A novel segmental cored column for upgrading the seismic performance of underground frame structures

Soil Dynamics and Earthquake Engineering 131 (2020) 106011

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Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn

A novel segmental cored column for upgrading the seismic performance of underground frame structures Dechun Lu a, *, Chunyu Wu a, Chao Ma b, Xiuli Du a, M. Hesham El Naggar c a

Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, 100124, China Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing, 102612, China c Department of Civil and Environmental Engineering, Faculty of Engineering, Western University, London, Canada b

A R T I C L E I N F O

A B S T R A C T

Keywords: Segmental cored column Underground frame structure Interlaminar deformability envelope Vertical bearing capacity Seismic performance

A novel segmental cored column (SCC) is proposed to enhance the seismic performance of underground frame structures, especially the interlaminar deformability of the intermediate columns. The basic composition and behaviour mechanism of the SCC are introduced. An analytical model for calculating the horizontal loaddisplacement curve and the interlaminar deformability of the SCC is established, and pushover simulations are conducted to verify its efficacy. The developed model is then employed to investigate the critical factors that may affect the interlaminar deformability envelope of the SCC. To further demonstrate the feasibility of the SCC in upgrading the seismic performance of underground frame structures, the seismic responses of the same structure are analysed considering alternative column design, i.e., conventional rectangular or circular columns, or the SCC. The obtained results demonstrate that the structure retrofitted with the SCC experiences less damage and exhibits better seismic performance compared to those designed with conventional rectangular or circular columns.

1. Introduction The seismic performance of underground frame structures has received increased attention since the collapse of the Daikai subway station during the Hyogoken-Nanbu Earthquake in 1995 [1]. The damaged Daikai subway station was selected as the target structure to investigate its seismic response characteristics and the failure mecha­ nisms [1–6], and researchers conducted extensive work on the dynamic response characteristics of various underground structures [7–9]. One salient feature emerged from these studies is that the seismic response of underground structures is dominated by the relative deformation of the surrounding soils rather than the inertial force of the structures. It was also found that the intermediate columns are the key structural component, and that insufficient horizontal interlaminar deformability of the intermediate columns was the leading cause of the collapse of the Daikai subway station [4,10]. Therefore, to upgrade the seismic per­ formance of underground frame structures, the seismic performance of the intermediate columns has to be addressed. The seismic performance of underground frame structures can be enhanced by changing the loading conditions and deformation modes of

the intermediate columns through two different approaches: reduce their deformation response using seismic isolation technologies [11]; or improve their horizontal interlaminar deformability to meet the large seism deformation demand. Meanwhile, the adopted solution has to provide sufficient vertical bearing capacity of the columns to ensure their main function of sustaining the vertical load [4]. Several types of seismic isolation bearings were applied to under­ ground frame structures, and were typically installed between the in­ termediate columns and beams to reduce the deformation response of the columns. Sliding isolation bearings [10], rolling friction pendulum systems [12], and flexible rubber bearings [13] were introduced into the Daikai station model to protect the columns from severe damage and thus control the failure mode of the structure. Research findings indi­ cated that the interlaminar deformation of the intermediate columns was replaced by the sliding or deformation of the bearings, thus the deformation response and internal force induced by earthquake were reduced, and consequently the associated damage of the intermediate columns was significantly decreased. The failure mode of the Daikai station model in these studies was effectively controlled by introducing these isolation bearings. Similarly, the shear panel damper bearings [14]

* Corresponding author. E-mail addresses: [email protected] (D. Lu), [email protected] (C. Wu), [email protected] (C. Ma), [email protected] (X. Du), naggar@ uwo.ca (M.H. El Naggar). https://doi.org/10.1016/j.soildyn.2019.106011 Received 18 September 2019; Received in revised form 13 November 2019; Accepted 12 December 2019 Available online 7 January 2020 0267-7261/© 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Configuration diagram of segmental cored column: (a) Stereoscopic diagram; (b) Core column; (c) Hollow segments; (d) Section 1-1.

and lead-rubber bearings [15] were used to upgrade the seismic per­ formance of both single-story and double-story underground frame structures. The analytical results demonstrated that the horizontal interlaminar deformation between the slabs increased slightly after adding the bearings, while the maximum shear force and bending moment of the columns decreased by more than 35%. Correspondingly, the damage of the intermediate columns decreased significantly and the seismic performances of underground structures were improved. These observations confirmed that reducing the deformation response of the intermediate columns is an effective strategy in improving the seismic performance of underground frame structures. An alternative solution to the isolation approach is to improve the horizontal interlaminar deformability of the columns without reducing their vertical bearing capacity. This can be achieved by utilizing confined concrete columns, such as stirrup encryption columns [3], hybrid FRP tubular columns [16], or concrete-filled steel tubular col­ umns [17], which have been proven to induce ductile deformability more than ordinary reinforced concrete columns. The interlaminar deformability of columns can also be improved by changing the struc­ tural form of the columns. For example, the split column [18] divides the monolithic column into several identical sub-columns each having the same height as the monolithic column, but a reduced cross-sectional area. The vertical bearing capacity of the split column is equivalent to that of the monolithic column when the sum of the cross-sectional area of the sub-columns is the same as the monolithic column. However, the slenderness ratio of each sub-column increases exponentially, resulting in a significant increase in the interlaminar deformability of the column. However, slender columns may undergo buckling failure under eccen­ tric compression [19]. Other solutions that were considered include the precast concrete segmental column [20,21] and the self-centering rocking column [22–25] that are connected to the foundation and the top beam through prestressing tendons. The gaps at the joints are allowed to open and the columns are allowed to uplift at the base under horizontal loadings [20,22]. The opening and uplifting behaviour leads to greater deformability of the column and minor damage at the column ends. These columns with novel structural forms are widely used in bridge structures; however, they are rarely implemented in underground frame structures due to long-term maintenance and performance con­ cerns. Therefore, there is motivation to develop equally innovative structural form for the columns while ensuring easy implementation in

