Poisson’s ratio

Porosity

1 2 3

3.0 47.0 10.0

19.0 19.3 19.3

25.2 39.3 ∼ 118.2 120.2

5.0 7.0 7.0

16 30 20

0.30 0.30 0.35

– 0.474 –

Mucky silty clay Fine-Silty Sand (moderate solid) Clay (hard)

4

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2m×1m 60m

1m×1m 2m×2m

1m×2m 231.5m

(a) SSI system

2m×1m 60m

1m×1m 2m×2m

1m×2m 231.5m

(b) SWSI system Fig. 2. Finite-element mesh.

STEP-1 Equilibrate geostatic loading

STEP-2 Convert boundary condition

RF

STEP-3 Input acceleration

RF

Acceleration

Fig. 3. The model boundary conditions transformation settings.

center point coordinate of the yield surface on the π deviatoric stress plane in the model were derived (Zhuang et al., 2015). In this model, a Biot-type theory for solid-fluid coupled analyses was also numerically implemented (Parra, 1996). In order to amend the improficiencies in hardening parameter increment calculation and the discontinuity of hardening rule in the original model by Yang and Elgamal (2002), the hardening rules in the dynamic visco-plastic memorial nested yield surface model for soft soil

are introduced (Elgamal et al., 2002). The hardening parameters in the model and the hardening increment formula for the center point of the yield surface on the deviatoric plane are derived. The multi-yield surface concept is adopted to allow all yield surfaces to be projected in stress space by the stress point without change in form. They consecutively touch and push each other but cannot intersect. Therefore, when the loading reverses, the prior yield surface is defined as the reversed yield surface fr. In the subsequent loading 1

1

f1

n 1

f1

fi fr

F

fi

O

F

a

fr

i

O

3

3

2

2

(a) Effective principal stress space

(b) Deviatoric plane

Fig. 4. Yield surface in principal stress space and deviatoric plane (Zhuang et al., 2008). 5

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Other parameters associated with the adopted model can be determined according to Yang and Elgamal (2002), which has been corroborated by a large number of relevant experiments (Elgamal et al., 2002). To verify the modified constitutive model, it is then implemented with Fortran codes to be integrated into a sophisticated FEA software Abaqus and 3D numerical model for saturated sand is built to simulate the dynamic responses of the sand sample tested in a dynamic triaxial machine with the confining stress of 100 kPa and the magnitude of cyclic loading of 288 N (Zhuang et al., 2015). As shown in Fig. 5, the simulated axial-strain time-history curve and the stress-strain relation of the modified model are compared with the results from the physical tests under the same conditions (Zhuang and Chen, 2011; Zhuang et al., 2015). The material parameters for the sand are shown in Table 2. In the present simulation, the non-liquefiable soils are modeled by the dynamic visco-plastic memorial nested yield surface model of soft soil proposed by Zhuang et al. (2008). It can simulate the dynamic accumulation of deformation and the hysteretic behavior of soils under irregular cyclic loadings effectively. It is worth mentioning that this constitutive model has been verified in various numerical nonlinear seismic simulations, such as for free field and soil-structure interaction systems, to reflect well the stress-strain behavior of the soft soils, and thus, has extensive application. Elaboration on the dynamic viscoplastic constitutive model can be referred to Zhuang et al. (2008).

process, all active yield surfaces fi are then tangent with the reversed yield surface at the reversed stress point, and their centers in the deviatoric stress subspace change along the direction θ defined from the center of the reversed yield surface to the reversed stress point, as shown in Fig. 4 (Zhuang et al., 2008). The increment of model hardening parameters M and α of the active yield surface is given as

dM t + Δt =

3(s − pa α ): ds +

6 M·dp ·(s − pa α ): θ + 2J '·M·dp

6 M·dp ·(s − pa α ): θ + 2J '·M·pa

t

2 (M t ·dp + pa ·dM t + Δt ): θ − dp ·α t 3

dM t + Δt =

(4)

(5)

whereas

3 (s − pa α ): (s − pa α ) 2

J' =

(6)

Thus, the elastoplastic tangent modulus H under cyclic loading can be expressed as

H = 2G (1 −

r 2 ) rmax

(7)

where r and rmax are the radii of the active yield surface and the corresponding damage surface in the deviatoric stress plane, respectively; and G stands for the initial shear modulus, which is defined as

G = G0 (

pa p0 − a

)n

2.4. Constitutive model for concrete (8) To simulate the mechanical behavior and crack damage of concrete by FEA software, the concrete viscoplastic dynamic damage model proposed by Lee and Fenves (1998) is adopted for concrete. Based on the fracture energy principle of concrete, this model is modified based on the plastic damage model by Lubliner et al. (1989), in which several hardening variables are adopted to modify the yield function. Two damage variables dt and dc, which define the stiffness attenuation law of concrete under tension and compression, are adopted. It should been explained here that the tensile fractures have appeared on the surface of concrete structure when the tensile damage factor (DAMAGET) dt > 0 and the concrete has been damaged completely by the tensile stress after dt > 1. To the compress damage, the concrete should be damaged after the compress damage factor (DAMAGEC) dc > 0 and cracked after dc ⩾ 1. The grade of concrete used in the present underground structure is No. C30, and its material properties are shown in Table 3. The two dynamic damage parameters of concrete are shown in Table 4 and Table 5, respectively. The steel rebar is assumed to be elastic material, which elastic modulus is 210 GPa.

whereas G0 represents the shear modulus measured at the reference confine pressure p0 (p0 = 100 kPa in this study); n denotes the material parameter measured by experiment (n = 0.5 in the current simulation); and p represents the normal contact stress on the contact surface. Therefore, the elastoplastic tangent modulus H under cyclic loading can be rewritten as

H = 2G (1 −

M 2 ) Mmax

(9)

wherein Mmax is the model parameter for the damaged surface F that corresponds to the active yield surface, which can be calculated as

Mmax =

6sinφ 3 − sinφ

(10)

The plastic modulus H' can then be derived as −1

1 1 ⎞ H′ = ⎛ − 2G0 ⎠ ⎝H

⎟

Fd

(11)

Fs 90

0.06

Rigid body

By developed model

ıc

Soil sample

ıc

Axial strain

0.04

Axial stress /kPa

⎜

By test

0.02

0 -0.02

-0.06 0

(a) Soil sample model

30 0

-30 -60

-0.04

Fixed rigid base

By developed model By test

60

5

Time/s

10

15

(b) Axial-strain time history

-90 -0.08

-0.04

0.04

(c) Strain–stress curve

Fig. 5. Comparison of FEM results with test results (Zhuang et al., 2015). 6

0 Axial strain

0.08

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Table 2 Material parameters in constitutive relationship for sand. Material parameters

