Seismic performance of beam-type covered bridge considering the superstructure – substructure interaction and bearing mechanical property

2.1. Benchmark covered bridge

An existing beam-type covered bridge in China has been selected in the present study. The total length of the bridge is 75.90 m, and the width is 29.20 m (Fig. 1). The site of the covered bridge is situated in Seismic Zone II of the Chinese seismic zoning. The designed peak acceleration of the ground motion for the covered bridge is 0.2 g, and the predominant period of site is 0.4 s.

The superstructure of the covered bridge is integrated onto the bridge. The local three-story frame structure has a height of 21.5 m, and dimension of 75.0 m×22.8 m. The concrete strength of members of the superstructure is 35 MPa. The reinforcements embedded in the covered bridge are HPB300, HRB335, and HRB400. The diameter of the columns from bridge deck to elevation of 6.400 m (the 1st floor) is 0.8 m, while the diameter of columns in other floors (the 2nd floor and 3rd floor) is 0.7 m. Longitudinal reinforcements vary in configuration depending on the position of the column, with main diameters of 32 mm, 28 mm, 25 mm, 22 mm, and 20 mm. The stirrups have a diameter of 8mm.

Fig. 1Configuration of the beam-type covered bridge (unit: cm)

The transverse layout of the beam-type covered bridge is as follows: 3.2 m (pedestrian street) + 2.4 m (veranda) + 18 m (shopping mall) + 2.4 m (veranda) + 3.2 m (pedestrian street). This design integrates the shopping mall and the bridge into an urban complex. The girder of the bridge is a cast-in-place box girder with variable height, having a length of 72 m, with the main span being 28 m and two end spans of 22 m each. The concrete strength of the bridge girder is 50 MPa. Spherical steel bearings (SSB) are used in the bridge structures.

Fig. 2Round ended solid wall pier (unit: cm)

a) Elevation

b) Lateral view

The girder bridge is supported by two round-ended reinforced concrete (RC) wall piers. The height of each pier is 4.1 m, having a sectional dimension of 30.70 m×1.5 m (Fig. 2). The concrete strength of the wall piers is 40 MPa, and the diameters of longitudinal reinforcements and stirrups in the piers are 28 mm and 12 mm respectively, with 16 mm tie bars.

2.2. Designed cases

The essence of different bearing types and arrangements is reflected in the mechanical characteristics of bearings. To explore the impact of bearing types on the seismic performance of covered bridges, this study compared the use of hyperbolic spherical isolation bearings (HSIB). Furthermore, 3 and 5 spherical steel bearings (SSB) were placed on each pier or abutment to investigate the influence of bearing arrangements. It is important to note that considering the interaction between the superstructure and substructure involves not only about changes in structural stiffness, but also changes in structural mass. Based on the research objectives, the cases of the beam-type commercial covered bridge are designed, as shown in Table 1. The nomenclature of the finite element models can be seen in Table 2.

The distinction between case B and case C, as well as case D and case E, mainly rests with the contrast in stiffness after bearings sliding. The diversity between case B and case F lies in the entire restoring force model, that is, the initial stiffness and the stiffness after sliding are inconsistent. The layout of bearings for case B and case D and case F are shown in Fig. 1. A0 and A3 represent abutments, and P1 and P2 denote wall piers. When spherical steel bearings are installed on the piers, P1 serves as a fixed pier. The bearing layouts for case C and case E indicates the installation of 5 bearings on each pier or abutment. *–1, *–2 and *–3 represent the bearings equipped on bridge abutments or piers.

2.3. Structural models

The general finite element analysis program OpenSEES was used to carry out all of the analyses. A series of 3D nonlinear models was constructed to encompass the inherent variability presented in the covered bridge considered in this study. Each of these models incorporated the major components such as the superstructure, i.e. building frame structure and substructure, i.e. bridge structure including bearings and wall piers.

The constitutive relationship of the concrete, as proposed by Kent-Scott-Park et al. [19], was defined using Concrete02. The reinforcement was defined using the Menegotto-Pinto [20] stress-strain relationship that included the isotropic strain hardening property. Steel02 was employed to accurately describe the deformation characteristics of bars. The initial loading curvature coefficient $R_0$ and the degeneration coefficients of curvature $a_1$ and $a_2$ under reciprocating loading, and the strain hardening coefficient $b$ of bars are taken as 18.5, 0.925, 0.15 and 0.01, respectively.