projects to improve the long-term seismic performance of underground structures. This study investigates a novel column structural form, denoted segmental cored column (SCC) [26], for upgrading the seismic perfor­ mance of underground frame structures. Detailed structure design of the SCC is illustrated and its load transfer mechanism is elaborated. The horizontal resistance and deformation characteristics of the SCC under different deformation states are evaluated employing an analytical so­ lution as well as pushover simulation. The interlaminar deformability envelopes of different columns are utilized to evaluate the seismic response of the whole structures. The numerical results demonstrated that the application of SCC in the structural model of the Daikai station can effectively improve its seismic performance by enhancing the interlaminar deformability of intermediate columns. 2. Development of the segmental cored column The horizontal shear loads of underground frame structures during earthquakes are primarily sustained by the lateral walls, while the ver­ tical loads are shared by the columns and the lateral walls. Thus, the main function of the columns in underground frame structures is sus­ taining the vertical loads [26]. During the Hyogoken-Nanbu earthquake, the collapse of Daikai subway station was caused by the loss of vertical bearing functionality of the intermediate columns, and the affordability loss was further attributed to the insufficient interlaminar deformability of the columns [2,10]. Therefore, the seismic performance of the col­ umns can be enhanced by improving the interlaminar deformability while ensuring their vertical bearing capacity. This is achieved by forming a composite column, denoted herein as segmental cored column (SCC), by stacking several hollow column segments with a central slender column as shown in Fig. 1. By constructing the SCC with the same effective cross-sectional area and material as the monolithic col­ umn, the vertical bearing capacities of the two systems are essentially equal. Meanwhile, the core column has a larger slenderness ratio and hence better interlaminar deformability. 2.1. Configuration of SCC and function of each component The core column (Fig. 1(b)) mainly bears the vertical loads, and regulates the horizontal movement of the hollow segments (Fig. 1(c)) at 2

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2.2. Performance mechanism of the SCC Fig. 2 presents a profile view of the SCC before and after horizontal interlaminar deformation, which explains the mechanical behaviour of the SCC. The vertical load transmitted from the top beam to the SCC is distributed to the core column and hollow segments proportional to their sectional compressive stiffness. The vertical bearing capacity of the SCC is equivalent to a monolithic column with the same effective crosssectional area. However, the shear capacity of the SCC is significantly reduced compared to the monolithic column due to the sliding behav­ iour of the hollow segments. As shown in Fig. 2, both ends of the core column extend into the top and bottom beams, forming fixed connections at both ends. Upon hor­ izontal loading, the hollow segments tend to slide in the same direction along the interfaces. Once the horizontal force resisted by the stacked segments reaches the maximum static friction force required for the sliding of a certain interface, sliding occurs along that interface. At the same time, the core column undergoes bending deformation. Due to the regulating function of the core column, other hollow segments succes­ sively slide in the same direction. The final deformation mode of the SCC (see Fig. 2 (b)) illustrate that the ultimate interlaminar deformation of the SCC allowed by the deformation space is geometrically related to δ and the number of segments. The SCC reaches its designed maximum interlaminar deformability when all the segments are closely fitted with the core column. The interlaminar deformability of the core column is assumed to be sufficient to meet the design requirements due to its large slenderness ratio.

Fig. 2. Deformation mode of the SCC: (a) before deformation and (b) after deformation.

different heights. The segments are allowed to slide at their interfaces, which is facilitated by introducing low friction layers (Fig. 1(d)) be­ tween adjacent segments to reduce the sliding resistance. The friction layers can be lubricated low friction contact surfaces or sliding support bearings [27]. Under horizontal loading, the stacked segments tend to slide to one side owing to the regulating function of the core column. On the other hand, the lateral constraint of the stacked segments prevents buckling failure of the core column. To prevent the shearing action of the segments on the core column, a deformation space (i.e., gap) is maintained between the core column and the segments, as shown in Fig. 1(d). The size of the gap is given by the difference between the inner radius of the hollow segments and the radius of the core column. By varying the inner radius of the hollow segments along the height, the gap width is narrowest at the end of the column for the top and bottom segments and increases monotonously toward the middle segments. For the middle segments, the gap width is narrowest in the middle and in­ creases at both ends. The maximum gap width, δ, is at the elevations of the friction layers as marked in Fig. 1(d).

3. Analytical model for the SCC Analytical methods are optional to clarify the motion and deforma­ tion characteristics of block assemblies [28]. Herein, an analytical model is developed to describe the mechanical behaviour of the SCC during the deformation process. The main assumptions are: (1) the effect of the deformation space on the calculated compressive stiffness of the segments is ignored. (2) the vertical loads shared by the core column and the hollow segments respectively remain the same during the defor­ mation process. (3) the maximum static friction force is the same as the sliding friction force without considering the change of the friction co­ efficient during the motion [29]. For simplicity, the SCC with only two segments is selected for the analysis, as illustrated in Fig. 3. Due to both ends of the SCC are

Fig. 3. Four stages of SCC under vertical load and horizontal load: (a) vertical compression stage; (b) non-sliding stage; (c) sliding stage; (d) ultimate deforma­ tion stage. 3

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the cross-sectional areas, Aa ¼ πr2, and Ab ¼ π (R2-r2), where r and R are the outer radius of the core column and the segments, respectively; and α is the compressive stiffness ratio of the core column, which is expressed as α ¼ Ea Aa/(Ea AaþEb Ab). 3.2. Non-sliding stage In the non-sliding stage, the vertical load P and the horizontal load F are simultaneously imposed on the SCC, but there is no relative sliding between the segments as shown in Fig. 3(b). In this stage, the inter­ laminar deformation of the SCC is insignificant, and the deformation mode is similar to the monolithic columns, as shown in Fig. 4(a). The shear force and bending moment diagrams of the column are shown in Fig. 4(b) and (c), respectively. For circular column with fixed ends, the horizontal loaddisplacement (F-Δ) relationship can be expressed as F¼

restrained by the rigid beams, the rotational degrees of the top and bottom sections of the SCC are constrained and they only experience translational movements. The deformation process of the SCC is sub­ divided into four stages according to the loading conditions and the deformation states as shown in Fig. 3: (1) vertical compression stage, (2) non-sliding stage, (3) sliding stage, and (4) ultimate deformation stage.

where Ie is the effective cross-sectional moment of inertia. Ig is the gross cross-sectional moment of inertia, which has two components repre­ senting the core column and the segments and are calculated as � (5) Ig;a ¼ πr4 4

When only vertical load P is imposed on the SCC, as shown in Fig. 3 (a), the vertical loads carried by the core column and the segments, Pa and Pb, respectively, can be calculated considering their vertical sectional compressive stiffness as

Pb ¼

Eb Ab P¼ Ea Aa þ Eb Ab

� 1

Ig;b ¼ π R4

r4

�� 4

(6)

FEMA 356 [31] suggests that the effective stiffness values be varied with the applied axial load ratio. The effective stiffness is taken as 0.50EIg when the axial load ratio of the column is less than 0.3 and as 0.7 EIg when the axial load ratio of the column is greater than 0.5 and varies linearly for intermediate axial load ratios. Substituting Eq. (5) and Eq. (6) into Eq. (4), and then substituting Eq. (4) into Eq. (3) yields � �� 3κπ Ea r4 þ Eb R4 r4 F¼ Δ (7) 3 h

(1) �

α P

(4)

Ie ¼ κIg

3.1. Vertical compression stage

Ea Aa P ¼ αP Ea Aa þ Eb Ab

(3)

where, h is the net height of the SCC, and Ie,a and Ie,b are the effective moment of inertia of the core column and the segments, respectively. The deformation process of an SCC involves geometric nonlinearity, material nonlinearity, and contact nonlinearity; thus, the stiffness ratio κ is used to reflect the stiffness reduction [30], i.e.