Value

Material parameters

Value

Reference shear modulus Reference mean pressure Pressure dependence exponent Friction angle Phase transformation angle Residual strength pressure

G0 = 33 MPa p0 = 100 kPa np = 0.5 ϕ = 31.6° ϕpt = 31.6° a = 5 kPa

Contraction parameters Hardening parameters Dilation parameters Locking strain parameters Locking release pressure Slip strain parameter

c1 = 0.12, c2 = 0 e1 = 0.8, e2 = 2.8 d1 = 0.5, d2 = 0 y1 = 0.015, y2 = 0 py = 0.5 kPa ysl = 0.01

structure in liquefiable ground (An et al., 2017). On the other hand, the above findings are at odds with the reported results for a two-story and three-span subway station with rectangular frame (Zhuang et al., 2016), which shows that the ground near the subway station is liable to liquefaction. The reason could be that the overload of 20 kPa on the ground surface. The ground static loading may have an unexpected effect on the liquefaction distribution of the site, which agrees with the reported findings by numerical analysis for seismic responses and flowslip characteristics of a slightly inclined liquefiable site (Wang et al., 2018). When the diaphragm wall is present in the SWSI system, unliquefied soil is observed in the area near the upper side wall and the middle plate elevation of the station structure in the immediate vicinity of the diaphragm wall. In general, the foundation liquefaction area, in spite of the structural configurations, expands with the increase of the earthquake intensity. The foundation liquefaction range of the lateral side of the lower side wall of the structure in the SWSI system is larger than that of the SSI system without diaphragm wall. In addition, significant liquefaction has been detected in the soil beneath structural floor and cantilever middle plate. The liquefaction area of soil beneath the cantilever plate in SSI model is limited to the height of the lower layer of the station. On the other hand, the depth of soil liquefaction under the substrate is considerable and gradually deepens with the increase of the PGA input. When subject to the Kobe motions of 0.1 g, 0.2 g and 0.3 g, the maximum depth of soil liquefaction is 26.82 m, 30.01 m, and 35.16 m, respectively, which is much higher than the standard depth of 20 m specified as the non-liquefaction vault value in Chinese design codes. The diaphragm wall promotes the spread of the soil liquefaction under structural slabs. In particular, the soil between the diaphragm walls is completely liquefied. When subject to the Kobe motions of 0.1 g, 0.2 g and 0.3 g, the maximal depth of the liquefied area is 32.15 m, 33.08 m, and 33.96 m, respectively. The deeper liquefaction at the bottom of the subway station is considered to be attributed to the effects of the diaphragm wall. It can be interpreted as that the diaphragm wall cuts off the passage for the pore water pressure linking between the bottom and the lateral soil of the structure extension of the liquefaction range between the walls (Liu and Song, 2006). In both the aforementioned earthquake cases, significant liquefaction is observed in depth of the soil beneath the structure. The reasons could be that the cross-sectional dimension of the new type unequalspan subway station is in phenomenal scale, even slight uplift of the soil beneath the structure by soil excavation leads to material increase of the EPWP ratio in this area. The subway station is uplifted by soil liquefaction in the shallow layer below the bottom of the structure, which again further promotes the liquefaction of the deep soil. The mutual strengthening interaction between the two results under seismic

2.5. Earthquake motion In this study, El-Centro motion, Kobe motion, and Nanjing artificial earthquake motion are selected as ground excitation in horizontal direction of the bedrock. Since the El-centro motion recorded in the 1940 Imperial Valley earthquake is widely used in engineering seismic analysis with an original peak ground acceleration (PGA) of 0.349 g and the main vibration duration is about 26 s, its simulated results are taken as a reference. The Kobe motion recorded in the 1995 Kobe earthquake is a representative near-field bedrock earthquake tremor. Its west-eastern component contains an original PGA of 0.85 g with the main frequency of the vibration lies in the range approximately from 0.5 Hz to 4.0 Hz. The Nanjing motion is a local bedrock seismic record, which is calculated by the COMPSYN software that developed by Institute of Engineering Mechanics (IEM), China Earthquake Administration. Its original PGA is 0.15 g and the main vibration duration is approximately 22 s. When the ground motions are applied to the bedrock, the duration is determined to be 40 s and the PGAs are adjusted to be 0.1 g, 0.2 g, and 0.3 g, respectively. The accelerograms and the normalized acceleration response spectra for the specified earthquake motions with PGA = 0.1 g are shown in Fig. 6. 3. Results and analyses 3.1. Site liquefaction distribution As shown in Fig. 7, the stress-strain response of soil near the underground structure has been presented. It can be stated that the expansion of saturated sand is obvious during the loading stage and a large change in shear strain with minimal change in shear stress in the vicinity of phase transformation. In order to demonstrate the influence of the diaphragm wall on liquefaction distribution of the ground around the large complex subway station during and after the earthquake, the liquefaction characteristics of soil in different interaction systems subject to Kobe motions are derived and shown in Fig. 8. The excess pore water pressure (EPWP) ratio, which was calculated from the pore pressure divided by the effective self-weight stress of the soil. When the value of EPWP ratio is greater than 1.0, the soil is considered to have been liquefied. When the effects of the diaphragm wall are ignored, the surrounding soils are affected by the subway structure prominently, which results in anti-liquefaction function for the adjacent site soils and no obvious liquefaction occurs. Underground structures can restrain the liquefaction of surrounding soil, which agrees with the findings by a shaking table test of the seismic response of a shield-enlarge-dig type subway Table 3 Material parameters for concrete No. C30. Material parameters Elastic modulus Poisson’s ratio Density Dilation angle Initial compressive yield stress

Value 4

E0 = 3.0 × 10 MPa ν = 0.2 ρ = 2450 kg/m3 ψ = 36.31° σc0 = 13 MPa

7

Material parameters

Value

Limited compressive yield stress Initial tensile yield stress Compression stiffness recovery parameter Tensile stiffness recovery parameter Damage variables

σcu = 20.1 MPa σt0 = 2.4 MPa ωc = 1.0 ωt = 0.0 dc (Table 4), dt (Table 5)

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Table 4 Relationship of compression stress and damage factor versus plastic strain. Plastic strain/%

0.0

0.04

0.08

0.12

0.16

0.20

0.24

0.36

0.50

0.75

1.00

Compressive stress/MPa dc

14.64 0.0

17.33 0.113

19.44 0.246

20.10 0.341

20.18 0.427

18.72 0.501

17.25 0.566

12.86 0.714

8.66 0.824

6.25 0.922

3.98 0.969

pressure of soil; and σ'v is the initial effective vertical stress of the soil. The reason could be that in the static and dynamic coupling analysis model, the initial average effective stress of the soil around the structure is reduced due to the uplift of the structure. The EPWP under the seismic load could exceed the effective confining pressure value of the soil, which has also been reported in a large-scale shaking table model test for the seismic performance on a three-arch type subway station (Chen et al., 2015). For the SWSI model, the EPWP ratio steeps up sharply within a range of 5 m laterally across the lower portion of the unequal-span subway station.