Fig. 3FEM of the beam-type covered bridge

The RC columns of the superstructure were modeled with the force-based beam column elements. The cross-section of the beam column element adopted the fiber cross-section was composed of concrete fibers for the core area, concrete fibers for the protective layer, and reinforcement fibers, as shown in Fig. 3. Corresponding material models were assigned to different fibers. Shear and torque springs were added to simulate the shear and torsion characteristics of the cross-section. For simplicity in modeling, elastic beam column elements were used for framed beams simulation. The floor panels and other ancillary facilities of the superstructure were applied as dead loads to the FEMs.

It is considered unlikely that the girder will behave in a nonlinear fashion under seismic excitation. Due to the large width of the main girder of the covered bridge, it is obviously not suitable to use a single beam element to simulate. In line with the position of the columns and bearings in the superstructure, the girder was divided into seven parts horizontally (Fig. 3). Each part was modeled using elastic beam element having equivalent stiffness and mass. The cross-sectional characteristics of the elements including sectional area, elastic modulus, and moment of inertia, etc. were obtained based on the material properties and cross-sectional dimensions of the girder. They were assigned to the elastic beam elements of girder in sequence. The separated parts were connected by rigid beams to form a grillage structure.

The bearings were modeled by a zero-length link element. The hysteretic behavior of SSB was represented using a bilinear kinematic model available in OpenSEES (Fig. 3). Parameters such as the initial stiffness $K_0$, post-yield hardening ratio $r$, and yield force $F_y$ were needed to define the hysteresis behaviors, which were obtained from the design parameters of SSB in the covered bridge. The HSIB can be used as both a fixed bearing and a sliding bearing, and had a large stiffness after yielding. The restoring force model of HSIB can be approximately bilinear, as shown in Fig. 4.

Fig. 4Details of hyperboloid spherical isolation bearing

a) Diagrammatic sketch

b) Restoring force model

The parameters of bearings for case B and case C, and case F were shown in Table 3. In the table, 0-0, 1-0, and 2-0 represent the side bearings when 5 bearings are arranged on the bridge abutment or pier. $K_0$ and $r$ represent the initial stiffness and stiffness yield ratio, respectively. The seismic actions were bidirectional input along the longitudinal (H1) and transverse (H2) directions of the structure.

The wall piers were modeled using a multi-layer shell element [21] (Fig. 3) based on the principle of composite strength of materials, which was divided into one or more orthotropic reinforcement layers and several concrete layers with equivalent thickness according to the reinforcement situation and actual size of the component. The concrete in the layered shell model was two-dimensional concrete material (nDMaterial PlaneStressMaterial) on basis of damage mechanics and diffuse crack model. $D_e$ is an elastic constitutive matrix, and $D_1$ and $D_2$ are scalar damages in tension and compression, respectively. It can be expressed as:

where, the relationship between equivalent stress $\tilde{\epsilon }$ and principal stress ${\epsilon }_i$ is as follows:

If ${\epsilon }_i\ge 0$, ${⟨{\epsilon }_i⟩}_{+}={\epsilon }_i$. Else, ${⟨{\epsilon }_i⟩}_{+}=0$. ${\epsilon }_{D_0}$is initial damage threshold, and when $\tilde{\epsilon }\le {\epsilon }_{D_0}$, $D=$0. $A_t$, $B_t$, $A_c$ and $B_c$ are the characteristic parameters of materials obtained from uniaxial tensile test and compression test, respectively. After concrete cracking, the model considered the degradation of concrete shear stiffness through a shear transfer coefficient less than 1. The reinforcement in shell element was simulated using a multi-dimensional reinforcement material (nDMaterial PlateRebar) in a dispersed reinforcement layer. This reinforcement model was foundation on the existing uniaxial steel model of OpenSEES and developed from the angle of bars. The piers and bearings at the abutments have been modeled as fixed at the base and the pounding effect was not considered. The piers have been modeled using various elements with mass lumped at discrete points. The total number of nodes is 506, and the total numbers of column elements, beam elements, girder elements, bearing elements, and pier elements are 190, 366, 91, 18, and 340. The sum number is 1005.