Fig. 4. Deformation mode and internal force analysis of the column: (a) deformation mode, (b) shear force diagram, and (c) bending moment diagram.

Pa ¼

12ðEa Ie;a þ Eb Ie;b Þ Δ h3

(2)

where subscripts a and b represent the core column and the segments, respectively; Ea and Eb are the Young’s elastic modulus; Aa and Ab are

The horizontal load shared by the segments is calculated as � 3κπEb R4 r4 Fb ¼ Δ h3

(8)

When Fb reaches the maximum static friction force between the hollow segments, relative sliding occurs. The sliding critical condition can be described by Fb ¼ μðPb þ PG Þ

(9)

where μ is the friction coefficient, and PG is the weight of the segments above the interface. Combining Eq. (8) and Eq. (9), the maximum displacement in the non-sliding stage can be calculated as: Δ

1

¼

μh3 ðPb þ PG Þ � 3κπEb R4 r4

(10)

3.3. Sliding stage Once the segments begin to slide, the shear force at the segments interface reaches the sliding friction force and remains constant as the segments slide; meanwhile, the core column continues to deform

Fig. 5. Complete horizontal load-displacement curve of the SCC obtained by the analytical model. 4

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form. That is, when the horizontal load carried by the core column is less than its shear resistance, the F-Δ relationship satisfies the linear corre­ lation expressed by Eq. (11). Once the horizontal load carried by the core column reaches its shear resistance, it remains unchanged with the increase of the imposed displacement. The shear resistance of the core column is calculated following the Chinese code for concrete design [32], i.e., V¼

(12)

where λ is the shear span ratio of the core column given by λ ¼ h/2h0 (with 1 � λ � 3); h0 is the effective depth of the section ¼ 1.6r; b is the section width ¼ 1.76r; ft is the concrete tensile strength; fyv is the tensile strength of stirrups; Asv and S are the cross-sectional area and spacing of stirrups, respectively; and Pa � 0.3fcAa, fc is the design value of concrete uniaxial compressive strength. When Fa ¼ V, the critical state of the SCC at which the core column reaches its plastic state can be obtained as:

Fig. 6. Critical section of the bottom segment.

horizontally. The shear force undertaken by the SCC can be expressed as 3κπEa r4 F ¼ Fa þ Fb ¼ Δ þ μðPb þ PG Þ h3

1:75 Asv ft bh0 þ fyv h0 þ 0:07Pa λþ1 S

Δ

(11)

2

¼

Vh3 3κπEc r4

(13)

The condition Δ >Δ2 indicates that the core column has reached its plastic state, hence substituting Δ ¼ Δ2 into Eq. (11) gives the maximum F2.

herein, Fa is the horizontal load carried by the core column. The F-Δ relationship of the core column is simplified as an ideal elastoplastic

3.4. Ultimate deformation stage When the segments are closely fitted with the core column as shown in Fig. 3(d), the SCC reaches its target design displacement, which is determined by δ and the number of segments, i.e. Δ

3

¼ 2ðn

1Þδ

(14)

where n is the number of segments. For an SCC with two segments, Δ3 ¼ 2δ. When the horizontal deformation exceeds the target design displacement (Δ3), the SCC is in the ultimate deformation stage. In this stage, the core column and the hollow segments would shear each other because of the limitation of the deformation space. Although the shear force and horizontal deformation of the SCC may continue to increase to some extent during the mutual shearing process (Δ >Δ3), further growth is no longer considered in this study. Therefore, the target design displacement Δ3 is taken as the ultimate displacement. Fig. 5 shows the typical F-Δ curve of the SCC. It can be seen that there are three characteristic points: (1) initiation of sliding (Δ1, F1): at which the horizontal load carried by the segments reaches the sliding critical state; (2) onset of plastic deformation (Δ2, F2): at which the horizontal load imposed on the core column reaches its shear strength; (3) target design displacement (Δ3, F3): at which the SCC reaches its target design displacement. 3.5. Failure identification method The above analytical model presents an idealized F-Δ curve that may not reflect the potential failure behaviour of the SCC during the defor­ mation process. For a properly designed SCC, the overall compressive stiffness of the hollow segments should be greater than that of the core column (i.e., the core column is softer than the stacked segments). In this case, the share of core column from the vertical load is reduced, and thus will not experience vertical compression failure. The core column plays an important role in regulating the horizontal displacement of the hol­ low segments. When the horizontal interlaminar deformation is beyond the elastic range, plastic hinges may develop at both ends of the core column. However, these plastic hinges do not significantly affect the regulating function of the core column and the overall vertical bearing function of the SCC. Additionally, when the friction coefficient of the

Fig. 7. Compression stress distributed on the critical section of the bottom segment: (a) Pb only; (b) full section compression under combined Pb and Fb; and (c) partial section compression under combined Pb and Fb. 5

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friction layer is small, smooth sliding can be easily achieved between the segments. The hollow segments carry little shear force and are not prone to shear failure. Therefore, the potential failure mode of the SCC is the compression failure of the hollow segments. As can be seen from Fig. 4, under horizontal load the bending moment is maximal at both ends of the stacked segments. During the sliding process, the bending moment at both ends generated by the eccentric action of the vertical load is also maximal. The bending moment causes an uneven distribution of compressive stress on the bottom section of the stacked segments (see Fig. 3). The stress concen­ tration areas are most likely to experience damaged due to excessive compressive stress. The dislocation between adjacent segments de­ creases the compressive area at the interface, which increases the compressive stress at the end of each segment. However, the additional increase of the compressive stress on the bottom section caused by the bending moment is more significant. Therefore, the bottom section of the bottom segment shown in Fig. 6 represents the most vulnerable re­ gion of the SCC. Correspondingly, the ultimate compressive stress at this section is used as the failure evaluation index to determine the inter­ laminar deformation of the SCC at failure. Three different possible forms of compression stress distribution on the critical section are illustrated in Fig. 7. Under vertical load only, the compression stress is evenly distributed across the section as shown in Fig. 7 (a). Under combined horizontal and vertical loads, the bending moments due to Fb and the Pb-Δ effect, significantly change the distri­ bution of compressive stress on the critical section. For simplicity, it is considered that compressive stress is linearly distributed on the critical section. Fig. 7(b) and (c) show two different distribution pattern of the compressive stress, the full section compression and the partial section compression, respectively. The ultimate compressive stress of the bottom segment is expressed as σ max. When the maximum compressive stress on the critical section reaches σ max, the SCC is considered to reach the ultimate state and the corresponding horizontal displacement is recorded as the ultimate interlaminar displacement.