loading finally results in the increase of soil liquefaction depth (Zhou et al., 2015). The remarkable uplift of the station structure is indirectly confirmed by the negative pore water pressure in the soil layer under the structural bottom plate and the middle plate of cantilever. On the other hand, the range of liquefaction in this area does not change substantially with the increase of the seismic intensity. These new findings indicate that the diaphragm wall have an significant influence on the liquefaction distribution of the site around the unequal-span subway station, which may not be negligible in the design of complex underground structures against earthquakes. Fig. 9 shows the EPWP ratio for the three simulated earthquake motions with the input PGA = 0.2 g. From the perspective of the overall liquefaction depth and scope of the far-field foundation, soil liquefaction depth is shallow subject to Nanjing motion, medium by Kobe motion, and maximum when El-centro motion is the excitation. It is interpreted that the frequency spectrum of the input ground motion instead of the strength of the ground motion has significant impact on the liquefaction state and distribution of the soil foundation. To further explore the response of underground structure systems on the liquefaction state of the site subject to earthquake, Fig. 10 shows time-history curves of the EPWP ratio of soil at the same elevation on both sides of the structure in different interaction models for the input PGA = 0.2 g. In general, the EPWP ratio of soil near the subway station is relatively low, and commensurately, the growth rate is low. The EPWP ratio of the soil increases with the increasing horizontal distance from the structural side wall. Compared to the lateral soils in the lower layer of the subway stations, the dynamic EPWP ratio of the topside soil around the structure for the SSI model is consistent with the simulated results from the SWSI model. On the other hand, the EPWP ratio of the surrounding soil in the lower layer of the structure increases first and then decreases with the increasing horizontal distance from the side wall. The liquefied range of soil reaches 5 m horizontally from the lower side wall of the structure. The EPWP ratio of soil decreases smoothly along the horizontal distance from 5 m to 10 m until that it increases again gradually with the increase distance. The soil at 25 m is liquefied subject to the El-centro motion, whereas it approaches liquefaction by Kobe and Nanjing excitations. From analysis of the results, it can be said that the EPWP ratio distribution subject to different earthquake motions applied in this study is slightly different but similar in principle. Fig. 11 shows the contour diagrams of the EPWP ratio in different systems subject to the Kobe motion with PGA = 0.2 g. It can be stated that the development of the EPWP ratio throughout the entire site can be clearly demonstrated that shallow soils are more likely to liquefy than deep soils. For the SWSI system, the EPWP ratio fields around the subway station are more complex than that in the SSI system. The dynamic EPWP ratio of some measurement points exceeds 1.0, which may be attributed to the calculation method, i.e.,

ru = EPP / σv'

3.2. Displacement of site The deformation of the soil foundation around the subway station for different structural models are then derived and analyzed. The final displacement vector and vertical displacement under the Kobe motion with PGA = 0.3 g are shown in Fig. 12 by using the same measurement scale. For the SSI model, the soil on both sides of the structure below the subway station collapse gradually as soon as the soil layer below the structure is liquefied, which further aggravates the uplift of the underground structure, as shown in Fig. 12(a). The uplifting mechanism by the liquefied soil around the large-scale underground structure is consistent with reported observation from shallow buried tunnels (Azadi and Hosseini, 2010a, 2010b; Chou et al., 2011). Specifically, the tectonic features of the upper protrusion and lower indent of the large unequal-span subway station are very apt to the surrounding soil towards the bottom of the structure. And the uplift region demonstrates approximately a triangular distribution. In addition, the structural system in the SWSI model tends to float upward, whereas its peak uplift displacement of subway station with diaphragm walls and the seismic subsidence of site on both sides are substantially smaller than those without walls, as shown in Fig. 12(b). According to the subsidence calculation and the vector displacement of the site, the path of the surrounding liquefied soil flowing to the bottom of the subway station is blocked by the diaphragm wall so as to reduce significantly the range and size of the surface seismic subsidence area (Liu and Song, 2006). When the input PGA of the Kobe motion are 0.1 g, 0.2 g, and 0.3 g in the SSI system, the respective distribution of the seismic subsidence area on ground surface ranges from 5 m to 16 m, 7–22 m, and 9–27 m, and the corresponding maximum values are 6.06 cm, 14.98 cm, and 30.48 cm. On the other hand, the range and the maximum seismic subsidence on ground surface in the SWSI system are approximately 6–15 m and 15.99 cm respectively, which means that the peak decrease drops as high as 47.52% under the simulated calculations of PGA = 0.3 g. In other words, the diaphragm wall can reduce the liquefaction-induced seismic subsidence of the site significantly subject to strong earthquake excitations. To further demonstrate the vertical displacement of the ground surface in various models, time-histories of the maximum settlement point and the structural uplifting-induced ground swell under Kobe motions are shown in Fig. 13. It can be seen from the vertical

(12)

where ru stands for the EPWP ratio; EPP is the excessive pore Table 5 Relationship of tensile stress and damage factor versus cracking displacement. Cracking displacement/mm

0.0

0.066

0.123

0.173

0.220

0.308

0.351

0.394

0.438

0.482

Tensile stress/MPa dt

2.4 0.0

1.617 0.381

1.084 0.617

0.726 0.763

0.487 0.853

0.219 0.944

0.147 0.965

0.098 0.978

0.066 0.987

0.042 0.992

8

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0.12

0.4

Acceleration /g

Response acceleration /g

El-Centro

0.08 0.04 0.00 -0.04 -0.08 -0.12

0

5

10

15

20 25 Time /s

30

35

El-Centro 0.3 0.2 0.1 0.0 1E-02

40

1E-01

Period /s

1E+00

1E+01

(a) El-Centro motion 0.4

0.12

Acceleration /g

Response acceleration /g

Kobe

0.08 0.04 0.00 -0.04 -0.08 -0.12

0

5

10

15

20 25 Time /s

30

35

Kobe 0.3 0.2 0.1 0.0 1E-02

40

1E-01

Period /s

1E+00

1E+01

(b) Kobe motion 0.12

0.4

Acceleration /g

Response acceleration /g

Nanjing

0.08 0.04 0.00 -0.04 -0.08 -0.12

0

5

10

15

20 25 Time /s

30

35

Nanjing 0.3 0.2 0.1 0.0 1E-02

40

1E-01

Period /s

1E+00

1E+01

(c) Nanjing motion Fig. 6. Acceleration time-history curves and its elastic response spectra (5% damping) of seismic motions with PGA = 0.1 g.