2.4. Ground motions

A set of suitable earthquake records was chosen from the Pacific Earthquake Engineering Research Center (PEER) database and scaled as the ground motion inputs, as shown in Table 4. The seismic responses of covered bridge components were gained through the IDA method.

Performance-based seismic design requires determining the seismic response and seismic capacity of a structure under a certain level of seismic action. At the core of assessing a structure's seismic performance lies the comparison between its capacity and demand. To ascertain if a structure's seismic response surpasses its capacity, conducting a seismic response analysis of the structure is paramount. The structural seismic response analysis is to establish the equations of the structure under seismic action, as shown in Eq. (4):

In the equation, [$\mathbf{M}$] represents the mass matrix, and [$\mathbf{C}$] is the damping matrix. [$\mathbf{K}$] is the structural stiffness matrix, and [$\mathbf{I}]$ denotes the identity matrix. $\left\{x\right\}$, $\left\{\dot{x}\right\}$, $\left\{\ddot{x}\right\}$ and $\left\{{\ddot{x}}_g\left(t\right)\right\}$ represent the displacement, velocity, acceleration vectors, and the acceleration time history of ground motion, respectively. Inputting a series of seismic ground motion intensities and conducting a nonlinear time history analysis allows to obtain a structure’s seismic response by Eq. (4).

The first step in analyzing the dynamic response of a MDOF system is to get the periods of free vibration and the corresponding mode shapes of the structure, as it provides information related to the seismic response of the structure. If the vibration mode Eq. (5) has the nonzero solution, frequency equation can be derived as Eq. (6):

where, ${\omega }^2$ is the eigenvalue, and $\left\{\widehat{x}\right\}$ represents the eigenvector.

The modal analyses were conducted for case A and case B, and their basic periods $T_1$ were 0.6937 s and 0.7178 s, respectively. It can be deduced that the structures belong to medium to long period structures. Previous research has shown that PGV and $S_a$ corresponding to the first natural vibration period have an ideal correlation with medium to long period structures [22]. Therefore, when conducting nonlinear dynamic analysis, the spectral acceleration $S_a$($T_1$, 5 %) was used as seismic intensity measurement (IM), and the seismic actions were bidirectional input [23]. The records were scaled based on the more severe component of the motion, and the same scale factor was applied to the other component as recommended by Somerville and Collins [24].

The Hunt & Hill method [25] was used to scale the seismic actions in order to study the responses of the covered bridge in the whole process from the elastic, elastoplastic and capacity limit state to the final collapse. The Hunt & Hill method was developed on the basis of the variable step method and has faster convergence.

Fig. 5Original ground motion record No. 3

a) Response spectrum

b) Acceleration time history

Fig. 5 shows the original record of ground motion No. 3 in the longitudinal direction taken as an example to illustrate the process of scaling. According to Fig. 5(a), the corresponding spectral acceleration with a damping ratio of 5 % is 0.1825 g, which means $S_a$($T_1$, 5 %) = 0.1825 g. If $S_a$($T_1$, 5 %) = 0.005 g was taken for the first analysis, the scaled coefficient $\lambda =$ 0.005/0.1825 = 0.0274. Then, the scaled coefficient $\lambda$ was multiplied by the acceleration value $a$ of the original seismic record at each moment to obtain the acceleration $a_m$ of the $m$-th analysis, i.e. $a_m={\lambda }_{m}a$.

The scaled coefficients are presented in Table 5. No. denotes the scaled number of each seismic record. Following 17 times time history analyses, the seismic responses of components were obtained. The PGA ranges of ground motions in two directions after scaled are between 0.002 g~1.228 g and 0.002 g~1.6722 g, respectively.