symmetry of the section, the minimum compressive stress decreases by the same value, which is marked as σ . The bending moment generated by the linearly distributed compressive stress on the critical section can be calculated as � Z R þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z r þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � � σ x σ x Mσ ¼ 4 ⋅ R2 x2 xdx ⋅ ðr2 x2 Þxdx R R 0 0 � πσ þ R4 r4 ¼ (18) 4R The bending moment produced by the combined Fb and the Pb - Δ effect is When the stacked segments are in the non-sliding stage, Fb is given by Eq. (8), and submitting Eq. (8) into Eq. (19) gives � 3κπhEb R4 r4 Δ M¼ þ Pb Δ (20) 3 2h Considering the equilibrium condition of bending moments on the critical section,

Pb þ PG � r2

The horizontal displacement can then be calculated by � πh2 R4 r4 σ þ � Δ¼ 4 4 6κπREb R r þ 4Pb Rh2

When σ ¼ σ Pb ¼ π R 2

max,

� 2

Introducing Eq. (23) into Eq. (22), the ultimate interlaminar displacement at failure, Δlim, is expressed as � πh2 R4 r4 ðσ max σ Þ � Δ lim ¼ (24) 6κπ REb R4 r4 þ 4Pb Rh2 The condition Δlim < Δ1 indicates that the bottom segment has indeed failed during the non-sliding stage. On the other hand, Δlim >Δ1 indicates that the bottom segment has not failed in the non-sliding stage and will enter the sliding stage. Then, substituting Eq. (9) into Eq. (19) and combining Eq. (18), Eq. (19), Eq. (21) and Eq. (23), Δlim can be calcu­ lated as � 2μhRðPb þ PG Þ πðσ max σ Þ R4 r4 Δ lim ¼ (25) 4Pb R 3.5.2.2. Partial section compression. For the case σ <σ max/2, as the maximum compressive stress on the critical section reaches σmax, a zero stress zone appears as shown in Fig. 7(c). The zero stress line is parallel to the y-axis, and the corresponding abscissa is l. The compressive stress distributed on the critical section at failure can be expressed as:

(16)

PG

Combining with Eq. (2), the vertical bearing capacity of the SCC is � � � ðEa Aa þ Eb Ab Þ π R2 r2 σ max PG P ¼ (17) Eb Ab

where k is the slope of the profile of compressive stress distributed on the critical section. For the case of -R < l < -r, the vertical load can be expressed by integrating the compressive stress distributed over a solid section with radius R minus the contribution of the hollow portion with radius r, i.e.

3.5.2.1. Full section compression. For σ >σ max/2, the whole critical section becomes under compression when the maximum compressive stress reaches σ max as shown in Fig. 7(b), where σ þis the additional compressive stress caused by the bending moments. Due to the

Z

R l

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi 2 R2 x2 kðx

Z

r

lÞdx

2 r

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðr2 x2 Þkðx

(26)

σ max ¼ kða þ RÞ

3.5.2. Combined vertical and horizontal loads

Pb ¼

(23)

σ þ σþ ¼ σ max

the vertical bearing capacity of the bottom segment is

r σ max

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi lÞdx ¼ kl2 R2 l2

(22)

The critical failure condition is given by

(15)

π R2

(21)

Mσ ¼ M

3.5.1. Vertical load only For the case of SCC subjected to axial load only as shown in Fig. 7(a), the interlaminar deformation is zero. The compressive stress on the critical section is calculated as

σ¼

(19)

M ¼ 0:5Fb h þ Pb Δ

� π kR2 l 2

6

arcsin

� l 2 þ k R2 R 3

l2

�32

þ klπ r2

(27)

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

For specified σmax and Pb, the value of k and l can be obtained by combining Eq. (26) and Eq. (27). If the calculated l satisfies -R < l < -r, then the bending moment generated by the compressive stress can be calculated as

Z

0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi B 2 R2 x 2 k B @x

R

Mσ ¼ l

1 Z

C lC Axdx

r

� pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðr2 x2 Þk x

� kl 2l2 R2 pffiffiffi2ffiffiffiffiffiffiffiffiffi2ffiffi R l 4

� k π R4 l xdx ¼ 8

r

kR4 l arcsin R 4

� 2kl 2 R 3

�32 l2

kπ r4 4

(28)

If the calculated l > -r, Eq. (27) should be updated to

Z

R

Pb ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi � 2 R2 x 2 k x

� l dx

Z

r

2

l

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi � ðr2 x2 k x

� l dx

l

pffiffiffiffiffiffiffiffiffiffiffiffiffi� r2 l2

�pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ kl2 R2 l2

� π kl R2 2

� r2

� l þ kl R2 arcsin R

�

�� l 2 r2 arcsin þ k R2 r 3

l2

(29)

3 2

�

�32

�� r2

l2

Similarly, the value of k and l can be updated by combining Eq. (26) and Eq. (29). If the updated l satisfies -r < l < r, Eq. (28) should be updated to

Z

R

Mσ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi � 2 R2 x 2 k x

� l xdx

l

¼

Z

r

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi � 2 ðr2 x2 k x

� l xdx

l

kπ R

4

8

r

4

�

�� kl 2l2 4

�pffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 R2 l2

� 2l2

�pffiffiffiffiffiffiffiffiffiffiffiffiffi� r2 r2 l2

� k 4 l R arcsin 4 R

Z l

R

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi 2 R2 x2 kðx

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi lÞdx ¼ kl2 R2 l2

� π kR2 l 2

arcsin

l r

�� 2kl R2 3

�32 l2

3 2

�

�� r2

(30)

l2

Then, Eq. (30) should be further updated to

If the updated l does not satisfy -r < l < r, l must be from r to R, Eq. (29) should be further updated to

Pb ¼

r4 arcsin

�

� l 2 þ k R2 R 3

7

l2

�32

(31)

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Fig. 9. Horizontal load-displacement curve obtained by pushover simulation.