80

Shear stress /kPa

60 40 20 0 -20 -40 -60 -80 -0.03

0.00

0.03

0.06 0.09 Shear strain

0.12

0.15

80

Shear stress /kPa

60 40 20 0 -20 -40 -60 -80 -0.02

Fig. 7. Stress-strain curves of liquefied soil elements subject to Kobe motion. 9

0.00

0.02 Shear strain

0.04

0.06

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EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model model

SWSI (a) PGA=0.1g

EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model model

SWSI (b) PGA=0.2g

EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model model

SWSI (c) PGA=0.3g Fig. 8. Distributions of EPWP ratio subject to Kobe motions.

motion and Kobe motion are similarly minimal, while the value from El-centro motion is more pronounced. When the horizontal distance from the structural side wall reaches 60 m and beyond in the SSI model, the impact of different earthquake motions on the vertical settlement of the ground surface is similar. It implies that the influence of the complex subway station on the development of lateral ground seismic subsidence is approximately limited to the range within twice the maximum width of the structure. It is observed that the scope of influence in the SWSI model is approximately limited to 35 m around the structure, which is helpful to regulate the codes for design of roads and adjacent buildings above the ground to avert the influence. The effects of vertical displacement on adjacent structures above the ground for different structural models are then analyzed by the slope of land subsidence i in the present study, i.e.,

displacement time-history that the maximum value of the seismic subsidence on both sides of the upper uplift area and the seismic swell above the structure increase with the increment of seismic intensity. Meanwhile, the overall tendency of the vertical displacement development process of the surface in the two model systems is generally consistent, whereas the difference of the displacement magnitude is remarkable. Specifically, the settlement curve crawling upwards in the time interval from 0 s to 5 s, while it steeps up from 5 s until 15 s. The advance of the settlement slows down slightly since 15 s until it stabilizes at 20 s. This observation is also true for uplift curves on ground surface. The development process of vertical displacement time-history is slightly delayed compared to that of the EPWP of the site, which indicates that the seismic subsidence and structural uplifting-induced swell of the ground are attributed mainly to the movement of surrounding soils towards the bottom of the subway station. Fig. 14 shows the final settlement curves of the ground surface subject to different earthquake excitations. Generally, the frequency characteristics of the input seismic motions have a significant impact on the field seismic subsidence. Amongst, the results from both Nanjing

i = h/l

(13)

where h is the difference between the surface measurement point and the lateral wall of the structure in the vertical direction of land subsidence; and l represents the horizontal distance between the surface 10

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EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model

SWSI model (a) El-Centro motion

EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model

SWSI model (b) Kobe motion

EPWP ratio

EPWP ratio

(Avg: 75%)

(Avg: 75%)

SSI model model

SWSI (c) Nanjing motion

Fig. 9. Distributions of EPWP ratio subject to different earthquakes with PGA = 0.2 g.

Compared to the counterparts from current calculation, the seismic subsidence of the lateral soil of the traditional two-story and three-span rectangular subway station is relatively small against that in the complex underground subway structure. where Sunequal-span is the peak seismic subsidence of the lateral foundation in the present study; and Srectangle is the peak seismic subsidence of the lateral foundation of a typical two-story and three-span subway station from Zhuang et al. (2015). As a result, when the Kobe motion of 0.1 g, 0.2 g, and 0.3 g is the excitation, the peak seismic subsidence of the lateral foundation in the present study increased by 67.87%, 157.39%, and 11.53%, respectively.

measurement point and the structural side wall. Thus, slope curves of land subsidence subject to Kobe motions are shown in Fig. 15. When the surface subsidence slope limit is assumed to be ± 1%, the seismic vertical displacement of the ground has little effects on adjacent infrastructures in Kobe motion with input PGA = 0.1 g. At an input PGA of 0.2 g, the station structure in the SSI model has an influence range of 20 m on the lateral surface buildings, while the size of the SWSI model is basically controlled within 5 m. When the input PGA continues to increase from 0.2 g to 0.3 g, the influence scopes of the SSI system and the SWSI system are expanded to 36.5 m and 21 m respectively. That is to say, the diaphragm wall is of great significance to reduce the influence on roads and adjacent building structures above the ground. The seismic subsidence of the lateral foundation for different type subway stations in liquefaction site is shown in Table 6. When the diaphragm wall isn’t present, according to Zhuang et al. (2015), it can be known that not only the vertical displacement of the ground is affected remarkably by the large-scale unequal-span subway station, but also the fluctuation range of the final settlement curve is more obvious.

3.3. Uplift feature of subway station During the earthquake, the site liquefaction occur simultaneously with the underground structural uplift. The flowing feature of the large complex subway station is more obvious than that of traditional rectangular station structure due to the prominent liquefaction of soil beneath the structure. Fig. 16 shows the uplift responses of the cross11

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Fig. 10. Time-history curves of EPWP ratio at lateral ground of underground structure subject to different earthquakes with PGA = 0.2 g.

of the station, and the distribution is featured by large buoyancy across the middle span and relatively small buoyancy across the cantilever span. The difference in the uplifting in the SWSI model is less conspicuous than those recorded in the SSI model due to the effects of diaphragm wall. From Fig. 16(c), the difference in the uplifting features persists even in small earthquakes, and the special uplifting feature does not change clearly with the increasing seismic excitation intensity. This new finding, which has not been obtained in previous studies on the traditional rectangular frame subway stations, should be helpful for appropriate design against ground liquefaction of large complex underground structures and the internal forces of structural cantilever spans. The currently simulated structural uplift time-histories are consistent with those from the field measurements of seismic subsidence, which indicates that the earthquake-induced uplift of the structure is primarily caused by the movement of the lateral liquefied soils (Chou

section station structure subject to Kobe motions to reveal the uplift characteristics of the liquefaction field for such subway stations. It is derived that the uplift of the underground structure increases with the increasing bedrock input PGA, and the liquefaction-induced uplift of the subway station in the SWSI model is significantly smaller than that in the SSI model, as shown in Fig. 16(a). From Fig. 16(b) and (c), differences in uplift between different spans of the large-scale unequalspan subway station are detected. Amongst, the uplift of the middle span is the largest, while the rotation of other positions gradually decreases with the increase of horizontal distance from the center point, and thus the uplift is minimized at the cantilever span. The reason for the difference in uplift should lie in the small liquefaction area of the soil layer under the structural cantilever plate and the large liquefaction depth under the bottom plate. Meanwhile, the unequal span of the structure leads to the difference in buoyancy in the transverse direction

12

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EPWP ratio (Avg: 75%)

(a) SSI system

EPWP ratio (Avg: 75%)