4.1. Superstructure

Fig. 7 shows the maximum interlayer drift ratios of the superstructure under longitudinal and transverse seismic actions. It can be evidently seen from Fig. 7(a) that when $S_a\le$ 0.763 g, the longitudinal peak value of the superstructure in case A is smaller than that in case B and case C, while the drift ratios in case B and case C are nearly equal. For $S_a>$ 0.763 g, case C always has a greater displacement demand than case B, with the peak drift responses of case A surpassing that of case B and case C initially, but subsequently becoming smaller than those of case C after 1.079 g. Therefore, it can be concluded that due to the interaction between the upper building frame structure and the bridge structure, significant differences in seismic responses exist between the conventional building structure and superstructure of the covered bridge. What can be drawn from case B and case C is that it is the sliding stiffness of the bearings lead to the variation in longitudinal interlayer drift ratios of the superstructure. A smaller sliding stiffness leads to the corresponding minor drift ratio. When $S_a=$ 0.555 g, the gaps of cases reaches the greatest, at which ${\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{A}}=$ 0.007, ${\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{B}}=$ 0.012, ${\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{C}}=$ 0.013. The gap in seismic response can be quantified using the following equation:

where, ${\delta }_1$ represents the structural seismic responses of case B, and ${\delta }_2$ represents the responses of case A, C, D, and E.

At the longitudinal seismic action of E1 and E2 IM levels, the maximum interlayer drift ratios of case B and case C are nearly identical, and the difference between the interlayer drift ratios of case A and case B are about 30.97 % and 43.42 %, respectively.

Fig. 7(b) illustrates that when $S_a>$ 0.97 g, the magnitude of interlayer drift ratio in sequence is case B, case A, and case C. However, at the lateral seismic action of E1 and E2 IM levels, the cases sustain an identical drift ratio. Therefore, it can be explained that under the earthquakes may occur, the interaction between the superstructure and substructure is unfavorable for the longitudinal performance of the building structure of the covered bridge, while it is not sensitive to the lateral seismic response. The displacement of frame structure fixed on the ground is 0, but the bottom end of the superstructure column of covered bridge is consolidated with the bridge deck. If the bridge structure is treated as a column bottom constraint of building structure, the stiffness of this constraint is related to the stiffness of bridge structure. The yield ratios of longitudinal bearing stiffness are smaller than those of transverse bearing stiffness, and the longitudinal stiffness of bridge wall piers is much smaller than transverse stiffness.

Fig. 7Interlayer drift ratios of superstructure

a) Longitudinal

b) Transverse

The $S_a$ at each limit state are summarized in Table 7, and the seismic performance of superstructures under seismic actions was evaluated.

At the longitudinal E1 IM level, the superstructure of case A and case C both enter the moderate damage state, while the superstructure of case B reaches severe damage. In the transverse direction, the superstructures of all cases are in the moderate damage state. At the E2 IM level, the superstructures of various cases in both directions are in a severe damage state.

Due to changes in the diameters of the frame columns on the 3rd floor, the peak drift ratio occurs at the 2nd floor of the superstructure. The drift ratios of building structure at E2 IM level are presented in Fig. 8. That indicates case A has a relatively small drift ratio at the 3rd floor. The time history curves of interlayer displacements for case A and case B within the first 40 seconds are shown in Fig. 9. The time at which the longitudinal interlayer drift ratio reaches its maximum is 7.34 s and 7.88 s, respectively, while in the transverse direction, it is 4.69 s and 7.14 s, respectively. This suggests that the peak response of case A emerges earlier but smaller compared to that of case B. In this study, the superstructure retains substantially identical transverse drift ratio at E2 IM level.

Overall, the interaction between the building and the bridge would significantly make it disadvantageous to the longitudinal interlayer drift ratio of the superstructure of the covered bridge when the bearings remain a large stiffness. At the longitudinal E1 and E2 IM level, the existence of the bridge structure results in a gap over 30 % of the interlayer drift ratio. The sliding stiffness of the bearings can affect the seismic response of superstructure under extremely rare earthquakes. Although the superstructure of case B has entered the severe damage state under the longitudinal E1 IM level, on the whole, the $S_a$ at this state is close to the drift ratio limit value corresponding to the severe damage limit state. Moreover, when the seismic action is rarer than E1 IM level, the bearing distribution of case B is more conducive to reduce the interlayer drift ratio of the superstructure. When considering potential earthquakes, superstructures situated on bridge structures are more likely to suffer longitudinal damage than those located on the ground. According to the divided limit states, case A, case B, and case C have basically encountered moderate damage at the E1 IM level, while severe damage is observed at the E2 IM level.