Combining the calculated Mσ with Eq. (20), Eq. (21), and Eq. (23), the Δlim in the non-sliding stage can be calculated as Δ lim ¼

Δ lim ¼

Table 1 CDP parameters for ABAQUS material of concrete. Given value

Meaning description

ψ

38

Dilation angle

ε

0.1

Eccentricity

fb0 = fc0

1.16

κ

0.667

μ

1e-5

The ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress The ratio of the second stress invariant on the tensile meridian Viscosity parameter

R

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi � 2 R2 x 2 k x

l

� k π R4 l xdx ¼ 8

Mσmax

0:5μhðPb þ PG Þ Pb

(34)

If Δlim<Δ3, it indicates that the bottom segment has failed before entering the ultimate deformation stage. If Δlim>Δ3, take Δ3 as the ul­ timate interlaminar displacement.

Parameter

Z

(33)

If Δlim>Δ1, substituting Eq. (9) into Eq. (19), the equilibrium con­ dition of bending moment on the critical section gives the Δlim in the sliding stage as

Fig. 8. FEM model of SCC.

Mσ ¼

3κπEb

2Mσ h2 � r4 þ 2Pb h2

R4

� kl 2l2 R2 pffiffiffi2ffiffiffiffiffiffiffiffiffi2ffiffi R l 4

4. Numerical verification of the analytical model and parameter analysis To verify the validity of the analytical model, pushover simulations of the SCC are carried out using the finite element method (FEM) considering a range of vertical load conditions. The horizontal load-

kR4 l arcsin R 4

�32

� 2kl 2 R 3

(32)

l2

Table 2 Material properties of concrete. Grade

Elastic modulus (GPa)

Poisson’s ratio

Characteristic value of cube strength fcu,k (MPa)

Compression yield stress (MPa)

Characteristic value of uniaxial compressive strength fck (MPa)

Tensile yield stress (MPa)

Density (kg/m3)

C40 C60

32.5 36.0

0.2 0.2

40 60

10.7 15.4

26.8 38.5

2.39 2.85

2400 2440

Table 3 Material properties of reinforcement. Type

Diameter (mm)

Elastic modulus (GPa)

Poisson’s ratio

Yield stress (MPa)

Density(kg/m3)

Longitudinal reinforcement Stirrup

28 12

200 200

0.3 0.3

36000 36000

7800

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s2. The vertical load is imposed on the top of the SCC as a constant pressure. The rotational degrees of freedom of all nodes at the top end of SCC are constrained. The displacement controlled loading is imposed on the top end of the SCC along x-direction, and increases gradually till failure occurs. The horizontal load and displacement at the top of the SCC are monitored during the loading process. The loading scheme applied and the boundary conditions are illustrated in the insert of Fig. 9, along with the obtained results presented in terms of F-Δ curve. As can be seen in Fig. 9, the horizontal load increases dramatically in the small deformation stage (i.e., high stiffness), followed by a region of limited load increase (low stiffness) then plateaus for a limited defor­ mation range before the horizontal load declines sharply as failure

Fig. 10. Numerical F-Δ curves of SCC under varying VLR (numbers next to each curve represent the VLR value).

displacement (F-Δ) curves and the interlaminar deformability envelope obtained by the numerical simulations are compared with the analytical results. The analytical model is then used to conduct parameter analyses on the interlaminar deformability envelope of the SCC. 4.1. Finite element model Finite element model of the SCC was built with radius R ¼ 0.50 m and overall height h ¼ 4 m as shown in Fig. 8. Specifically, the radius of the core column, r ¼ 0.17 m, surrounded by five hollow segments each is 0.8 m in height. The maximum gap width δ ¼ 0.02 m. The frictional behaviour between the segments is represented by the friction coeffi­ cient. To facilitate the sliding of the segments at their interfaces, thin steel plates are added to the end of each segment, which has the steel on steel lubricated sliding friction coefficient of about 0.05 [33]. The interaction between the core column and the hollow segments is simu­ lated as hard contact for normal behaviour and frictionless for tangential behaviour. The concrete damage plasticity model (CDP) [34] is adopted to simulate the mechanical behaviour of the concrete. Five plasticity pa­ rameters are needed to define the mechanical behaviour of concrete in ABAQUS, as listed in Table 1. The stress-strain-damage relationships of the concrete under tensile and compression conditions are determined according to code [32]. High-strength concrete C60 is used for the segments to improve the compressive performance and vertical bearing capacity, while C40 is adopted for the core column. Both the core column and the segments are reinforced with longitudinal rebars (28 M bars) and stirrups (12 M bars) as shown in Fig. 8. The core column is reinforced with 10 longitudinal rebars evenly spaced along the circumference, with round stirrups spaced at 0.2 m. The hollow segments are reinforced with two layers of stirrups and longitudinal rebars inside and outside the ring section. The stirrups are spaced at 0.1 m and include an inner hoop, an outer hoop and a tie bar connecting the inner and outer hoops. There are 6 longi­ tudinal rebars arranged on the inner side of the segments and 12 lon­ gitudinal rebars arranged on the outer side. Steel bars are idealized in the finite element as elastic-perfectly plastic material. The specific ma­ terial properties of concrete and reinforcement steel used in the simu­ lation are tabulated in Table 2 and Table 3, respectively. The concrete is modelled using 8-node brick element with reduced integration (C3D8R). The element size of the core column is meshed finely to match the mesh of the segments. Truss elements (T3D2) are adopted to simulate the mechanical behaviour of the steel bars. The truss elements are embedded into the surrounding concrete to simulate the interaction between the steel bars and concrete. The bottom end of the SCC is completely fixed, and the gravity load is applied to the whole model with a gravitational acceleration, g ¼ 9.8 m/

Fig. 11. Comparison of F-Δ curves and ultimate deformation points obtained by analytical and numerical methods. (a) low VLR; (b) medium VLR; (c) high VLR. 9