(b) SWSI system Fig. 11. Contour diagrams of EPWP ratio subject to Kobe motions with PGA = 0.2 g.

et al., 2011).

foundation, it is observed that the diaphragm wall also changes the anti-lateral stiffness of the structure with further analysis of the simulated deformation (Zhuang et al., 2019). Fig. 17 presents the horizontal relative displacement time-history of the lateral wall along the structural height corresponding to the maximum horizontal swing difference

3.4. Lateral deformation of underground structure While promoting the liquefaction extension of the surrounding

(a) SSI system

(b) SWSI system Fig. 12. Vertical displacements and displacement vectors subject to Kobe motions with PGA = 0.3 g. 13

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0.00

40 (-12.89%) 57.28mm (-38.79%)

-0.10 -0.15 -0.20

144.83mm (-47.52%)

Kobe-0.1g(SSI) Kobe-0.2g(SSI) Kobe-0.3g(SSI) Kobe-0.1g(SWSI) Kobe-0.2g(SWSI) Kobe-0.3g(SWSI)

-0.25 -0.30 -0.35 0

5

10

Vertical displacement /cm

Vertical displacement /m

-0.05

-0.40

Kobe0.1g(SSI) Kobe0.2g(SSI) Kobe0.3g(SSI) Kobe0.1g(SWSI) Kobe0.2g(SWSI) Kobe0.3g(SWSI)

7.82mm

15 Time /s

20

25

30

20

10

0

30

207.03mm (-57.97%)

80.08mm 8.84mm (-67.86%) (-54.01%) 0

5

(a) Settlement time-history

10

15 Time /s

20

25

30

(b) Uplift time-history

Fig. 13. Time-history curves of vertical displacement on ground surface subject to Kobe motions.

1

between the top slab and the bottom slab of the main subway-station structure. When the Kobe motion is the excitation, the lateral displacement of the subway station in the two models are strikingly different. The left swing amplitude of station structure in the SSI system is larger than that in the right, whereas the station structure in the SWSI system demonstrates the opposite. In addition, the horizontal relative displacement curves of subway station demonstrate wavy ε-shape when the diaphragm wall is not present. On the other hand, when the diaphragm wall is in position, the curves of the structural lower layer and upper layer are approximately linear. It could be attributed to the diaphragm wall’s contribution to the lateral stiffness since it overlaps partly with the side walls of the subway station to strengthen it. Therefore, the deformation of the joints between the bottom slap and the side wall is mainly sustained by the floor, resulting in an approximately linear horizontal relative displacement curves. Fig. 18 shows the relative interlayer horizontal displacement (IHD) time histories between different floors of the subway station. The relative IHD curves between the upper and lower layers is consistent with the overall deformation tendency, whereas the peak value of the lower layer is slightly higher than that in the upper layer. When the diaphragm wall is installed, the relative IHD responses are significantly higher than the counterpart without walls, which is conforming to the result in Fig. 17. When the PGA is 0.3 g, the interlayer displacement angle (IDA) between the upper and lower layers of the SWSI model structure is 1/231 and 1/222 respectively, which exceeds the 1/250 elastoplastic limit specified in section 7.7.2 of the Code for Seismic Design of Urban Rail Transit Structures (GB 50909-2014) in China. Serious damages are considered to be identified. The reason could be related to the degree of liquefaction of surrounding soils. The lateral foundation liquefaction level of station structure in the SWSI system is

Slope of land subsidence /%

0

-3

Kobe-0.1g(SSI) Kobe-0.2g(SSI) Kobe-0.3g(SSI) Kobe-0.1g(SWSI) Kobe-0.2g(SWSI) Kobe-0.3g(SWSI)

-4 -5

-7

0

10 20 30 40 50 Horizontal distance to the upper side wall /m

Table 6 Settlement of ground surface for different subway stations subject to Kobe motions. Case

Peak vertical displacement on ground surface/cm

Sunequal-span Srectangle

PGA = 0.1 g

PGA = 0.2 g

PGA = 0.3 g

6.06 3.61

14.98 5.82

30.47 27.32

0.6 El-Centro Kobe Nanjing

0.4 0.2

Settlement /m

0.2 0.0 -0.2 -0.4

0.0 -0.2 -0.4

0

10

20

30

40

50

60

Fig. 15. Slope curves of land subsidence subject to Kobe motions.

El-Centro Kobe Nanjing

0.4

Settlement /m

-2

-6

0.6

-0.6

-1

-0.6

60

Horizontal distance to the upper side wall /m

0

10

20

30

40

50

Horizontal distance to the upper side wall /m

(b) SWSI system

(a) SSI system

Fig. 14. Final settlement curves of ground surface subject to different earthquakes with PGA = 0.2 g. 14

60

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Vertical displacement /cm

40 30

Kobe-0.1g(SWSI) Kobe-0.2g(SWSI) Kobe-0.3g(SWSI)

Kobe-0.1g(SSI) Kobe-0.2g(SSI) Kobe-0.3g(SSI)

20 10 0 -10

0

4

8

12 16 20 Horizontal distance /m

24

28

32

(a) Uplifting curves of structural roof

(b) Dynamic deformation shape of subway station in the SSI model amplified by 50 times

Vertical displacement /cm

40

Kobe-0.3g

A B C D

30

20 Kobe-0.2g 10 Kobe-0.1g 0 -5

0

5

10

15 Time /s

20

25

30

(c) Uplifting time-histories of structural roof in the SSI model Fig. 16. Uplifting responses of subway station subject to Kobe motions.

deformation. In realization of the adverse effects of the diaphragm wall on the subway station, especially for such large and complex underground structures, design and installation of the diaphragm wall should be more appropriately rationalized.

significantly higher than that in the SSI system, resulting in more serious weakening of soil strength and larger relative IHD responses of subway station consequently. Analysis of the results reveals that, for the SSI model, the subway station will be damaged due to large horizontal deformation in spite of low degree of site liquefaction (PGA ≤ 0.2 g), whereas the seismic damage of the structure will be mainly attributed to the considerable uplift when the degree of liquefaction is further increased (PGA = 0.3 g). For the SWSI model, although the diaphragm wall restrains the uplift of the overall structure effectively, the failure of the main structure of the station is dominated by the large horizontal shear

3.5. Acceleration of subway station Fig. 19 shows the peak acceleration of the subway station subject to different ground motions. From Fig. 19(a), the peak acceleration of the structure increases with the increment of the bedrock PGA, which conforms to the general understanding. For the SSI system, when the 15

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14

12

12

10

10

Kobe-0.1g(SSI) Kobe-0.2g(SSI) Kobe-0.3g(SSI) Kobe-0.1g(SWSI) Kobe-0.2g(SWSI) Kobe-0.3g(SWSI) -0.06