Fig. 8Interlayer drift ratios of superstructure at E2 IM level

a) Longitudinal

b) Transverse

Fig. 9Time history curves of interlayer displacements at E2 IM level

a) Case A

b) Case B

4.2. Bearings

The displacement of sliding spherical steel bearing (SSB) for case B and case C is plotted in Fig. 10. Fig. 10(a) indicates that when $S_a\ge$ 0.97 g, the bearing shifted from the normal working stage to the damage stage. Case B exhibits a less conservative demand in terms of longitudinal bearing displacement compared to the one from case C. This is because the bearings in case B provide smaller stiffness after sliding. Regardless of the magnitude of longitudinal motions, the sliding of the bearings in case B ultimately led to a collision between the girder and abutment, whereas the bearings in case C only reached the severe failure state.

It is evident in Fig. 10(b) that the lateral displacement of the bearings is minimally impacted by the sliding stiffness, but eventually leads to moderate failure. Both case B and case C only achieved the slight damage state at the E1 and E2 IM levels.

In this study, the time history analyses of case B, case C, case D and case E were performed by inputting the ground motion after 17-scaled seismic action of No. 1, so as to deeply investigate the influences of the superstructure – substructure interaction on the components of covered bridge. The effects of this interaction on the sliding displacement of the bearings are depicted in Fig. 11. It can be observed that the displacements of the bearings of case D and case E are generally greater than those of case B and case C. The longitudinal displacements of case D and case E exhibits significant dispersion, similar to Fig. 10(b), the transverse displacements shows a slight distinction due to the sliding stiffness. The bearings of case D even suffered complete damage in the longitudinal direction. However, the comparison here involves the seismic response generated by the scaled seismic action No.1, where the bearings of case B and case C only entered the slight damage state, whereas bearings of case D and case E both reached the moderate damage state.

Fig. 10Bearing displacements

a) Longitudinal

b) Transverse

Fig. 11Bearing displacements under the seismic action No. 1

a) Longitudinal

b) Transverse

Fig. 12The bearing displacement time-histories at E2 IM level of seismic action No. 1

a) Longitudinal

b) Transverse

It can be concluded that the existence of the upper building significantly contributes to reducing the bearing displacements of the lower bridge structure. At the E2 IM level, the longitudinal displacement of the bearings in case D and case E increased by 2.30 and 1.02 times compared to case B, while the transverse displacement increased by 1.27 and 0.93 times, respectively. The time history curves of the bearing displacements in various cases at the E2 IM level are plotted in Fig. 12. The displacement in case D exceeds other cases, and it could not be restored to its original location in the longitudinal direction.

The drift ratio of the superstructure and the bearing displacement of the bridge indicate that, in potential seismic events, the stiffness distribution of the bearings has a limited effect on the structural seismic response of the covered bridge. But the existence of the lower bridge structure is adverse to the longitudinal seismic performance of the superstructure, while the presence of the upper building structure clearly mitigated the seismic response of the bearings. It can be revealed that the interaction between the building and bridge of the covered bridge has the opposite effects on the seismic response of the superstructure and bearings. Nevertheless, more details should be given to the seismic response of the bridge piers for a more comprehensive understanding.

The influences of the sliding stiffness of the bearings on the structural response were discussed in the previous section. The emphasis was placed on the sliding stiffness because the fixed bearing was installed, and its initial stiffness was relatively large, which played a decisive role in the seismic response of each component prior to sliding. To account for the impacts of the initial stiffness on the seismic response of the bridge, hyperboloid spherical isolation bearings (HSIB) were employed. Furthermore, $S_a$ in the longitudinal and transverse directions of seismic motions were adjusted to the corresponding spectral acceleration value of E1 and E2 to input for case F for comparison. It was found that the displacement of the wall pier is fractional, indicating that the HSIB reduced the displacement response of the pier. Thus, this study only focused on the seismic response of the frame building structure on the bridge and bearing itself when the HSIB was utilized.