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

ranges of VLR value: low (0 < VLR <0.8), medium (0.8 < VLR < 1.4) and high (VLR > 1.4). Fig. 11 shows that the F-Δ curves obtained by the analytical model agree well with the numerical results. 4.3.2. Interlaminar deformability envelope In order to establish the interlaminar deformability envelope of the SCC, the ultimate deformation points on the numerical F-Δ curves have to be determined first. As can be seen in Fig. 11, for 0 < VLR <0.8, F-Δ curves have steep slope in the initial non-sliding stage, followed by a mild slope after entering the sliding stage. Each F-Δ curve has a specific point at Δ approaching Δ3, after which the curve exhibits a relatively high slope. Any further increase in F indicates initiation of shearing action between the segments and the core column. Thus, this point is selected as the ultimate deformation point. For 0.8 < VLR <1.4, the F-Δ curve is similar to that for 0 < VLR <0.8, but it displays a point at which F drops sharply during the sliding stage, indicating the onset of failure of the SCC. In this case, the ultimate deformation point is taken as the peak point. For VLR >1.4, the SCC fails in the non-sliding stage and the ul­ timate deformation point is taken as the peak point. The ultimate deformation points are marked as solid dots on the numerical F-Δ curves. For the analytical F-Δ curves, the ultimate deformation points are marked as hollow dots. The interlaminar deformability envelopes of the SCC are respectively obtained based on the ultimate deformation points of the numerical results and the Δlim calculated in the analytical model, and are presented in Fig. 12. The vertical and horizontal axes represent VLR and the interstory drift ratio (IDR), respectively, where IDR is defined as:

Fig. 12. Comparison of the interlaminar deformability envelopes obtained by analytical and numerical methods.

occurs. Of particular note, the two inflexion points on the F-Δ curve are, as discussed previously, the sliding point and ultimate deformation point (as denoted in Fig. 9). 4.2. Numerical horizontal load-displacement curves of the SCC The vertical load ratio (VLR) is defined to express the magnitude of the vertical load, which is calculated as: VLR ¼

P fc A

IDR ¼

(35)

Δlim � 100% h

(36)

It can be seen from Fig. 12 that the interlaminar deformability en­ velope obtained by the analytical model is in good agreement with the numerical result. Fig. 12 also demonstrates that VLR has a significant influence on the interlaminar deformability of the SCC, and there are two points (corresponding to VLR ¼ 0.8 and VLR ¼ 1.4) at which the interlaminar deformability envelope changes slope. When VLR< 0.8, the interlaminar deformability of the SCC is about 4%, corresponding to the target design interlaminar displacement of the SCC. When VLR is be­ tween 0.8 and 1.4, the interlaminar deformability decreases rapidly with increasing VLR. When VLR ¼ 1.4, the interlaminar deformability drops to approximately 0.5%. With further increase of VLR, the interlaminar deformability will continue to drop until the SCC is crushed directly under the vertical load. The numerical verification results show that the analytical model can properly evaluate the F-Δ curves and the interlaminar deformability envelope of the SCC, which verifies its validity.

where P is the vertical load; fc is taken as the design value of concrete uniaxial compressive strength of the core column; and A is the gross cross-sectional area of the SCC. If the concrete material of the segments is the same as the core column, the VLR is the same as the concept of axial load ratio. Note that, fc is equal to the characteristic value of uni­ axial compressive strength (fck) divided by the partial factor (γc ¼ 1.4), and fck is the reduced value of the characteristic value of cube strength (fcu,k) [32]. Therefore, fc is less than the actual compressive strength of concrete, and hence the value of VLR can be greater than 1 or even 2 under high vertical load conditions. Pushover simulations of the SCC under varying VLR values are conducted, and the obtained F-Δ curves are plotted in Fig. 10. The F-Δ curves fall into three groups according to the horizontal deformation stage corresponding to onset of failure of the SCC. For 0 < VLR <0.8, the horizontal displacement of the SCC may reach Δ3 (Δ3 ¼ 0.16 m obtained from Eq. (14)), and the horizontal load displays a clear upward trend for Δ > 0.16 m. For 0.9 < VLR <1.4, the SCC fails in the sliding stage and the maximum displacement cannot reach Δ3. When VLR >1.6, the SCC is failed in the non-sliding stage.

4.4. Parameter analysis of the interlaminar deformability envelope of SCC Based on the analytical model and the basic parameters in Section 4.3, the influences of five key factors, σ max, μ, R, δ, and n, on the inter­ laminar deformability envelope of the SCC are analysed by the control variable method, and the results are presented in Fig. 13. The interlaminar deformability envelopes of the SCC with different σ max, μ and R are shown in Fig. 13(a), (b) and (c), respectively. These figures show that the maximum interlaminar deformability equals 4% when VLR is relatively small, which indicates that the parameters σmax, μ and R do not affect the interlaminar deformability under low VLR. As VLR increases, the larger σmax and R values or the smaller μ result in a larger interlaminar deformability. When VLR is high, the interlaminar deformability becomes very small because the SCC fails in the nonsliding stage. The interlaminar deformability envelopes of the SCC with different δ and n are shown in Fig. 13(d) and (e), respectively. As can be noted from both figures, n and δ affect only the target interlaminar deformability of

4.3. Comparison of the analytical results with the numerical results The numerical results are used to verify the validity of the analytical model. First, the developed analytical model was used to calculate the FΔ curves and the ultimate interlaminar displacements of the SCC under varying VLR. The geometrical parameters and material properties used in the analytical model are the same as the numerical model, i.e., r ¼ 0.17 m, R ¼ 0.5 m, h ¼ 4 m, n ¼ 5, δ ¼ 0.02 m, μ ¼ 0.05, Ea ¼ 32.5 GPa, Eb ¼ 36 GPa, and σ max ¼ 49 MPa. Then, the analytical F-Δ curves and the analytical interlaminar deformability envelope of the SCC are compared with those obtained from the numerical analysis. 4.3.1. Horizontal load-displacement curve The numerical and analytical F-Δ curves are presented for three 10

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

Fig. 13. Parameters analysis of factors affecting the interlaminar deformability envelope of the SCC.

the SCC. Larger n and δ values result in higher interlaminar deform­ ability under low VLR; however, both parameters have no effect on the interlaminar deformability under medium or high VLR. Since the deformation space has a weakening effect on the cross-sectional area, the vertical bearing capacity of the SCC is reduced. Therefore, the pa­ rameters δ and n need to be carefully designed to improve the inter­ laminar deformability while ensuring the vertical bearing capacity.

5. Seismic resistance analysis and discussion The integral analysis method considering soil-structure interaction is widely used in seismic response and damage analysis of underground structures [4,10,35,36]. To evaluate the efficiency of SCC for seismic design of underground structures, seismic resistance analysis of the Daikai station retrofitted with SCC was conducted using the integral analysis method. For comparison, the structures with rectangular col­ umns and circular columns were also simulated under the same 11

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

Fig. 15. History of ground acceleration. (a) Horizontal ground acceleration time history; (b) Vertical ground acceleration time history.