-0.05

-0.04

6 4 2

Hight of structure /m

8

Hight of structure /m

14

0

-0.03

-0.02

-0.01

8 Kobe-0.1g(SSI) Kobe-0.2g(SSI) Kobe-0.3g(SSI) Kobe-0.1g(SWSI) Kobe-0.2g(SWSI) Kobe-0.3g(SWSI)

6 4 2 0

0.00

0.00

Horizontal relative displacement of the side wall /m

0.01

0.02

0.03

0.04

0.05

0.06

Horizontal relative displacement of the side wall /m

(a) Swing to left

(b) Swing to right

Fig. 17. Horizontal relative displacements of structural side wall subject to Kobe motions.

the time period from 0.1 s to 2.5 s and the peak value is reached in the time interval of 0.4–0.5 s or 0.8–0.9 s with the input of PGA = 0.1 g. When the input PGA is increased to 0.2 g and 0.3 g, the amplification range of the top plate acceleration response does not change much. On the other hand, when the diaphragm wall isn’t present, the increasing rate of acceleration of the middle plate and the bottom plate are very high in the time period from 0.01 s to 0.08 s, especially with high seismic intensity. This phenomenon has also been observed for the twostory and three-span subway station buried in liquefiable soils with slight ground surface inclination (Wang et al., 2018), which should be mainly attributed to the liquefaction-induced softening.

bedrock PGA = 0.1 g, the peak acceleration of the structure increases along with the increasing height of the subway station constantly. When the input PGA increases to 0.2 g and 0.3 g, the acceleration decreases first and then increases along with the increasing structural height. This observation is also true for El-centro motion and Nanjing motion. On the other hand, for the SWSI model under Kobe motion, the peak acceleration of the subway station increases linearly with the increasing structural height. Compared to the peak acceleration of the structural slab in groundless wall working condition, the peak acceleration of the bottom plate with the diaphragm wall is relatively smaller. Thus, the peak acceleration of the middle plate and the top plate for the SWSI system is smaller than that of the SSI model only at PGA = 0.1 g. When the input PGA are 0.2 g and 0.3 g, the peak accelerations of the middle plate and the top plate of the SWSI model are more prominent. It can be stated that the frequency contents rather than the magnitude of the seismic motion has great influence on the peak acceleration of the subway station, as shown in Fig. 19(b). To further demonstrate the effects of the diaphragm wall on the acceleration responses of the metro station, elastic response acceleration spectra of slabs under Kobe motions are given with a damping ratio of 5% in Fig. 20. Generally, the response accelerations are magnified in

3.6. Damage of subway station and diaphragm wall To assess the damage of the complex subway station, the compression and tensile damage of the subway station under different models subject to Kobe motions is recorded as shown in Fig. 21. Parameters DAMAGEC and DAMAGET in the figure represent the degree of compression damage and tensile damage of the concrete structure respectively. When the parameter value reaches 1.0, it is considered that the concrete is completely damaged.

Fig. 18. Relative IHD responses of subway station subject to Kobe motions. 16

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14

A1

Hight of structure /m

12 10 8 A2 6

Kobe-0.1(SSI) Kobe-0.2(SSI) Kobe-0.3(SSI) Kobe-0.1(SWSI) Kobe-0.2(SWSI) Kobe-0.3(SWSI)

4 2 0 0.0

A3 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Peak accleration of the subway station /(m·s-2)

(a) Kobe motion 14

A1

12

12

10

10

Hight of structure /m

Hight of structure /m

14

8 A2 6 El-Centro(SSI) Kobe(SSI) Nanjing(SSI)

4 2 0 0.0

1.0

1.5

2.0

2.5

3.0

3.5

8 A2 6 El-Centro(SWSI) Kobe(SWSI) Nanjing(SWSI)

4 2

A3 0.5

A1

0 0.0

4.0

Peak accleration of the subway station /(m·s-2)

A3 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Peak accleration of the subway station /(m·s-2)

(b) Different earthquakes with PGA=0.2g Fig. 19. Peak accelerations for slabs of subway station subject to different earthquakes.

sustains severe tensile damage at the cross-sections where the diaphragm wall intersects the bottom slab, the range below the bottom plate as well as adjacent the lower side walls. The tensile damage of the subway station in El-centro motion is more remarkable than that in Kobe and Nanjing motion. The reason is that the diaphragm wall produces different degrees of stress concentration where the stiffness changes in different earthquake excitation, which has also been found on the two-story and three-span subway station buried in soft soils (Zhuang et al., 2019). It should be noted that the penetrating damage by the diaphragm wall in the intersection with the structural bottom plate may ensue the wall to break along the cross section and thus reduce the anti-uplifting capacity of the structure during strong earthquakes. More research is desired to explore on this aspect.

On the whole, the compression damage of station structure in the SWSI model is severer than that of the subway station in the SSI model. Although the compression damage at the end of the column increase with the increasing input PGA, the overall compression damage of the underground structure is insignificant. On the other hand, the tensile damage of the unequal-span subway station is very prominent, especially for the components of the cantilever span. Besides, tensile damage is observed at the bottom ends of the lower side wall and both ends of the upper side wall in the SSI model. Generally, severe tensile damage at the cantilever span is observed even in low earthquake motion (PGA = 0.1 g) and increase dramatically with the increasing seismic intensity. When the input PGA increases to 0.3 g, the tensile damage at the cantilever span penetrates the whole cross-sections and to break it, which should be attributed to the uneven liquefaction-induced uplift. In addition, the tensile damage diagrams of the subway station are affected significantly by the diaphragm wall. It is found that damages, when the diaphragm walls are installed, at the cross-sections of the top slab in the cantilever span, the ends of the middle slab in the cantilever span, and the both ends of the side walls, are greatly alleviated, while damages at the two ends of the columns and the two ends of the bottom slab are intensified. On one hand, the anti-lateral stiffness of the lower layer of the structure is distinctly enhanced, which leads to the deformation of the joint between the bottom slap and the side wall is mainly borne by the bottom plate. On the other hand, as the diaphragm wall reduces the overall uplift and uneven uplift of the structure, the components of cantilever span in the upper layer of the subway station are less damaged by tension. These findings show that the seismic damage mechanism and internal force distribution of the subway station will be modulated by the diaphragm wall. Fig. 22 shows the tensile damage of the diaphragm wall subject to there selected motions with PGA = 0.3 g. The diaphragm wall mainly