Fig. 13Comparison of inter story drift ratios

a) Longitudinal

b) Transverse

Fig. 13 displays the comparison of the interlayer drift ratios of the building fixed on the ground and the building of the covered bridge with SSB and HSIB, while Fig. 14 pictures the displacements of the two types of bearings. It is notable that $b_B\ll b_F$. At the E1 IM level, ${\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{B}}>{\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{A}}>{\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{L},\mathrm{C}}$ and ${\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T},\mathrm{A}}>{\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T},\mathrm{B}}>{\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T},\mathrm{C}}$. The contrastive result of interlayer drift ratios in the longitudinal and transverse directions at the E2 IM level is consistent with the trend at the longitudinal E1 IM level. The isolation effectiveness for the superstructure at the two levels are 40.54 %, 86.57 % respectively in the longitudinal direction, and they are 39.33 %, 68.36 % in the transverse direction. The damage state of the superstructure at E1 IM level changes from moderate to slight, which alters from severe to slight at E2 IM level in the longitudinal direction, while it shifts from severe to intact in the transverse direction. The SSB suffers the minor damage due to the fixed bearings based on the DMs, and the HSIB generates a significant amount of energy dissipation under the seismic actions. At the longitudinal and transverse E1 IM level, the displacements of HSIB are 46.97 mm and 44.10 mm, respectively, and those at the E2 IM level are 106.66 mm and 104.84 mm, respectively. The peak transverse displacements of the building structure are 59.81 mm, 59.70 mm, 125.96 mm, and 132.74 mm, respectively.

Fig. 14Comparison of bearing displacements

Case A can be conceptualized as having infinitely large bearing stiffness, while the stiffness of case F is smaller than that of case B. Fig. 13 illustrated that the greater the stiffness of the bearings, the greater the inter story drift ratios of the superstructure, especially when considering the interaction between the building and bridge. The HSIB significantly reduced the seismic response of building structure. Fig. 14 depicted the reason for this phenomenon, which was that the HSIBs have undergone a noticeable sliding, causing the translation of the upper building. However, case A was consolidated and the bearing stiffness of case B was relatively high, which was equivalent to strong constraints, leading to the more obvious vibration of the upper building during earthquakes. Due to the large lateral stiffness of the bridge pier and the bearings compared to both in the longitudinal direction, case A has a negligible dissimilarity in transverse interlayer drift ratios with case B. If only the influence of bearings is considered, the longitudinal response of the superstructure of case B should theoretically be weaker than that of case A. But Fig. 13(a) contradicted the notion. Thereupon, it can be concluded that the longitudinal stiffness and mass of wall piers amplified the seismic response of the superstructure of covered bridge.

Referring to the limit states above, the superstructure of the covered bridge installed with HSIB is only slightly damaged. The seismic performance for HSIB necessitates that the restrainer be damaged to allow the bearings to fulfill their role in seismic reduction and isolation, while the bridge piers and foundations remains elastic or nearly elastic under designed and rare earthquakes. The displacements of HSIB have exceeded the yield displacement, but they still fell within the design displacement range. It can be considered that the HSIB is within the slightly damaged state. However, the sliding of the HSIB could potentially cause collisions between the main girder and abutment or stop. Although collision effects were not considered in this article, it is essential to note that the overall structure of the covered bridge may actually face safety risks.

4.3. Wall pier

Fig. 15 illustrates the influences of the bearing stiffness on the displacement response of wall piers. All analyses in this study centered on fixed pier without considering the transverse damage of wall pier. The values of LSs were calculated based on Table 6 and the height of pier.

The longitudinal displacement of bridge pier in case B consistently remains smaller than that of case C when $S_a\ge$ 0.304 g, and the transverse displacement demand contains below that of case C after $S_a\ge$ 0.45 g. Under the seismic actions, case B remains slightly damaged as the ground motion intensity increased, while case C ultimately reaches the moderate damage state at the E2 IM level, with the displacement of the bridge pier in case C being 2.16 times that of case B. As a result, it can be explained that a well-considered distribution of bearings can effectively reduce the damage to bridge piers.