[4,6,37,38]. In this study, a 3D soil-structure interaction FEM model of Dakai station, with dimensions of 68 m length, 20 m width and 24 m height, is built for the seismic resistance analysis as shown in Fig. 14(a). A 3D model of the prototype structure is shown in Fig. 14(b). The monitoring plane is taken as the middle section, which is minimally affected by the boundary conditions. The prototype rectangular column has a cross-section of 0.4 m � 1.0 m, and the reinforcement ratio (ρ) and volumetric stirrup ratio (ρv) are 6% and 0.26% [1], respectively. Based on the principle of equivalent area, the SCC and circular monolithic column with radius R ¼ 0.36 m are applied to replace the prototype rectangular column for comparative analyses. 3D FEM models of the three columns are shown in Fig. 14(c). For simplicity, the rectangular column and the circular column are abbreviated as RC and CC, respectively. The reinforcement ratio and the volumetric stirrup ratio of the CC are consistent with those of RC. For the

Fig. 14. FEM model. (a) Transverse section of the FEM model, (b) 3D FEM model of the structure, (c) 3D FEM model of the three types of columns.

Table 4 Material parameters of soil. Parameter

Value

Parameter

Value

Density (kg/m3) Poisson’s ratio Frictional angle

1960 0.3 35�

Initial pore ratio Swelling index Isotropic compression index

0.6 0.008 0.12

Table 5 Material parameters of steel. Parameter

Value

Parameter

Value

Density (kg/m3) Poisson’s ratio

7800 0.2

Young’s modulus (GPa) Yield stress (MPa)

200 240

conditions. Detailed comparisons were carried out to analyze the effect of retrofitting the SCC on the seismic performance of underground frame structures. 5.1. Target structure and FEM model The Daikai station is the first well-documented underground struc­ ture, which has been seriously collapsed during an earthquake. The collapsed section was widely used as a representative case to study the seismic performance and failure mechanism of underground structures

Fig. 16. Interlaminar deformability envelopes of the three columns. 12

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

Fig. 17. Equivalent plastic strain of structures. (a) Rectangular column, (b) Circular column, (c) SCC.

SCC, r ¼ 0.12 m. According to the load-bearing mechanism, the core column should have better interlaminar deformability, and the segments should have better vertical bearing capacity and provide lateral con­ straints for the core column. Thus, the reinforcement of the SCC is designed as: ρ ¼ 17% and ρv ¼ 0.74% for the core column; ρ ¼ 4% and ρv ¼ 0.38% for the segments. The overall equivalent reinforcement ratio and the volumetric stirrup ratio of the SCC are 5.5% and 0.42%, respectively. The soil is simulated employing an elastoplastic constitutive model [39,40] that describes the 3D strength property and the accumulation characteristics of soil plastic deformation under 3D stress state. The material parameters of the soil are listed in Table 4. The plastic damage model is used to describe the mechanical behaviour of the concrete. The concrete strength grade is C60 for the segments, and for the other components, the grade is C40. The corresponding material parameters are presented in Tables 1 and 3. The steel is idealized as an elastic-perfectly plastic material, with the material parameters listed in Table 5. The viscoelastic boundary condition is utilized to deal with the lateral and bottom boundaries in order to reflect the influence of infinite domain soil on the near field. The wave field decomposition method is used to implement the seismic input. The horizontal and vertical com­ ponents of ground motions are shown in Fig. 15, which were measured at the Kobe meteorological observatory close to the Daikai station. In this study, the penalty function method is used to simulate the contact behaviour between the soil and the structure, as well as the contact behaviour between the segments. The friction coefficient between the soil and structure is taken as 0.4 [4,6,41–43]. The friction coefficient between the segments is taken as 0.05, which is consistent with the pushover analysis in Section 4.1.

envelopes of the three columns are calculated, and the deformability envelopes are used to evaluate the seismic response state of the structures. 5.2.1. Interlaminar deformability envelopes of different columns Two groups of pushover simulations were carried out to obtain the interlaminar deformability envelopes of RC and CC. The boundary conditions and loading scheme are the same as those illustrated in Fig. 9. Here, the onset of failure is defined as when the horizontal load falls to 85% of its peak value [4]. Additionally, the analytical model is used to calculate the interlaminar deformability envelope of the SCC. The interlaminar deformability envelopes of the three columns are plotted in Fig. 16. As can be observed from Fig. 16, when VLR <1.5, the deform­ ability of SCC is highest, followed by the RC, and the deformability of the CC is the lowest. When VLR ¼ 0, the deformability is 3.5% and 1.8% for the RC and the CC, respectively. The deformability of both column forms decreases rapidly with increasing VLR. For the SCC, the deformability reaches 4.19% as VLR ranges from 0 to 0.8. When VLR >0.8, the deformability of SCC decrease sharply. Particularly, since the integrity of the SCC is affected by the interfaces, the vertical bearing capacity and interlaminar deformability of SCC is lower than the RC and the CC for VLR>1.5. For a normally designed SCC, the vertical load ratio will hardly 1.5 even under seismic loadings. 5.2.2. Seismic response analysis of the three structures with different columns The seismic responses at monitoring plan in Fig. 14(b) are recorded to analyze the seismic response characteristics of the structures. The equivalent plastic strain (abbreviated as PEEQ) of the structures at the onset of failure and the final loading state are expressed in Fig. 17. The PEEQ represents the magnitude of plastic strain, which is defined as R pl ε_ c dt. As can be seen in Fig. 17, the RC exhibits bending failure char­ acteristics at 5.8 s, while the CC exhibits shear failure characteristics at 5.7 s. The PEEQ is distributed along the column height of the RC, whereas, it is concentrated at the bottom of the CC. At the end of loading

5.2. Seismic response analysis and evaluation of the structures To clearly explain the damage process and failure mechanism of the structure during an earthquake, the interlaminar deformability 13