4. Discussions and conclusions In this paper, the effects of diaphragm wall on seismic responses of a large unequal-span underground subway station in liquefiable soils subject to strong earthquake excitations have been explored with a sophisticated commercial FEM software Abaqus. A revised constitutive model for sand and the Arbitrary Lagrange-Euler (ALE) adaptive method to maintain high-quality mesh by rectifying mesh distortion are adopted to implement the nonlinear static and dynamic coupling finiteelement simulation. From the simulation, the liquefaction and deformation distributions of the site, the uplift and damage characteristics of the station structure are derived. Conclusions are drawn as follows: (1) Underground structures restrain the liquefaction of lateral surrounding soils subject to earthquake excitation. Meanwhile, the ground static loading may have an unexpected effect on the liquefaction distribution of the site. Substantial liquefaction occurs in the 17

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Fig. 20. Elastic response spectra (5% damping) of subway station subject to Kobe motions.

soil beneath structural floor and the cantilever middle plate. The diaphragm wall cuts off the passage for the pore water pressure linking between the bottom and the lateral soil of the structure extension of the liquefaction range between the walls. (2) The tectonic features of the upper protrusion and lower indent of the large unequal-span subway station are more favorable for the surrounding soil to move to the bottom of the structure, resulting in an approximately triangular distribution of the uplift region of the model. It should also be mentioned that the range and maximum value of the field seismic subsidence area on both sides of the upper uplift area increase with the increasing seismic intensity. The path of the surrounding liquefied soil flowing to the bottom of the subway station is blocked by the diaphragm wall, and thus, the liquefaction-induced seismic subsidence of the site are significantly reduced subject to strong earthquake excitations, which is helpful to reduce the seismic damages of the roads and ground buildings adjacent to the underground structure. (3) The featured uneven uplift between different spans of the largescale unequal-span subway station are detected. Amongst, the uplift of the middle span is the largest, while the rotation of other positions gradually decreases with the increase of horizontal distance

from the center point, and the uplift is minimized at the cantilever span. The peak uplift displacement of subway station with diaphragm walls is substantially smaller than that without walls. (4) When the diaphragm wall is in position, the curves of the structural lower layer and upper layer are approximately linear, which could be attributed to the diaphragm wall’s contribution to the lateral stiffness since it overlaps partly with the side walls of the subway station to strengthen it. The lateral foundation liquefaction level of station structure in the SWSI system is significantly higher than that in the SSI system, resulting in more serious weakening of soil strength and larger relative IHD responses of subway station consequently. (5) It can be stated that the frequency contents rather than the magnitude of the seismic motion has great influence on the peak acceleration of the subway station. With the increase of the seismic intensity, the accelerations of the middle plate and the bottom plate steep up sharply in the time period from 0.01 s to 0.08 s when the underground diaphragm wall isn’t present. (6) The severe tensile damage at the cantilever span penetrates the whole cross-sections to ensue overall breakage when subject to strong earthquake excitations, which is mainly attributed to the 18

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SSI system

SWSI system

SSI system

SWSI system

(a) PGA=0.1g

SSI system

SSI system

SWSI system

SWSI system

(b) PGA=0.2g

SSI system

SWSI system

SSI system

SWSI system

(c) PGA=0.3g Fig. 21. Seismic damages of subway station subject to Kobe motions.

seismic design of the large-scale unequal-span subway station, especially for the diaphragm wall and the structural cantilever span. (7) It should be noted here that the above new findings and conclusions should be more available for the underground subway station in this study, which could be referenced discreetly by other kinds of underground subway station. However, the analysis methods shown in this study could be effectively used in analyzing the earthquake responses of other kinds of underground subway station.

uneven liquefaction-induced uplift. The seismic damage mechanism and internal force distribution of the subway station will be modulated by the diaphragm wall. When the diaphragm wall is installed, the tension damage degree of the bottom plate of the subway station are intensified, while the components of cantilever span in the upper layer suffer the less. The diaphragm wall is susceptible to severe tensile damage at the cross-sections where the diaphragm wall intersects the bottom slab, the specific range below the bottom plate, and the location adjacent the lower side walls. It should be taken into account appropriately to rationalize the

(a) El-Centro motion

(b) Kobe motion

(c) Nanjing motion

Fig. 22. Tension damages of diaphragm wall subject to different earthquakes with PGA = 0.3 g. 19

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Acknowledgments

underground structures induced by soil liquefaction. Comput. Geotech. 33, 209–221. Lubliner, J., Oliver, J., Oller, S., Onate, E., 1989. A plastic-damage model for concrete. Int. J. Solids Struct. 25 (3), 299–326. Ma, C., Lu, D.C., Du, X.L., 2018. Seismic performance upgrading for underground structures by introducing sliding isolation bearings. Tunn. Undergr. Space Technol. 74, 1–9. Miao, Y., Yao, E.L., Ruan, B., Zhuang, H.Y., 2018. Seismic response of shield tunnel subjected to spatially varying earthquake ground motions. Tunn. Undergr. Space Technol. 77, 216–226. Nomura, T., Hughes, T.J.R., 1992. An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Comput. Meth. Appl. Mech. Eng. 95 (1), 115–138. Orense, R.P., Morimoto, I., Yamamoto, Y., Yumiyama, T., Yamamoto, H., Sugawara, K., 2003. Study on wall-type gravel drains as liquefaction countermeasure for underground structures. Soil Dyn. Earthq. Eng. 23 (1), 19–39. Parra, E., 1996. Numerical Modeling of Liquefaction and Lateral Ground Deformation Including Cyclic Mobility and Dilation Response in Soil Systems. PhD thesis. Rensselaer Polytechnic Institute, Troy, N.Y. Pastor, M., Zienkiewicz, O.C., Chan, A., 1990. Generalized plasticity and the modelling of soil behaviour. Int. J. Numer. Anal. Meth. Geomech. 14 (3), 151–190. Senzai, S., Hajime, O., Takashi, M., 1997. A study of the damage of subway structures during the 1995 Hanshin-Awaji earthquake. Cem. Concr. Compos. 19 (3), 223–239. Suzuki, T., Adachi, Y., Tanaka, M., 1995. Application of microtremor measurements to the estimation of earthquake ground motions in Kushiro city during the Kushiro-Oki earthquake of 15 January 1993. Earthq. Eng. Struct. Dyn. 24, 595–613. Tamari, Y., Towahata, I., 2003. Seismic soil-structure interaction of cross sections of flexible underground structures subjected to soil liquefaction. Soils Found. 43 (2), 69–87. Tsinidis, G., 2017. Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking. Tunn. Undergr. Space Technol. 62, 1–22. Unutmaz, B., 2014. 3D liquefaction assessment of soils surrounding circular tunnels. Tunn. Undergr. Space Technol. 40, 85–94. Wang, J.N., 1993. Seismic Design of Tunnels: A Simple State of the Art Design Approach. Parsons Brinckerhoff Inc., New York. Wang, R., Zhang, J.M., Wang, G., 2014. A unified plasticity model for large post-liquefaction shear deformation of sand. Comput. Geotech. 59, 54–66. Wang, R., Zhuang, H.Y., Chen, G.X., Fu, J.S., 2018. Seismic response of subway underground station buried in liquefiable soil foundation with the ground surface slight inclined. Earthq. Eng. Eng. Dyn. 38 (2), 130–140. Watanabe, K., Sawada, R., Koseki, J., 2016. Uplift mechanism of open-cut tunnel in liquefied ground and simplified method to evaluate the stability against uplifting. Soils Found. 56 (3), 412–426. Yang, Z.H., Elgamal, A., 2002. Influence of permeability on liquefaction-induced shear deformation. J. Eng. Mech. 128 (7), 720–729. Zhang, J.M., Wang, G., 2012. Large post-liquefaction deformation of sand, part I, physical mechanism, constitutive description and numerical algorithm. Acta Geotech. 7, 69–113. Zhou, J., Jiang, J.H., Chen, X.L., 2015. Micro- and macro-observations of liquefaction of saturated sand around buried structures in centrifuge shaking table tests. Soil Dyn. Earthq. Eng. 72, 1–11. Zhuang, H.Y., Chen, G.X., Zhu, D.H., 2008. Dynamic visco-plastic memorial nested yield surface model of soil. Front. Archit. Civil Eng. 2 (1), 49–55. Zhuang, H.Y., Chen, G.X., 2011. Constitutive model for large liquefaction deformation of sand and its implementation in ABAQUS software. World Earthq. Eng. 27 (2), 45–50. Zhuang, H.Y., Hu, Z.H., Wang, X.J., Chen, G.X., 2015. Seismic responses of a large underground structure in liquefied soils by FEM numerical modelling. Bull. Earthq. Eng. 13 (12), 3645–3668. Zhuang, H.Y., Chen, G.X., Hu, Z.H., Qi, C.Z., 2016. Influence of soil liquefaction on the seismic response of a subway. Bull. Earthq. Geol. and Environ. 75 (3), 1169–1182. Zhuang, H.Y., Wang, R., Shi, P.X., Chen, G.X., 2019. Seismic response and damage analysis of underground structures considering the effect of concrete diaphragm wall. Soil Dyn. Earthq. Eng. 116, 278–288.