Fig. 16 further demonstrates that whether there is a superstructure or not, the stiffness of bearings has an important impact on the seismic response of the pier. Case D and case E indicate that this effect is more pronounced when there is no interaction between the building and the bridge. The pier displacements of case B and case D are under the displacement demands of case C and case E. The displacement gap between case B and case D is minimal, while case C and case E exhibit a relatively significant disparity. That implies the effect of the upper building on reducing the seismic response of the bridge piers equipped with bearings of smaller sliding stiffness is limited, which contrasts with the impact on wall piers installed with stiffer bearings.

Fig. 15Displacements of wall pier: (Part I)

a) Longitudinal

b) Transverse

Fig. 16Displacements of wall pier: (Part II)

a) Longitudinal

b) Transverse

The displacement cloud maps of case B, case C, case D, and case E at E2 IM level are depicted in Fig. 17. Fig. 17(a) indicates that the maximum longitudinal displacements of the pier in cases B and D are located at the intermediate bearings, whereas the maximum longitudinal displacements of cases C and E position near the end bearings. Fig. 17(b) throw light on that the maximum lateral displacement occurs at the middle bearings, which is consistent with the theoretical expectations. Because of the assigned end bearings at the wall pier, cases C and E exhibit a broader range of transverse displacement response, covering almost the entire pier. The displacement cloud map shows that the displacement at each node of the same pier height of the wall type bridge pier is not the same. The reason is that due to the arrangement of larger stiffness bearings allowing for the complete transmission of seismic forces to the bridge piers, while the geometric characteristics of wall piers with larger widths indicate that their displacements are not identical as ordinary column piers. Consequently, it proclaims the distribution of bearings not only affects the value of displacement, but also plays an indispensable role in the displacement response of the wall pier at various locations. The closer to the bearings, the greater the deformation of the bridge pier due to its constraint effect, and the more significant the change in displacement.

Fig. 17Pier displacements at E2 IM level (unit: m)

a) Longitudinal

b) Transverse

The stress S11, S22, S12, and S23 of the wall pier are depicted in Fig. 18 to Fig. 21. Here, S11 and S22 represent the principal stresses, while S12 and S23 represent the shear stresses. These stresses are expressed in the local coordinate system. In terms of superstructure - substructure interaction, there is no significant difference in displacement response between case B and case D at E2 IM level, as discussed in preceding section. As a consequence, the cloud atlases including VON-Mises stress of the two cases are in good agreement, as revealed from Fig. 16 to Fig. 22.

The figures demonstrate that the distribution of bearings can reflect the stress of the wall pier shafts. The coverages of S11 and S22 in case C are wider than those normal stresses of case B, and a similar comparison can be made between case E and case D. The stress range here refers to the area over which the stress occurs. However, the bearing arrangements in case D and case E are more favorable for S12. The stress concentrations can be observed in pier shafts of case C and case E in Fig. 18. Fig. 19 shows the peak S22 in case B is 4 MPa larger than stress of case C, the more dispersed vertical loads borne by the bearings in case C. But S23 and S12 in case C and case E present the contrary behavior to case B and case D, respectively. That indicates that larger sliding stiffness leads to higher shear stress, which is also well illustrated from Von-Mises stress. The peak stress on the wall pier remains within the strength of C40, satisfying with a given performance objective.

Fig. 18S11 at E2 IM level (unit: MPa)

a) Case B

b) Case C

c) Case D

d) Case E

Fig. 19S22 at E2 IM level (unit: MPa)

a) Case B

b) Case C

c) Case D

d) Case E

Research has shown that arranging bearings with lower sliding stiffness on each bridge pier is profit for withstanding the seismic forces acting on the superstructure. Irrespective of whether the interaction between the upper building structure and lower bridge structure is considered, these bearings disposing also helps to reduce the displacement and stress on wall piers. Considering the interaction between the upper building and the bridge can effectively decrease the displacement and stress distribution range of bridge piers with bearings of higher stiffness. Yet, the impact on the displacement and normal stress response of the bridge piers with bearings of lower stiffness is limited.

Fig. 20S23 at E2 IM level (unit: MPa)

a) Case B

b) Case C

c) Case D

d) Case E

Fig. 21S12 at E2 IM level (unit: MPa)

a) Case B

b) Case C

c) Case D

d) Case E

Fig. 22Von-Mises at E2 IM level (unit: MPa)

a) Case B

b) Case C

c) Case D

d) Case E