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

and then plummets to 0.139 at 4.76 s. This is mainly due to the bending deformation of the column caused by the P-Δ effect. After that, the interlaminar deformation of the structure continues to grow to 2.1% at 4.94 s within the interlaminar deformability envelope. Further, the interlaminar deformation reaches the interlaminar deformability enve­ lope at 5.68s, followed by a continuously increasing and irreversible horizontal deformation, causing severe damage of the column and eventually leading to the collapse of the whole structure. The seismic response of the structure with CC is shown in Fig. 18(b). The interlaminar deformation reaches the interlaminar deformability envelope at 5.66s, and the VLR of the CC has only small fluctuations before 5.66 s. Then, the VLR drops rapidly from 0.32 at 5.70 s to 0.06 at 5.88 s, which indicates that the CC has lost vertical bearing capacity. Finally, the top slab collapses. Fig. 18(c) shows that the IDR of the SCC reaches 1.5% at 4.88 s and 2.1% at 5.90 s, respectively. However, the seismic response of the SCC does not reach the interlaminar deformability envelope. The SCC still performs well after the earthquake without losing its vertical bearing capacity. Therefore, the whole structure does not experience severe damage during the earthquake. The comparative analysis of the three simulations demonstrates that the SCC is effective in improving the seismic performance of the Daikai station. Therefore, enhancing the interlaminar deformability of the in­ termediate column while ensuring its vertical bearing capacity can effectively upgrade the seismic performance of underground frame structures. 6. Conclusions This study proposes a novel segmental cored column for under­ ground frame structures, which consists of a slender core column and several hollow segments. Firstly, the performance mechanism of the SCC was introduced. The vertical bearing capacity of the SCC can be equiv­ alent to the monolithic column with the same cross-sectional area. Meanwhile, the interlaminar deformability of the SCC depends on the core column, which has a larger slenderness ratio and better interlam­ inar deformability. An analytical model was developed to describe the mechanical behaviour of the SCC during the deformation process. According to the load conditions and the deformation states, the deformation process of the two-segment SCC was subdivided into four stages: (1) vertical compression stage, (2) non-sliding stage, (3) sliding stage, and (4) ulti­ mate deformation stage. The horizontal load-displacement relationships of the SCC in different stages and the corresponding failure identifica­ tion method were established. Based on the same SCC, the horizontal load-displacement curves and the interlaminar deformability envelope obtained by the analytical model agree well with the numerical results, demonstrating that the proposed analytical model is reasonable. Finally, the efficiency of using the SCC for upgrading the seismic performance of underground structures was evaluated. The interlaminar deformability envelopes were used to quantitatively evaluate the seismic response states of the structures. The numerical results showed that the structures with rectangular columns and circular columns were severely damaged during the earthquake and eventually leading to the collapse of the whole structure. However, the SCC performed well during the earthquake without losing vertical bearing capacity, and the whole structure sustained less damaged. It can be concluded that the SCC is effective in upgrading the seismic performance of underground structure.

Fig. 18. Seismic responses and interlaminar deformability envelopes of different columns. (a) Rectangular column, (b) Circular column, (c) SCC.

(t ¼ 29 s), the RC and the CC are completely destroyed, and the roofs collapse. However, the SCC shows good interlaminar deformability and better vertical bearing capacity during the earthquake. The settlement of the top slab during the earthquake is significantly reduced for the structure retrofitted with SCC. The interlaminar deformability envelopes are used to quantitatively analyze the seismic response state of the structures. The seismic re­ sponses of different column configurations with the corresponding interlaminar deformability envelopes are plotted in Fig. 18. As shown in Fig. 18(a), the VLR of RC reaches its maximum (VLR ¼ 0.435) at 4.74 s

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Soil Dynamics and Earthquake Engineering 131 (2020) 106011

CRediT authorship contribution statement

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Dechun Lu: Methodology, Writing - review & editing, Funding acquisition, Resources. Chunyu Wu: Conceptualization, Methodology, Data curation, Writing - original draft. Chao Ma: Software, Visualiza­ tion, Formal analysis. Xiuli Du: Project administration, Supervision. M. Hesham El Naggar: Writing - review & editing. Acknowledgments The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant Nos. 51778026; 51421005; U1839201). References [1] Iida H, Hiroto T, Yoshida N, Iwafuji M. Damage to Daikai subway station. Soils Found 1996;36:283–300. [2] Parra-Montesinos GJ, Bobet A, Ramirez JA. Evaluation of soil-structure interaction and structural collapse in Daikai Subway Station during Kobe earthquake. ACI Struct J 2006;103(1):113–22. [3] An XH, Shawky AA, Maekawa K. The collapse mechanism of a subway during the Great Hanshin earthquake. Cement Concr Compos 1997;19:241–57. [4] Ma C, Lu DC, Du XL, Qi CZ, Zhang XY. Structural components functionalities and failure mechanism of rectangular underground structures during earthquakes. Soil Dyn Earthq Eng 2019;119:265–80. [5] Xu ZG, Du XL, Xu CS, Hao H, Bi KM, Jiang JW. Numerical research on seismic response characteristics of shallow buried rectangular underground structure. Soil Dyn Earthq Eng 2019;116:242–52. [6] Huo H, Bobet A, Fern� andez G, Ramírez J. Load transfer mechanisms between underground structure and surrounding ground: evaluation of the failure of the Daikai station. J Geotech Geoenviron Eng 2005;131(12):1522–33. [7] Zhao HL, Yu HT, Yuan Y, Li P, Chen JT. Cyclic loading behavior of a repaired subway station after fire exposure. Tunn Undergr Space Technol 2019;84:210–7. [8] Zhao HL, Yuan Y, Ye ZM, Yu HT, Zhang ZM. Response characteristics of an atrium subway station subjected to bidirectional ground shaking. Soil Dyn Earthq Eng 2019;125:105737. [9] Miao Y, Yao EL, Ruan B, Zhuang HY. Seismic response of shield tunnel subjected to spatially varying earthquake ground motions. Tunn Undergr Space Technol 2018; 77:216–26. [10] Ma C, Lu DC, Du XL. Seismic performance upgrading for underground structures by introducing sliding isolation bearings. Tunn Undergr Space Technol 2018;74(2): 1–9. [11] Makris N. Seismic isolation: early history. Earthq Eng Struct Dyn 2019;48(2): 269–83. [12] Tao LJ, An JH, Ge N. Isolation effect analysis on bidirectional RFPS bearing applied in the metro stations engineering. Earthq Eng Eng Dyn 2016;36(1):52–8. [13] Mikami A, Konagai K, Sawada T. Stiffness design of isolation rubber for center columns of tunnel. Proc Jpn Soc Civil Eng 2001;682:415–20. [14] Chen ZY, Chen W, Bian GQ. Seismic performance upgrading for underground structures by introducing Shear Panel Dampers. Adv Struct Eng 2014;17(9): 1343–57. [15] Chen ZY, Zhao H, Lou ML. Seismic performance and optimal design of framed underground structures with lead-rubber bearings. Struct Eng Mech 2016;58(2): 259–76. [16] Yu T, Zhao HC, Ren T, Remennikov A. Novel hybrid FRP tubular columns with large deformation capacity: concept and behaviour. Compos Struct 2019;212: 500–12. [17] Jia PJ, Zhao W, Chen Y, Li SG, Han JY, Dong JC. A case study on the application of the steel tube slab structure in construction of a subway station. Appl Sci 2018;8 (9):1437.

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