The authors wish to acknowledge the research funding provided by the National Science Foundation of China (NSFC, Grant Nos. 51778290 and 51778282), the Natural Science Foundation of Jiangsu Province (NSFJ, Grant No.·16KJA560001) and the Graduate Student Innovation Foundation of Hebei Province (GSIFH, Grant No.·CXZZBS2018038). References An, J.H., Tao, L.J., Wang, H.J., Li, J.D., 2017. Shaking table experiments on seismic response of a shield-enlarge-dig type subway station structure in liquefiable ground. Chin. J. Rock Mech. Eng. 36 (8), 2018–2030. Azadi, M., Hosseini, M.M., 2010a. The uplifting behavior of shallow tunnels within the liquefiable soils under cyclic loadings. Tunn. Undergr. Space Technol. 25, 158–167. Azadi, M., Hosseini, M.M., 2010b. Analyses of the effect of seismic behavior of shallow tunnels in liquefiable grounds. Tunn. Undergr. Space Technol. 25, 543–552. Chen, G.X., Chen, S., Qi, C.Z., Du, X.L., Wang, Z.H., Chen, W.Y., 2015. Shaking table tests on a three-arch type subway station structure in a liquefiable soil. Bull. Earthq. Eng. 13, 1675–1701. Chen, R.R., Taiebat, M., Wang, R., Zhang, J.M., 2018. Effects of layered liquefiable deposits on the seismic response of an underground structure. Soil Dyn. Earthq. Eng. 113, 124–135. Chen, S., Tang, B.Z., Liu, A.W., Chen, G.X., Li, X.J., 2016a. 3-D numerical simulation on seismic behavior of variable cross-section subway station structure in complex geological ground. Seismol. Geomag. Obser. Res. 37 (5), 41–48. Chen, Z.Y., Chen, W., Li, Y.Y., Yuan, Y., 2016b. Shaking table test of a multi-story subway station under pulse-like ground motions. Soil Dyn. Earthq. Eng. 82, 111–122. Chian, S.C., Madabhushi, S.P.G., 2012. Effect of buried depth and diameter on uplift of underground structures in liquefied soils. Soil Dyn. Earthq. Eng. 41, 181–190. Chian, S.C., Tokimatsu, K., Madabhushi, S.P.G., 2014. Soil liquefaction-induced uplift of underground structures physical and numerical modeling. J. Geotech. Geoenviron. Eng. 140 (10), 31–40. Chou, J.C., Kutter, B.L., Travasarou, T., Chacko, J.M., 2011. Centrifuge modeling of seismically induced uplift for the BART Transbay Tube. J. Geotech. Geoenviron. Eng. 137 (8), 754–765. Elgamal, A., Yang, Z.H., Parra, E., 2002. Computational modeling of cyclic mobility and post-liquefaction site response. Soil Dyn. Earthq. Eng. 22 (4), 259–271. Hashash, Y.M.A., Hook, J.J., Schmidt, B., Yao, J.I., 2001. Seismic design and analysis of underground structures. Tunn. Undergr. Space Technol. 16 (4), 247–293. Hu, J.L., Chen, Q.H., Liu, H.B., 2018. Relationship between earthquake-induced uplift of rectangular underground structures and the excess pore water pressure ratio in saturated sandy soils. Tunn. Undergr. Space Technol. 79, 35–51. Huo, H., Bobet, A., Fernández, G., Ramírez, J., 2005. Load transfer mechanisms between underground structure and surrounding ground: evaluation of the failure of the Daikai station. J. Geotech. Geoenviron. Eng. 131 (12), 1522–1533. Iida, H., Hiroto, T., Yoshida, N., Iwafuji, M., 1996. Damage to Daikai subway station. Soils Found. Special Issue 283–300. Kang, G.C., Tobita, T., Iai, S., 2014. Seismic simulation of liquefaction-induced uplift behavior of a hollow cylinder structure buried in shallow ground. Soil Dyn. Earthq. Eng. 64, 85–94. Kjellgren, P., Hyvärinen, J., 1998. An Arbitrary Lagrangian-Eulerian finite element method. Comput. Mech. 21 (1), 81–90. Koseki, J., Matsuo, O., Sasaki, T., Saito, K., Yamashita, M., 2000. Damage to sewer pipes during the 1993 Kushiro-Okiand and the 1994 Hokkai-do-Toho-Oki earthquakes. Soils Found. 40 (1), 99–111. Lee, J., Fenves, G.L., 1998. Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124 (8), 892–900. Liu, H.B., Song, E.X., 2006. Working mechanism of cutoff walls in reducing uplift of large

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